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  • Articles  (130)
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  • Springer  (130)
  • American Geophysical Union
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  • 1
    Electronic Resource
    Electronic Resource
    Discrete stability of the Differential System Method evaluated with geostatistical techniques (1998)
    Springer
    Stochastic environmental research and risk assessment 12 (1998), S. 191-204 
    Details
    ISSN: 1436-3259
    Keywords: Keywords: groundwater flow ; inverse problems ; stability ; geostatistical interpolation ; kriging.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques. We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated measurement errors and interpolation errors. The numerical results show that the DSM is stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004770050017
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of relative equilibria in arbitrary axisymmetric gravitational and magnetic fields (1999)
    Springer
    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    Details
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008388105585
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  • 3
    Electronic Resource
    Electronic Resource
    Unrestricted Planar Problem of a Symmetric Body and a Point Mass. Triangular Libration Points and Their Stability (1999)
    Springer
    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    Details
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008337017789
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  • 4
    Electronic Resource
    Electronic Resource
    Normal Form Invariants Around Spin-orbit Periodic Orbits (2000)
    Springer
    Celestial mechanics and dynamical astronomy 78 (2000), S. 227-241 
    Details
    ISSN: 1572-9478
    Keywords: stability ; normal form ; spin-orbit resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends upon the parameters provided by the equatorial oblateness of the satellite and its orbital eccentricity. Normal form transformations around the main spin-orbit resonances are carried out explicitly. As an outcome, one can compute some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariants provides also the stability of the spin-orbit resonances, since it guarantees the existence of invariant curves surrounding the periodic orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011161605935
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  • 5
    Electronic Resource
    Electronic Resource
    Analytical investigation of non-linear stability of the Lagrangian pointL 4 around the commensurability 1:2 (1995)
    Springer
    Celestial mechanics and dynamical astronomy 63 (1995), S. 205-225 
    Details
    ISSN: 1572-9478
    Keywords: Restricted three body problem ; Lagrangian points ; resonances ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem of stability of the Lagrangian pointL 4 in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displacement from the equilibrium point as function of the mass parameter μ close to the commensurability. A rigorous treatment close to the resonance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type variables. Then using an isolated resonance approach, only the slowly varying terms are kept in the equations and two independent isolating first integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are compared to numeric integration of the equations of motion and are found to be in perfect agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00693415
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  • 6
    Electronic Resource
    Electronic Resource
    Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 181-196 
    Details
    ISSN: 1572-9478
    Keywords: Periodic solutions ; stability ; restricted three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00048514
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  • 7
    Electronic Resource
    Electronic Resource
    Stability and Geometry of Third-Order Resonances in four-Dimensional Symplectic Mappings (1997)
    Springer
    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
    Details
    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008288826727
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  • 8
    Electronic Resource
    Electronic Resource
    Position and velocity sensitivities at the triangular libration points (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 1-19 
    Details
    ISSN: 1572-9478
    Keywords: Three body problem ; stability ; surface of section ; commensurability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L4 triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios (μ) ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of μ are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051686
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  • 9
    Electronic Resource
    Electronic Resource
    Stability of axial orbits in analytical galactic potentials (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 261-285 
    Details
    ISSN: 1572-9478
    Keywords: galactic dynamics ; periodic orbits ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the stability of axial orbits in analytical galactic potentials as a function of the energy of the orbit and the ellipticity of the potential. The problem is solved by an analytical method, the validity of which is not limited to small amplitudes. The lines of neutral stability divide the parameter space in regions corresponding to different organizations of the main families of orbits in the symmetry planes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051897
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  • 10
    Electronic Resource
    Electronic Resource
    Stability of the triangular libration points of the circular restricted problem in the presence of resonances (1996)
    Springer
    Celestial mechanics and dynamical astronomy 66 (1996), S. 191-202 
    Details
    ISSN: 1572-9478
    Keywords: resonance ; restricted problem ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ω1 = 2ω2 and ω1 = 3ω2. The motion is unstable for all the values of parameters q and A when ω1 = 2ω2 and the motion is unstable and stable depending upon the values of the parameters q and A when ω1 = 3ω2. Here q is the radiation parameter and A is the oblateness parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00054964
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  • 11
    Electronic Resource
    Electronic Resource
    Existence and Stability of L4,5 In The Relativistic Restricted Three-Body Problem (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
    Details
    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008271021060
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  • 12
    Electronic Resource
    Electronic Resource
    Long Time Stability for the Main Problem of Artificial Satellites (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
    Details
    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008277122375
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  • 13
    Electronic Resource
    Electronic Resource
    Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem (1998)
    Springer
    Celestial mechanics and dynamical astronomy 70 (1998), S. 41-58 
    Details
    ISSN: 1572-9478
    Keywords: three-body problem ; libration points ; stability ; normal forms.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008250207046
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  • 14
    Electronic Resource
    Electronic Resource
    Three Dimensional Laser Simulation Code on a Desktop Personal Computer (1999)
    Springer
    Optical review 6 (1999), S. 28-36 
    Details
    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10043-999-0028-1
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  • 15
    Electronic Resource
    Electronic Resource
    Stability of axial motions of nonlinearly elastic loops (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    Details
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00915277
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  • 16
    Electronic Resource
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    Surf-riding and oscillations of a ship in quartering waves (1995)
    Springer
    Journal of marine science and technology 1 (1995), S. 24-36 
    Details
    ISSN: 1437-8213
    Keywords: surf-riding ; nonlinear ; wave ; ship motion ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01240010
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  • 17
    Electronic Resource
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    Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 313-320 
    Details
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007622208894
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  • 18
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    On the Composition of the Solar Interior Rapporteur Paper I (1998)
    Springer
    Space science reviews 85 (1998), S. 141-158 
    Details
    ISSN: 1572-9672
    Keywords: equation of state ; opacity ; helium abundance ; lithium abundance ; tachocline ; solar neutrinos ; helioseismology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Standard solar models, although they are free from the influence of much of the fluid motion that is bound to be present in the Sun, have been shown by helioseismology to represent the spherically averaged structure of the Sun amazingly well. This state of affairs has come about after painstaking refinements by a great many people of the pertinent microphysics, including that which controls the equation of state, the opacity, the nuclear reaction rates and the diffusion that inhibits gravitational segregation of chemical elements. It has instilled confidence in the modellers in being able to predict the composition of the solar interior. But there are consequences of the flow, related particularly to redistribution of chemical species, that can be difficult to identify observationally, yet which may degrade any inferences we might make. Their potential presence must at least be acknowledged by anyone who tries to asses the reliability of the models. This report summarizes the discussions in the preceding pages of this volume of the current theoretical and observational status of the subject, pointing to many of the caveats that have been raised, and attempting at the same time to put them into a seemingly coherent discourse in the context of our present understanding of the workings of the solar interior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005105224272
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  • 19
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    Stable Quasicrystalline Ground States (1997)
    Springer
    Journal of statistical physics 88 (1997), S. 691-711 
    Details
    ISSN: 1572-9613
    Keywords: Quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; ground states ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:JOSS.0000015168.25151.22
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  • 20
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    Renormalization of the Chapman–Enskog Expansion: Isothermal Fluid Flow and Rosenau Saturation (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 285-305 
    Details
    ISSN: 1572-9613
    Keywords: Chapman–Enskog expansion ; Burnett equation ; Boltzmann equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper continues the author's study of procedures for rewriting the well-known Chapman–Enskog expansion used in the kinetic theory of gases. The usual Chapman–Enskog expansion, when used in isothermal fluid motion, will introduce nonlinear instability at super-Burnett order O(ε3) truncation. The procedure given here eliminates the truncation instability and produces the desired dissipation inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023048322851
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  • 21
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    Classical Lattice-Gas Models of Quasicrystals (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 835-850 
    Details
    ISSN: 1572-9613
    Keywords: quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; nonperiodic ground states ; nonperiodic Gibbs states ; stability ; frustration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004542115011
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  • 22
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    Non-Self-Similar Behavior in the LSW Theory of Ostwald Ripening (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 867-902 
    Details
    ISSN: 1572-9613
    Keywords: kinetics of phase transitions ; domain coarsening ; asymptotic behavior ; self-similarity ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The classical Lifshitz–Slyozov–Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.
