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  • Articles  (59)
  • stability  (59)
  • Springer  (59)
  • American Geophysical Union (AGU)
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  • Institute of Physics
  • 1995-1999  (52)
  • 1980-1984  (7)
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  • Physics  (59)
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  • Articles  (59)
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  • Springer  (59)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • Institute of Physics
  • Wiley-Blackwell  (7)
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  • 1
    Electronic Resource
    Electronic Resource
    Three-dimensional disturbances of planar viscometric flow (1983)
    Springer
    Rheologica acta 22 (1983), S. 284-290 
    Details
    ISSN: 1435-1528
    Keywords: Viscometric flow ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01359128
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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
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    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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  • 10
    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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  • 11
    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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  • 12
    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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  • 13
    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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  • 14
    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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  • 15
    Electronic Resource
    Electronic Resource
    A stability investigation for an incompressible simple fluid with fading memory (1980)
    Springer
    Archive for rational mechanics and analysis 72 (1980), S. 203-218 
    Details
    ISSN: 1432-0673
    Keywords: simple fluid ; viscoelastic ; fading memory ; stability ; Liapunov function ; dynamical system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the “finitelinear” viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281589
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  • 16
    Electronic Resource
    Electronic Resource
    Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems II. Bose-Einstein and Fermi-Dirac statistics (1980)
    Springer
    Journal of statistical physics 23 (1980), S. 701-753 
    Details
    ISSN: 1572-9613
    Keywords: Correlation inequalities ; classical and quantum continuous systems ; positive type potentials ; stability ; thermodynamic limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study quantum mechanical systems of particles with Bose or Fermi statistics interacting via two-body potentials of positive type in thermal equilibrium. We rewrite partition functions, reduced density matrices (RDMs), and correlation functions in terms of Wiener and Gaussian functional integrals (sine-Gordon transformation). This permits us, e.g., to apply correlation inequalities. Our main results include an analysis of stability versus instability in the grand canonical ensemble and, for charge-conjugation-