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    URL: http://dx.doi.org/10.1023/A:1004546215920
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  • 23
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    Stability of Attractive Bose–Einstein Condensates (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 731-746 
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    ISSN: 1572-9613
    Keywords: attractive Bose–Einstein condensates ; nonlinear Schrödinger equation ; stability ; ground state ; variational arguments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.
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    URL: http://dx.doi.org/10.1023/A:1026437923987
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  • 24
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    A general approach to association using cluster partition functions (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1287-1306 
    Details
    ISSN: 1572-9613
    Keywords: Association ; phase equilibrium ; statistical mechanics ; partition function ; chemical engineering ; equation of state ; chemical equilibrium ; cluster distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181285
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  • 25
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    A catastrophe analysis on the stability of the crack growth in three-point bending specimens (1996)
    Springer
    Acta mechanica solida Sinica 9 (1996), S. 179-183 
    Details
    ISSN: 0894-9166
    Keywords: crack growth ; stability ; cusp catastrophe ; J-integral ; three-point bending specimen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents an attempt at the application of catastrophe theory to the stability analysis ofJ-controlled crack growth in three-point bending specimens. By introducing the solutions ofJ- integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.
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    URL: http://dx.doi.org/10.1007/BF02209162
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    Room-temperature compressibilities of MnO and CdO: further examination of the role of cation type in bulk modulus systematics (1999)
    Springer
    Physics and chemistry of minerals 26 (1999), S. 644-648 
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    ISSN: 1432-2021
    Keywords: Key words MnO ; CdO ; rock-salt monoxides ; X-ray diffraction ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Room-temperature volume measurements up to 8.1 GPa reveal that rock-salt structured MnO and CdO have identical compressibility in the pressure range studied. In the plot of bulk modulus vs unit-cell volume, CdO plots well above the trend of the 3d transition metal monoxides, a behavior that deviates from empirical predictions of constant K 0 V 0. The present observations are in favor of our earlier suggestion that, for isostructural solids, the empirically predicted bulk modulus-volume relationship may be limited to their subsets that share the same valence electron character (i.e., s vs 3d vs 4d). For cations forming transition metal monoxides, variations of Pauling electronegativity with ionic radius show differences that are qualitatively similar to the observed trends of bulk modulus, suggesting that bond covalency differences may contribute to the different behaviors between the 3d and 4d transition metal monoxides.
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    URL: http://dx.doi.org/10.1007/s002690050229
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    Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning (1999)
    Springer
    Biological cybernetics 81 (1999), S. 211-225 
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    ISSN: 1432-0770
    Keywords: Key words: Hebbian learning rule ; attractor dynamics ; symmetric connections ; multiplicative normalization ; self-organization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.
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    URL: http://dx.doi.org/10.1007/s004220050557
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    Relative equilibria of Hamiltonian systems with symmetry: Linearization, smoothness, and drift (1995)
    Springer
    Journal of nonlinear science 5 (1995), S. 373-418 
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    ISSN: 1432-1467
    Keywords: Hamiltonian system with symmetry ; relative equilibria ; perturbation ; linearization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However, interesting evolution along that orbit, here called drift, does occur. In this article, linearizations of relative equilibria are used to construct a first order perturbation theory explaining drift, and also to determine when the set of relative equilibria near a given relative equilibrium is a smooth symplectic submanifold of phase space.
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    URL: http://dx.doi.org/10.1007/BF01212907
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    Energetics of growing epilayer-substrate combinations of comparable bond strength and in Kurdjumov-Sachs orientation (1996)
    Springer
    Interface science 3 (1996), S. 303-316 
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    ISSN: 1573-2746
    Keywords: epitaxy ; Krudjumov-Sachs ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper we address the problems related to critical misfit and thickness in epilayer-substrate combinations of comparable bond strengths; specifically the case in which a pseudomorphic monolayer (ML) is stable and the critical thickness is about three MLs or less. Of particular interest are the average energies related to misfit strain f KS and misfit dislocations (MDs)—in the latter case the individual contributions of the oscillatory strains 〈V〉 and the epilayer-substrate disregistry 〈V〉MD. The individual energies are of interest because they may play different roles in the realization of specific growth modes. The analytical approach involves the following assumptions: (a) a rigid substrate as source of a periodic epilayer atom-substrate interaction potential which we model in terms of a low order truncated Fourier series; and (b) an epilayer which (i) deforms harmonically with zero strain gradient normal to the film plane, (ii) grows in Kurdjumov-Sachs (KS) orientation due to small misfit. f KS and in the layer-by-layer growth mode. Arguments are presented claiming that this interfacial situation may be approximated by a one-dimensional problem in which epilayer stiffness constants and equilibrium structure, as well as epilayer-substrate interaction depend on epilayer thickness; which poses a complex problem. An approximate solution could be obtained by assuming these quantities to be independent of thickness and proximities of the vacuum and the substrate. The most prominent conclusions are that the equilibrium density of MDs and hence the transition from misfit accommodation by MS to one containing MDs is a catastrophic process and that sustained minimum energy may require the overcoming of an energy barrier. While elementary implementation of the results to equilibrium growth mode theory suggests—independently of the catastrophic nature—that energetically favored misfit strain relief by misfit dislocations may, or may not, effect a transition to Stranski-Krastanov growth, a crude numerical calculation favors the transition. A proper implementation of the results require extensive numerical calculations and is planned for the near future.
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    The breakup and atomization of a viscous liquid jet (1996)
    Springer
    Acta mechanica Sinica 12 (1996), S. 124-134 
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    ISSN: 1614-3116
    Keywords: jet ; stability ; breakup ; atomization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet. With respect to the spatial growing disturbance mode, the numerical results obtained from the solution of the dispersion equation reveal that a dimensionless parameterJ e exists. AsJ e〉1, the axisymmetric disturbance mode is most unstable; and whenJ e〈1, the asymmetric disturbances come into being, their growth rate increases with the decrease, ofJ e, till one of them becomes the most unstable disturbance. The breakup of a low-speed liquid jet results from the developing of axisymmetric disturbances, whose instability is produced by the surface tension; while the atomization of a high-speed liquid jet is brought about by the evolution of nonaxisymmetric disturbance, whose instability is caused by the aerodynamic force on the interface between the jet and the ambient gas.
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    Stability of linear time variant dynamic systems with multiple time delays (1998)
    Springer
    Acta mechanica Sinica 14 (1998), S. 274-282 
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    ISSN: 1614-3116
    Keywords: time delay ; stability ; frozen time approach ; retarded dynamic systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives.
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    Bifurcations of a cantilevered pipe conveying steady fluid with a terminal nozzle (2000)
    Springer
    Acta mechanica Sinica 16 (2000), S. 264-272 
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    ISSN: 1614-3116
    Keywords: nonlinear dynamics ; bifurcation ; stability ; fluid-solid interaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
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    Periodic vibro-impacts and their stability of a dual component system (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 366-376 
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    ISSN: 1614-3116
    Keywords: vibro-impact ; stability ; multiplicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.
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    The stability of viscous liquid jets in a swirling gas (1998)
    Springer
    Acta mechanica Sinica 14 (1998), S. 226-233 
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    ISSN: 1614-3116
    Keywords: jet ; stability ; dispersion equation ; swirling gas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameterJ e is again introduced, in the meantime, another dimensionless parameterE called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value ofE, in pace with the changing ofJ e , the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin whenJ e 〉1; but in the range ofJ e 〈1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much stronger whenJ e ≪1.
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    A study of the construction of lyapunov function for a class of fourth order nonlinear systems (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 195-202 
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    ISSN: 1573-2754
    Keywords: nonlinear ; stability ; Lyapunov function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the paper Lyapumov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.
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    Stability for the equilibrium state of Chaplygin's systéms (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 635-642 
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    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
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    Stability analysis of linear and nonlinear periodic convection in thermohaline double-diffusive systems (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 869-877 
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    ISSN: 1573-2754
    Keywords: thermohaline double-diffusive system ; periodic solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A shortout analytic method of stability in strong nonlinear autonomous system is introduced into stability analysis of the thermohaline double-diffusive system. Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotomic branch and oscillatory branch are outilined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value µ c in this case of 0〈rs-rsc≪1. The stability conclusions under different direction of vortex are drawn out.
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    The auto-adjustable damping method for solving nonlinear equations (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 163-168 
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    ISSN: 1573-2754
    Keywords: nonlinear equation ; stability ; Newton's method ; auto-adjustable damping method ; the vector of damping factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
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    Disturbances to a rotating fluid with a sphere moving along the axis of rotation (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 861-867 
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    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Stability of a class of neural network models with delay (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 912-916 
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    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    Bifurcations in Spherical MHD Models (1998)
    Springer
    Studia geophysica et geodaetica 42 (1998), S. 320-327 
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    ISSN: 1573-1626
    Keywords: MHD ; stability ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Notes: Abstract A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.
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    The stability in neural networks with interneuronal transmission delays (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 457-462 
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    ISSN: 1573-2754
    Keywords: neural networks ; equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type $$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t 〉 0;i = 1,2, \cdots ,n)} $$
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    A method for following the unstable path between two saddle-node bifurcation points in nonlinear dynamic system (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
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    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    Some dynamical properties of a viscoelastic cylindrical shell (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 233-240 
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    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.
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    The Equation of State of Lakes (2000)
    Springer
    Aquatic geochemistry 6 (2000), S. 1-17 
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    ISSN: 1573-1421
    Keywords: lakes ; density ; compressibility ; expansibility ; conductivity ; stability ; pvt properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract In recent years, a number of workers have studied the stability of deep lakes such as Lake Tanganyika, Lake Baikal and Lake Malawi. In this paper, the methods that can be used to determine the effect that the components of lakes have on the equation of state are examined. The PVT properties of Lakes have been determined by using apparent molal volume data for the major ionic components of the lake. The estimated PVT properties (densities, expansibility and compressibilities) of the lakes are found to be in good agreement with the PVT properties (P) of seawater diluted to the same salinity. This is similar to earlier work that showed that the PVT properties of rivers and estuarine waters could also be estimated from the properties of seawater. The measured densities of Lake Tanganyika were found to be in good agreement (± 2 × 10-6 g cm-3) with the values estimated from partial molal properties and the values of seawater at the same total salinity (ST = 0.568‰). The increase in the densities of Lake Tanganyika waters increased due to changes in the composition of the waters. The measured increase in the measured density (45 × 10-6 g cm-3) is in good agreement (46 × 10-6 g cm-3) with the values calculated for the increase in Na+, HCO3 -, Mg2+, Ca2+ and Si(OH)4. Methods are described that can be used to determine the conductivity salinity of lakes using the equations developed for seawater. By combining these relationships with apparent molal volume data, one can relate the PVT properties of the lake to those of seawater.
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    Orbital Migration Of Giant Planets: Using Numerical Integration To Investigate Consequences For Other Bodies (1999)
    Springer
    Earth, moon and planets 87 (1999), S. 103-115 
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    ISSN: 1573-0794
    Keywords: Accretion ; exoplanetary system ; extrasolar planets ; numerical integration ; orbital migration ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational interaction with a residual planetesimal disk together with several means of halting inward migration have been identified. These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration. The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient algorithms.
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    A microstructural investigation of the nonlinear response of electrorheological suspensions (1995)
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    Rheologica acta 34 (1995), S. 417-429 
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    ISSN: 1435-1528
    Keywords: Electrorheology ; nonlinear ; simulations ; stability ; steady shear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Particle-level simulations are employed to investigate the transition from linear to nonlinear rheological behavior for electrorheological suspensions under start-up of steady shear flow. This transition is found to first arise from the very slight rearrangement of structures, as opposed to the gross rupture of particulate columns. Linear stability analysis shows that these rearrangements occur when the structures are sheared into electrostatically unstable configurations. The rearrangements also produce a second type of relaxation phenomenon that appears at low frequencies and finite strain amplitudes. Incorporating more realistic force descriptions into the idealized simulation model shifts the transition to nonlinear deformation to smaller strain amplitudes, approaching experimentally observed values. The role of the rearrangement of unstable structures on the oscillatory shear flow response is investigated in the following paper, Part II.
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    A microstructural investigation of the nonlinear response of electrorheological suspensions (1995)
    Springer
    Rheologica acta 34 (1995), S. 430-439 
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    ISSN: 1435-1528
    Keywords: Electrorheology ; nonlinear ; simulations ; stability ; viscoelasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In the preceding paper, Part 1, the transition from linear to nonlinear behavior for electrorheological (ER) suspensions under start-up of steady shear flow was found to first arise from the slight rearrangement of unstable structures. In this paper, we investigate the transition to nonlinear behavior for ER suspensions under oscillatory shear flow, focusing on the role of the rearrangement of unstable structures, and employing experimental and simulation results. Again, we find that nonlinear deformation first arises from these rearrangements, as opposed to the gross rearrangement or rupture of particulate chains. The Fourier transform of the simulated time-dependent shear stress is employed to quantify the dependence of the critical strain on the deformation frequency and electric field strength. The predicted behavior is consistent with experimental trends. Methods for verifying the predictions are discussed, as well as possible avenues for exploiting this information in improved operating strategies and improved ER fluids.
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    Stability of viscoelastic flow around periodic arrays of cylinders (1997)
    Springer
    Rheologica acta 36 (1997), S. 367-383 
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    ISSN: 1435-1528
    Keywords: Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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    Stability of viscoelastic flow around periodic arrays of cylinders (1997)
    Springer
    Rheologica acta 36 (1997), S. 367-383 
    Details
    ISSN: 1435-1528
    Keywords: Key words Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (We c ), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above We c which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above We c a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplified spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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    Microphysics: Equation of State (1998)
    Springer
    Space science reviews 85 (1998), S. 49-60 
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    ISSN: 1572-9672
    Keywords: helioseismology ; equation of state ; helium abundance ; excited states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The equation of state is one of the three fundamental ingredients used to construct stellar models. The plasma of the interiors of stars such as the Sun is only slightly non-ideal. However, the extraordinary accuracy of the helioseismological data requires refined equations of state. It turned out to be necessary to include a Coulomb correction, commonly evaluated in the Debye-Hückel approximation. Higher-order non-ideal effects have implications as well, both for plasma physics and for solar physics. As a typical example, the recently studied thermodynamic consequence of excited states in compound particles is discussed. This effect is of considerable relevance in the helioseismic determination of the helium abundance in the solar convection zone.
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    On stable spherical configurations of artificial protocells (1995)
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    Journal of biological physics 20 (1995), S. 223-227 
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    ISSN: 1573-0689
    Keywords: protocells ; microsphere ; thermal proteinoid ; stability ; surface energy ; bulk energy ; electrostatic energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract The stability of protocells is discussed in terms of macroscopic energies. It is shown that bulk and surface energy contributions alone cannot lead to stable protocells. If electrostatic energy, due to transmembrane voltage, is taken into account, stable hollow spheres are proved to exist. For several reasons, however, this result should not be regarded as an ultimate explanation.
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    Coulomb Systems at Low Density: A Review (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 1163-1330 
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    ISSN: 1572-9613
    Keywords: Coulomb ; plasma ; Saha ; screening ; Debye–Hückel ; virial ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.
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    A reaction-diffusion equation for a cyclic system with three components (1997)
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    Journal of statistical physics 87 (1997), S. 1145-1164 
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    ISSN: 1572-9613
    Keywords: Fisher-Kolmogorov equation ; traveling fronts ; fixed points ; population dynamics ; bifurcations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.
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    Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 101-110 
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    ISSN: 1572-9567
    Keywords: equation of state ; R 134a ; refrigerants ; simulated annealing ; stepwise regression ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.
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    Equations of state for the thermodynamic properties of R32 (difluoromethane) and R125 (pentafluoroethane) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 79-89 
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    ISSN: 1572-9567
    Keywords: difluoromethane (R32) ; equation of state ; pentafluoroethane (R125) ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Thermodynamic properties of difluoromethane (R32) and pentafluoroethane (R125) are expressed in terms of 32-term modified Benedict-Webb-Rubin (MBWR) equations of state. For each refrigerant, coefficients are reported for the MBWR equation and for ancillary equations used to fit the ideal-gas heat capacity and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined with a multiproperty fit that used the following types of experimental data: PVT: isochoric, isobaric, and saturated-liquid heal capacities; second virial coefficients; and properties at coexistence. The respective equations of stale accurately represent experimental data from 160 to 393 K and pressures to 35 MPa for R32 and from 174 to 448 K and pressures to 68 MPa for R125 with the exception of the critical regions. Both equations give reasonable results upon extrapolation to 500 K and 60 MPa. Comparisons between predicted and experimental values are presented.
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    A fundamental equation of state for 1,1-difluoroethane (HFC-152a) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 91-100 
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    ISSN: 1572-9567
    Keywords: equation of state ; Helmholtz free energy ; HFC-152a ; refrigeranis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable (p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.
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    Determination of thermodynamic properties from the speed of sound (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 663-673 
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    ISSN: 1572-9567
    Keywords: equation of state ; speed of sound ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We describe methods by which all of the observable thermodynamic properties of a compressed gas, including the compressibility factor and the isochoric heat capacity, may be determined from sound speed data by numerical integration of a pair of partial differential equations. The technique may be employed over a wide range of conditions. Initial values are required. but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of analytic and numerical results. The results indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.
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    Molecular simulation and theory of associating chain molecules (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 705-713 
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    ISSN: 1572-9567
    Keywords: associating fluids ; chain fluids ; computer simulations ; equation of state ; hydrogen bonding ; Lennard-Jones ; Monte Carlo
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A closed-form statistical mechanical based equation of state for associating chain fluids is presented. A Lennard-Jones chain is used as a reference to account for the repulsive, dispersive and anisotropic (size) contributions, while the short-range directional attraction is treated as a perturbation expansion based on Wertheim's first-order theory of associating fluids. A model fluid composed of a chain of tangently bonded Lennard-Jones spheres with an associating square-well site at one of the end spheres is studied. Isobaric-isothermal Monte Carlo simulations were performed for this model at subcritical and supercritical temperatures at a association strength typical of hydrogen-bonding systems. The theory is seen accurately to predict the simulation results subject to the limitations of the equation of state of the reference fluid. The system studied has some of the main complexities found in associating chain molecules such as organic acids, alkanols, and primary amines.
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    The ISM Equation of State Applied to Refrigerants (1999)
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    International journal of thermophysics 20 (1999), S. 1547-1555 
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    ISSN: 1572-9567
    Keywords: cohesive energy ; equation of state ; non-polar fluids ; refrigerants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this work, we apply an equation of state based on statistical–mechanical perturbation theory to liquid refrigerants and their mixtures. Three temperature-dependent parameters are needed to use the equation of state: the second virial coefficient, B 2(T), an effective van der Waals covolume, b(T), and a scaling factor, α(T). The second virial coefficients are calculated from a correlation based on the heat of vaporization, ΔH vap, and the liquid density at the freezing point, ρfp. α(T) and b(T) can also be calculated from the second virial coefficient by a scaling rule. Based on the theory, these two temperature-dependent parameters depend only on the repulsive branch of the potential function, and therefore, by our procedure, can be found from ΔH vap and ρfp. The theory has considerable predictive power, since it permits the construction of the p–v–T surface from the heat of vaporization plus the triple-point density. The equation of state is tested for pure, two- and three-component liquid refrigerant mixtures.
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    Equation of State for Molten Alkali Metal Alloys (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1575-1585 
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    ISSN: 1572-9567
    Keywords: alkali metal alloys ; cohesive energy ; equation of state ; statistical mechanics ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Calculated results of the liquid density of binary molten alloys of Na–K and K–Cs over the whole range of concentrations and that of a ternary molten eutectic of Na–K–Cs from the freezing point up to several hundred degrees above the boiling point are presented. The calculations were performed with the analytical equation of state proposed by Ihm, Song, and Mason, which is based on statistical-mechanical perturbation theory. The second virial coefficients were calculated from the corresponding-states correlation of Mehdipour and Boushehri. Calculation of the other two temperature-dependent parameters was carried out by scaling. The calculated results cover a much wider range of temperatures and are more accurate than those presented in our previous work.
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    Compressibilities of ternary mixtures C1-nC16-CO2 under pressure from ultrasonic measurements of sound speed (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 851-871 
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    ISSN: 1572-9567
    Keywords: compressibility ; equation of state ; high pressure ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Speed of sound measurements have been performed on three mixtures of the ternary system methane + carbon dioxide + normal hexadecane. The systems have been investigated from 12 to 70 MPa in the temperature range from 313 to 393 K. Furthermore, these measurements have allowed the evaluation of the isothermal and the isentropic compressibilities up to 70 MPa from low pressure (〈40-MPa) density data.
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    Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 909-944 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; ethane ; methane ; plait point ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.
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    Equation of state for compressed liquids from surface tension (1996)
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    International journal of thermophysics 17 (1996), S. 945-957 
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    ISSN: 1572-9567
    Keywords: compressed liquids ; corresponding states ; equation of state ; surface tension
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    Topics: Physics
    Notes: Abstract A method for predicting an analytical equation of state for liquids from the surface tension and the liquid density at the freezing temperature (γ 1,ϱ 1) as scaling constants is presented. The reference temperature. Tref. is introduced and the product (T ref T 1 1 2 ) is shown to be an advantageous corresponding temperature for the second virial coeflicienls. B2(T). of spherical and molecular fluids. Thus, B2(T) follows a promising corresponding states principle and then calculations forα(T) andb(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, (γ 1,ϱ 1) are sufficient for the determination of thermophysical properties of fluids from the freezing line up to the critical temperature. The present procedure has the advantage that it can also be used in cases whereT c andP c are not known or the vapor pressure is too small to allow accurate measurements. We applied the procedure to predict the density of Lennard-Jones liquids over an extensive range of temperatures and pressures. The results for liquids with a wide range of acentric factor values are within 5%.
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    Thermodynamic Properties of Sulfur Hexafluoride (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 739-765 
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    ISSN: 1572-9567
    Keywords: Burnett measurements ; equation of state ; heat capacity ; intermolecular potential ; speed of sound ; sulfur hexafluoride ; SF6 ; thermodynamic properties ; vapor pressure ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present new vapor phase speed-of-sound data u(P, T), new Burnett density–pressure–temperature data ρ(P, T), and a few vapor pressure measurements for sulfur hexafluoride (SF6). The speed-of-sound data spanned the temperature range 230 K≤T≤460 K and reached maximum pressures that were the lesser of 1.5 MPa or 80% of the vapor pressure of SF6. The Burnett ρ(P, T) data were obtained on isochores spanning the density range 137 mol·m−3≤ρ≤4380 mol·m−3 and the temperature range 283 K≤T≤393 K. (The corresponding pressure range is 0.3 MPa≤P≤9.0 MPa.) The u(P, T) data below 1.5 MPa were correlated using a model hard-core, Lennard–Jones intermolecular potential for the second and third virial coefficients and a polynomial for the perfect gas heat capacity. The resulting equation of state has very high accuracy at low densities; it is useful for calibrating mass flow controllers and may be extrapolated to 1000 K. The new u(P, T) data and the new ρ(P, T) data were simultaneously correlated with a virial equation of state containing four terms with the temperature dependences of model square-well potentials. This correlation extends nearly to the critical density and may help resolve contradictions among data sets from the literature.
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    Small-Angle Neutron Scattering Studies of Vesicle Stability (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 461-470 
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    ISSN: 1572-9567
    Keywords: small-angle neutron scattering ; stability ; vesicles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Small-angle neutron scattering (SANS) was used to investigate the structure of mixed colloids of egg yolk phosphatidylcholine (EYPC) with the bile salt, cholylglycine (CG), in D2O as a function of pressure (P) and temperature (T). At atmospheric pressure, the system forms an isotropic phase of mixed, single-bilayer vesicles (SLVs). Increasing the external hydrostatic pressure brought about significant changes in particle morphology. At T=25°C, application of a pressure of 3.5 MPa resulted in collapse of the SLVs. A further increase in P, up to 51.8 MPa, resulted in a transition from a phase of ordered (stacked), collapsed vesicles to one of stacked, ribbon-like particles. A similar collapse of the vesicles was observed at a higher temperature (T=37°C) with increasing P, but at this temperature, no ribbon phase was found at the highest pressure explored.
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    Chempak: Physical-Properties Database Structure and Development (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 771-779 
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    ISSN: 1572-9567
    Keywords: databases ; equation of state ; thermodynamic properties ; transport properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Chempak (commercial physical properties database and properties estimation software) gives the thermodynamic and transport properties of pure compounds as functions of temperature and pressure for both liquid and vapor phases. Compound liquid properties are defined from the melting to the critical points. Vapor properties are defined from the melting point to 1300 K. The user may define up to 50 mixtures of compounds drawn from the database. In addition, the user may add up to 100 additional compounds defined by using the same techniques employed to construct the main database. Vapor properties are defined by the use of the Lee–Kesler and the Wu and Stiel equations of state. Vapor viscosity and thermal conductivity are defined using corresponding states methods. Liquid thermodynamic properties (except specific heat) are derived from the equation of state. All other liquid properties are defined by setting 11 data values from the melting to the critical point. The resulting property data arrays are interpolated against temperature.
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    Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 217-228 
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    ISSN: 1572-9567
    Keywords: air ; equation of state ; fundamental equation ; high pressure ; high temperature ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A thermodynamic property formulation for standard dry air based upon experimental P–ρ–T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.
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    URL: http://dx.doi.org/10.1023/A:1021450818807
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    Properties of Optical Phase-Locked Loop Based on Four Wave Mixing in Semiconductor Laser Amplifiers (1998)
    Springer
    International journal of infrared and millimeter waves 19 (1998), S. 1721-1734 
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    ISSN: 1572-9559
    Keywords: optical phase-locked loop ; stability ; phase jitter ; four-wave mixing ; semiconductor laser amplifier
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, the properties of the optical phase-locked loop(PLL) based on the four-wave mixing in the semiconductor laser amplifiers (SLAs) are discussed. The components that achieve the function of detecting the bit phase of the input optical signal are concerned and discussed in detail together as a function module named as the optical bit phase detector referred to the general electronic PLL. Therefore, most of the properties of the optical PLL can be analyzed by applying the general phase-locked theory. Here the stability of the optical PLL is discussed. It's shown that the variance of input signal power in the practical application will cause optical PLL system unstable because of its long loop delay. The influence on the output phase jitter of the optical PLL is also investigated.
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    URL: http://dx.doi.org/10.1023/A:1021775428899
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    A new nonrandom lattice fluid model and its simplification by two-liquid theory for phase equilibria of complex mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 723-731 
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    ISSN: 1572-9567
    Keywords: complex mixtures ; equation of state ; multiphase equilibria ; nonrandom lattice theory ; polymer solutions ; supercritical fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new riogorous equation of state (EOS) and its simplified version have been proposed by the present authors based on the full Guggenheim combinatorics ] of the nonrandom lattice hole theory. The simplified EOS. with the introduction of the concept of local composition, becomes similar to the density-dependent UNIQUAC model. However, im the present approach we have a volumetric EOS instead of the excess Gibbs function. Both EOSs were tested for their applicability in correlating the phase equilibria behavior of pure components and complex mixtures. Comparison of both models with experiment includes such systems as nonpolar nonpolar, nonpolar polar, and polar polar hydrocarbons, supercritical systems, and polymer solutions. With two parameters for each pure component and one binary interaction energy parameter, results obtained to date demonstrate that both formulations are quantitatively applicable to complex systems oer a wide range of temperatures, pressures, and concentrations.
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    URL: http://dx.doi.org/10.1007/BF01438857
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    Thermodynamic properties of the generalized Murnaghan equation of state of solids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1009-1026 
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    ISSN: 1572-9567
    Keywords: Anderson-Grüneisen ; bulk modulus ; equation of state ; expansivity ; high pressure ; Murnaghan equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In the Murnaghan approximation, an isothermal relation between pressure (P) and volume (V) for solids is derived from the assumption that the isothermal bulk modulus (B) is a linear function ofP. This paper presents a thermodynamic analysis of a generalized form of the equation, based on treating all its various parameters [viz., V, B, and (∂B/∂P) T atP=0] as functions of temperature. Extending a previous study, the effect ofT upon (∂B/∂P) T is accounted for by using a dimensionless parameter introduced by us, which is used in formulating general expressions for the volume dependence of various thermophysical quantities,viz., the thermal expansion coefficient (α), the productαB, and the Grüneisen and Anderson-Grüneisen parameters. Some combinations of these parameters are identified, which show a simple dependence uponP. The new expressions are used in analyzing current approximations and the behavior of the solid in the low-compression range. In particular, an expression forα at highP is reported which generalizes the Anderson equation and previous results by us.
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    URL: http://dx.doi.org/10.1007/BF02093479
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    Application of nonlinear regression in the development of a wide range formulation for HCFC-22 (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1155-1164 
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    ISSN: 1572-9567
    Keywords: chlorodifluoromethane ; equation of state ; HCFC-22 ; nonlinear fitting ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based onP-ρ-T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.
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    URL: http://dx.doi.org/10.1007/BF02081283
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    Vapor-liquid equilibrium, coexistence curve, and critical locus for binary HFC-32/HFC-134a mixture (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1175-1184 
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    ISSN: 1572-9567
    Keywords: binary interaction parameter ; critical density ; critical temperature ; equation of state ; R-32/134a mixture ; vapor-liquid coexistence curve ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Two kinds of equilibrium measurements of binary R-32/134a mixtures were carried out. The vapor-liquid equilibria were measured by the static method in the temperature range between 283 and 313 K. On the basis of the present experimental data, the temperature dependence of the binary interaction parameterk 12 for two equations of state, namely, the Soave-Redlich-Kwong equation and Carnahan-Starling-De Santis equation, was discussed. The vapor-liquid coexistence curve near the critical point was also measured by the observation of meniscus disappearance. The critical temperatures and critical densities of 30 and 70 wt% R-32 mixtures were determined on the basis of the saturation densities along the coexistence curve in the critical region. In addition, a correlation of the critical locus for this mixture is proposed as a function of composition.
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    The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1165-1174 
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    ISSN: 1572-9567
    Keywords: activity coefficient ; equation of state ; MHV-2 ; refrigerants ; R32 ; R134a ; R125 ; vapor-liquid equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper reports on the development and application of a thermodynamic model based on the second-order Modified Huron Vidal equation of state (MHV-2) to predict the properties of ternary mixtures of the refrigerants R32, R125, and R134a. The mixing rules of this equation of state have been used to incorporate directly an activity-coefficient model for the excess Gibbs free energy. The parameters for the activity-coefficient model have been derived from experimental VLE data for binary mixtures. This methodology has enabled the production of a thermodynamically consistent model which can be used to predict the phase equilibria of R32/R125/R134a mixtures. The input data used in the model are presented in the paper and the predictions of the model are compared with available experimental data. The model has been used to predict the behavior of ternary refrigerant blends of R32/R125/R134a in fractionation scenarios, such as liquid charging and vapor leakage, which are of direct interest to the refrigeration industry. Details of these applications and comparisons with experimental data are discussed, along with other general uses of the thermodynamic model.
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    Prediction of multiphase equilibria in associating fluids by a contact-site quasichemical equation of state (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1287-1297 
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    ISSN: 1572-9567
    Keywords: associating fluids ; contact-site model ; equation of state ; group contribution ; monomer fraction ; multiphase equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A contact-site quasichemical equation of state has been used Tor the modeling of different kinds of fluid phase equilibria (between a gas phase and one or more liquids) over a wide range of conditions. Among the systems of interest are the ternary mixtures water + alkanols + hydrocarbons (alkanes or alkynes), water + alkanols (or acetone)+ CO2, water + polyoxyethyleneglycol ethers + heavy alkanes. The model has been applied to describing the thermodynamic properties of the binary subsystems and to predict the phase behavior of the ternary systems. For longer-chain alkanols and hydrocarbons a group-contribution approach is implemented, which allows the modeling when no experimental data are available. The model gives reasonable predictions of phase behavior and the correct trends in the calculated phase diagrams in most cases. The concentrations of associates in liquid and gas phases are estimated by the model and compared with some experimental and computer simulation data. The predictive abilities of the model, its limitations, and possible ways of its improvement are discussed.
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    URL: http://dx.doi.org/10.1007/BF02081296
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    A New equation of state for square-well molecules (1995)
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    International journal of thermophysics 16 (1995), S. 1277-1286 
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    ISSN: 1572-9567
    Keywords: equation of state ; molecular simulation ; perturbation theory ; second virial coefficient ; square-well molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents a new equation of state for the square-well fluid based on perturbation theory. This equation has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and accurately interpolates between the two limits. Monte Carlo simulations were performed to evaluate the limiting behavior of the theory in the dilute-gas regime. Comparison of the theory with the simulation results shows excellent agreement between the equation-of-state predictions and the data.
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    Ideal-gas thermodynamic properties for natural-gas applications (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1381-1392 
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    ISSN: 1572-9567
    Keywords: caloric properties ; equation of state ; ideal gas ; isobaric heat capacity ; natural gas ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Calculating caloric properties from a thermal equation of state requires information such as isobaric heat capacities in the ideal-gas state as a function of temperature. In this work, values for the parameters of thec p 0 correlation proposed by Aly and Lee were newly determined for 21 pure gases which are compounds of natural gas mixtures. The values of the parameters were adjusted to selectedc p 0 data calculated from spectroscopic data for temperatures ranging from 10 to 1000 K. The data sources used are discussed and compared with literature data deduced from theoretic models and caloric measurements. The parameters presented will be applied in a current GERG project for evaluating equations of state (e.g., the AGA 8 equation) for their suitability for calculating caloric properties.
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    An analytical method of predicting Lee-Kesler-Plöcker equation-of-state binary interaction coefficients (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1393-1411 
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    ISSN: 1572-9567
    Keywords: computer algorithm ; binary interaction coefficient ; equation of state ; mixture ; nonpolar and polar substances ; thermodynamic properties ; reduced properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An analytical method is proposed for finding numerical values of binary interaction coefficients for the Lee-Kesler-Plöcker (LKP) equation of state. The method is based on solving simultaneous equations from Plöcker's mixing rules for pseudocritical parameters of a mixture and the Lee-Kesler equation for the saturation line. For mixtures of hydrocarbons containing from two to nine carbon atoms, the divergence between calculated and experimentally based interaction coefficients (ICs) is no more than ±0.4%. The method is extended to mixtures of polar substances. For polar mixtures, aneffective molar composition concept is introduced which takes into account the impact of dipole moments on the process of molecular associations. Formulas for finding the effective molar composition of mixtures containing polar and/or nonpolar constituents and the binary interaction coefficient (κ ij) based on this effective composition and pure component properties are shown. Calculatedκ ij values for 12 binary mixtures of polar substances differ by 0.4 % or less from correspondingκ ij values obtained by processing experimental data on saturated pressure (P s) and saturated temperature (T s) lines for these same mixtures. A simplified alternativeκ ij approximation method with an error (2–5 %) is also given for mixtures of polar substances.
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    A corresponding-states principle for the equation of state of linear homonuclear fused-hard-sphere fluids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1413-1419 
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    ISSN: 1572-9567
    Keywords: equation of state ; corresponding states ; fused-hard-sphere fluids ; hard spheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A theoretically based corresponding-states principle previously developed for the equation of state of hard-convex-body fluids is extended to rigid linear homonuclear fused-hard-sphere fluids. Effective volumes and shapes are introduced in order to account for the nonconvexity of the molecules. The excess compressibility factor, reduced by means of a parameter which can be determined analytically, is a common function of the effective packing fraction. The analytical expression for the function can be obtained from the equation of state of the hard-sphere fluid. Existing simulation data for diatomics, triatomics and tetraatomics show excellent agreement with the corresponding-states principle.
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    An analytical equation of state for molten alkali metals (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1429-1438 
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    ISSN: 1572-9567
    Keywords: cohesive energy ; equation of state ; molten alkali metals ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper brings the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range. As for normal fluids, the latent heat of vaporization and density at freezing temperature are the only inputs (scaling factors). The correspondingstates correlation of normal fluids is used to calculate the second virial coefficient,B 2(T), of alkali metals, which is scarce experimentally and its calculation is complicated by dimer formation. Calculations of the other two temperature-dependent constants,α(T) andb(T), follow by scaling. The virial coefficients of alkali metals cannot be expected to obey a law of corresponding states for normal fluids. The fact that two potentials are involved may be the reason for this. Thus, alkali metals have the characteristics of interacting through singlet and triple potentials so that the treatment by a single potential here is fortuitous. The adjustable parameter of the equation of state,γ, compensates for the uncertainties inB 2(T). The procedure used to calculate the density of liquids Li through Cs from the freezing line up to several hundred degrees above the boiling temperatures. The results are within 5 %.
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    Solubilities of long-chain hydrocarbons in carbon dioxide (1996)
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    International journal of thermophysics 17 (1996), S. 23-33 
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    ISSN: 1572-9567
    Keywords: equation of state ; heavy hydrocarbons ; natural gas ; supercritical carbon dioxide ; wax deposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Heavy hydrocarbons are becoming an increasingly important problem for the natural gas industry as it develops more costly gas reserves, such as those in the deep Gulf of Mexico. The waxy substances precipiate during natural gas processing, causing blockage of transmission pipelines. Knowledge of the solubility behavior of these hydrocarbon solids is therefore necessary to develop solutions to the solid deposition problem. This work reports solid-supercritical fluid equilibrum data for long-chain n-alkanes in carbon dioxide, a component of natural gas, over a range of temperatures and pressures that are typical of natural gas processing. A flow apparatus was used to measure the solubility, and the data were correlated by the Patel-Teja equation of state. Satisfactory agreement was obtained between calculated and experimental values, so the equation of state may be used to estimate the conditions for solid deposition and the amounts of solids formed at typical processing conditions.
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    An accurate Van der Waals-type equation of state for the Lennard-Jones fluid (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 391-404 
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    ISSN: 1572-9567
    Keywords: coexistence curve ; equation of state ; Lennard Jones fluid ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new equation of state (EOS) is proposed for the Helmholtz energyF of the Lennard Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation.F =F u +F v. WhereF u is a hard body contribution andF A an anttractive dispersion force contribution. The expression forF H is closely related to the hybrid Barker Henderson pertubation theory. The construction ofF A is accomplished with the Setzmann Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS of Johnson et al. shows improvement in the description of the vapor liquid coexistence properties, thepvT data. and in peculiar, of the calorie properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still by about 30%.
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    Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 455-484 
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    ISSN: 1572-9567
    Keywords: CF4 ; C2F6 ; equation of state ; hexafluoroethane ; speed of sound ; tetrafluoromethane ; thermodynamic properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A cylindrical resonator was employed to measure the sound speeds in gaseous CF4 and C2F6. The CF4 measurements span the temperature range 300 to 475 K, while the C2F6 measurements range from 210 to 475 K. For both gases, the pressure range was 0.1 MPa to the lesser of 1.5 MPa or 80% of the sample’s vapor pressure. Typically, the speeds of sound have a relative uncertainty of less than 0.01 % and the ideal-gas heat capacities derived from them have a relative uncertainty of less than 0.1%. The heat capacities agree with those determined from spectroscopic data. The sound speeds were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two models for the virial coefficients were employed, one based on square-well potentials and the second based on a Kihara spherical-core potential. The resulting virial equations reproduce the sound-speed measurements to within 0.005 % and yield densities with relative uncertainties of 0.1% or less. The viscosity calculated from the Kihara potential is 2 to 11% less than the measured viscosity.
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    Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1629-1638 
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    ISSN: 1572-9567
    Keywords: equation of state ; mixtures ; R-32 ; R-125 ; R-134a ; R-152a ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mixture model explicit in Helmholtz energy has been developed that is capable of predicting thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, and R-152a. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single equation that is applied to all mixtures used in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate thermodynamic properties of mixtures, including dew and bubble point properties and critical points, generally within the experimental uncertainties of the available measured properties. It incorporates the most accurate published equation of state for each pure fluid. The estimated uncertainties of calculated properties are ±0.25% in density, ±0.5% in the speed of sound, and ±1% in heat capacities. Calculated bubble point pressures are generally accurate to within ±1%.
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    An Equation of State for 1,1,1-Trifluoroethane (R-143a) (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1639-1651 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; Helmholtz energy ; R-143a ; 1,1,1-trifluoroethane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P–ρ–T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.
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    Determination of Second Virial Coefficients and Virial Equations of R-32 (Difluoromethane) and R-125 (Pentafluoroethane) Based on Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1677-1688 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; hydrofluorocarbon ; R-32 ; R-125 ; second virial coefficient ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The second virial coefficients, B, for difluoromethane (R-32, CH2F2) and pentafluoroethane (R-125, CF3CHF2) are derived from speed-of-sound data measured at temperatures from 273 to 343 K with an experimental uncertainty of ±0.0072%. Equations for the second virial coefficients were established, which are valid in the extensive temperature ranges from 200 to 400 K and from 240 to 440 K for R-32 and R-125, respectively. The equations were compared with theoretically derived second virial coefficient values by Yokozeki. A truncated virial equation of state was developed using the determined equation for the virial coefficients. The virial equation of state represents our speed-of-sound data and most of the vapor PρT data measured by deVries and Tillner-Roth within ±0.01 and ±0.1%, respectively.
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    Application of New, Modified BWR Equations of State to the Corresponding-States Prediction of Natural Gas Properties (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1721-1735 
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    ISSN: 1572-9567
    Keywords: corresponding states ; density ; equation of state ; Lee–Kesler ; natural gas mixtures ; n-heptane ; n-pentane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The accurate description of mixtures includes both single-phase (bulk) properties and the location of phase equilibrium boundaries, e.g., properties that depend upon partial molar properties. In order to estimate these properties, many variants of corresponding-states theory have been developed, especially for nonpolar mixtures such as those found in natural gas systems, In this work we have developed two new, modified BWR equations of state for two natural gas components (n-pentane and n-heptane) and used these equations in a reformulated (Teja-like) Lee–Kesler model. The reformulated model has been tested on bulk-phase properties of hydrocarbon systems, in both the pure and the mixed states. Results have been obtained using the original Lee–Kesler model, the extended corresponding-states theory, and the multifluid corresponding-states principle using several combinations of reference fluids chosen from this and previous equation of state studies. Details of the new equations of state and theoretical comparisons are reported.
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    Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1557-1574 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical properties ; critical volume ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.
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    URL: http://dx.doi.org/10.1023/A:1021453524742
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    Speed of Sound in the Liquid Phase of the R134a/152a Refrigerant Blend (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1689-1697 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; experimental method ; phase equilibrium parameters ; refrigerant ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in the liquid phase of the binary blend of R134a and R152a and its components has been studied. The speed of sound was measured by means of the impulse method at a frequency of 2.1 MHz. The temperature range was 230 to 350 K at pressures up to 16 MPa. The values of speed of sound were measured with a standard error of not more than 0.25%. The results obtained for both components of the blend are represented with expressions based on a physical model. The standard deviation (versus the model) of the measured data is 0.09%, On the basis of the results obtained, the Redlich–Kister correlation has been used over the entire ranges of composition, temperature, and pressure to determine the speed of sound in the liquid phase and at the bubble point of the blend investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022653828617
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  • 90
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    Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 805-829 
    Details
    ISSN: 1572-9567
    Keywords: BCl3 ; boron trichloride ; equation of state ; HBr ; hydrogen bromide ; speed of sound ; thermodynamic properties ; transport properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in gaseous hydrogen bromide (HBr) and boron trichloride (BCl3) was measured using a highly precise acoustic resonance technique. The HBr speed-of-sound measurements span the temperature range 230 to 440 K and the pressure range from 0.05 to 1.5 MPa. The BCl3 speed-of-sound measurements span the temperature range 290 to 460 K and the pressure range from 0.05 MPa to 0.40 MPa. The pressure range in each fluid was limited to 80% of the sample vapor pressure at each temperature. The speed-of-sound data have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacities as a function of temperature with a relative standard uncertainty of 0.1%. The heat capacities agree with those calculated from spectroscopic data within their combined uncertainties. The speeds of sound were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on the hard-core square-well intermolecular potential model and the second based on the hard-core Lennard–Jones intermolecular potential model. The resulting virial equations of state reproduced the speed-of-sound measurements to 0.01% and can be expected to calculate vapor densities with a relative standard uncertainty of 0.1%. Transport properties calculated from the hard-core Lennard–Jones potential model should have a relative standard uncertainty of 10% or less.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006627306105
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  • 91
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    Thermodynamic Properties of Sutherland Fluids from an Analytical Perturbation Theory (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 899-908 
    Details
    ISSN: 1572-9567
    Keywords: Barker–Henderson perturbation theory ; equation of state ; hard-sphere fluid ; radial distribution function ; Sutherland potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Analytical expressions are obtained for the thermodynamic properties of fluids with potentials consisting of a spherical hard core plus an attractive tail of the form 1/r γ (Sutherland fluids). To this end, use is made of the Barker–Henderson perturbation theory together with an analytical expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid. This expression was derived previously on the basis of the analytical solution of the Percus–Yevick integral equation theory. The results are compared with available simulation data for a wide range of densities, temperatures, and values of the potential parameter γ. The overall agreement is good, and the accuracy is similar to that obtained using more accurate solutions for the radial distribution function of the hard-sphere fluid leading to nonanalytical expressions for the thermodynamic properties of the fluid considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006614324761
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  • 92
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    Vapor–Liquid Equilibria for the 1,1,1-Trifluoroethane (HFC-143a)+1,1,1,2-Tetrafluoroethane (HFC-134a) System (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 871-881 
    Details
    ISSN: 1572-9567
    Keywords: binary interaction parameters ; equation of state ; HFC-134a ; HFC-143a ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor–liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-143a+HFC-134a system. Fifty-four equilibrium data are obtained for the HFC-143a+HFC-134a system over the temperature range from 263.15 to 313.15 K at 10 K intervals. The experimental data were correlated with the Carnahan–Starling–De Santis (CSD) and Peng–Robinson (PR) equations of state. Based upon the present data, the binary interaction parameters for the CSD and PR equations of state were calculated for six isotherms for the HFC-143a+HFC-134a system. The binary interaction parameters for both equations of state were fitted by a linear equation as a function of temperature. The present data were in good agreement with the calculated results from the CSD equation of state, and the deviations were less than 1.0% with the exception of two points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006610223852
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  • 93
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    Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1373-1405 
    Details
    ISSN: 1572-9567
    Keywords: associating fluids, critical state ; crossover theory ; equation of state ; enthalpies ; heat capacities ; n-alkanols ; thermodynamic properties ; speed of sound ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006657410862
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  • 94
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    Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13) (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1097-1121 
    Details
    ISSN: 1572-9567
    Keywords: calorimeter ; chlorotrifluoromethane ; density ; equation of state ; heat capacity ; isochoric ; liquid ; R13 ; vapor ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Measurements of the molar heat capacity at constant volume C v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, ρ, T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, ρ, T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C v predictions with measurements was found. Published C v(ρ, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026446004383
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  • 95
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    Aqueous Electrolytes at Near-Critical and Supercritical Temperatures (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 355-366 
    Details
    ISSN: 1572-9567
    Keywords: aqueous electrolytes ; calcium chloride ; equation of state ; near-critical properties ; phase-diagram type ; potassium chloride ; sodium chloride ; supercritical properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The aqueous electrolyte systems $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O, KCl}}{\kern 1pt} {\text{ - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O and CaCl}}{\kern 1pt} {\text{ - H}}_{\text{2}} {\text{O}}$$ are of great interest both geologically and industrially. Equations of state were developed recently for these systems; they are based on theoretical modeling for mixtures of hard spheres with appropriate diameters and dipole moments for H2O, NaCl, and KCl and with a quadrupole moment for CaCl2. Empirical terms are added as required to fit the available experimental data. The fit to the compositions and densities at equilibrium of the saturated vapor and liquid constitutes a severe test, in addition to properties in the single-phase regions. Temperatures range upward from 300°C for NaCl and KCl and from 250°C for CaCl2 for these equations. Complications from hydrolysis and alternate equations valid at lower temperatures are discussed briefly. In addition, there is a very important theoretical aspect relating to the general phase diagrams. With the high ratio of critical temperatures of the salts to that of water, complex diagrams involving liquid–liquid phase separation near the critical point of water are expected. But no such effect is observed experimentally; instead, one finds simple type I phase diagrams. This is particularly clear in the case of $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O}}$$ , where the database is very accurate and extends above 1000 K.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022549024247
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  • 96
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    Mixing Rules for van der Waals-Type Equations of State Based on Activity-Coefficient Models (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 1429-1445 
    Details
    ISSN: 1572-9567
    Keywords: activity coefficient models ; equation of state ; excess functions ; mixing rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new approach for incorporation of the excess free energy from an activity coefficient model (ACM) into an equation of state (EOS) has been proposed. The approach is based on a concept that any ACM is valid at a low but finite value of compressibility factor. This condition allows us to analyze the “infinite pressure” approximation in a general way. It is shown that the “infinite pressure” approach neglects the contribution of the repulsive term of the EOS to the excess free energy of a mixture. This, in turn, introduces inconsistency which results in the difference in the calculated excess free energy of the EOS and the base ACM. The new approach defines parameter a of the EOS as an implicit function of compositions and temperature, thus requiring an iterative procedure using the “infinite pressure limit” as a starting point. The new approach can be modified to provide the correct composition dependence of a mixture second virial coefficient. Applicability of the new method has been tested for binary systems under vapor–liquid and liquid–liquid equilibrium conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021987603498
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    Thermodynamic Properties for R-404A (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 129-140 
    Details
    ISSN: 1572-9567
    Keywords: correlation ; equation of state ; R-125 ; R-134a ; R-143a ; R-404A ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m−3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.
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    URL: http://dx.doi.org/10.1023/A:1021434415173
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    Equation of state for fluid alkali metals: Binodal (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 533-543 
    Details
    ISSN: 1572-9567
    Keywords: alkali metals ; binodal ; corresponding states ; equation of state ; fluid metals ; rectilinear diameter ; thermodynamic similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The three-parameter generalized van der Waals equation of state for liquids and gases is analyzed. This equation contains the generalized expressiona/V" for the molecular pressure: here the parametern takes into account the specificity of intermolecular attractive forces for various substances. The equation is presented in the reduced form, from which follows the single-parameter law of corresponding states with the thermodynamic similarity parametern. 11 is established that for alkali metals the value of the parameter it is the same and does not depend on temperature substantially. From the given generalized equation, the expressions for the binodal (equilibrium curve of the liquid and vapor phases) are obtained. For cesium. rubidium, and potassium, the temperature dependence of density is calculated over the temperature range from their melting point to the critical point: the results of the calculations agree with experimental data. It is established that for alkali metals, the law of rectilinear diameter breaks down in the vicinity of the critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01441919
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    A thermodynamic property formulation for cyclohexane (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 519-531 
    Details
    ISSN: 1572-9567
    Keywords: cyclohexane ; equation of state ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A formulation for the thermodynamic properties of cyclohexane is presented. The equation is valid for single-phase and saturation states from the melting line to 700 K at pressures up to 80 MPa. It includes a fundamental equation explicit in reduced Helmholtz energy with independent variables of reduced density and temperature. The functional form and coefficients of the ancillary equations were determined by weighted linear regression analyses of evaluated experimental data. An adaptive regression algorithm was used to determine the final equation. To ensure correct thermodynamic behavior of the Helmholtz energy surface the coefficients of the fundamental equation were determined with multiproperty fitting, Pressure-density-temperature (P-p-T) and isobaric heat capacity (C p -P-T) data were used to develop the fundamental equation, SaturationP-p-T values, calculated from the estimating functions, were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Separate functions were used for the vapor pressure, saturated liquid density, saturated vapor density. ideal-gas heat capacity. and pressure on the melting curve, Comparisons between experimental data and values calculated using the fundamental equation are given to verify the accuracy of the formulation. The formulation given here may be used to calculate densities within ±0.1 %, heat capacities to within ±2 %. and speed of sound to within ± 1 %, except near the critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01441918
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  • 100
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    Vapor–Liquid Equilibrium of HFC-32/134a And HFC-125/134a Systems (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 519-530 
    Details
    ISSN: 1572-9567
    Keywords: activity coefficients ; binary interaction parameters ; equation of state ; fugacity coefficients ; HFC-32/134a mixture ; HFC-125/134a mixture ; thermodynamic consistency ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor-liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-32/134a and HFC-125/134a systems. Twenty-two equilibrium data are obtained for the HFC-32/134a system over the temperature range from 258.15 to 283.15 K at 5 K intervals and the composition range from 0.2 to 0.8 liquid mole fraction. Twenty-five equilibrium data are obtained for the HFC-125/134a system over the temperature range from 263.15 to 303.15 K at 10 K intervals and the composition range from 0.18 to 0.81 liquid mole friction. These data have been tested and found to be thermodynamically consistent. Based upon the present data, the binary interaction parameters of the Carnahan-Starling-De Santis (CSD) and Redlich–Kwong–Soave (RKS) equations of state are calculated for five isotherms for the HFC-125/134a mixture and six isotherms for the HFC-32/134a mixture. The calculated results from the CSD equation are compared with data in the open literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022605104490
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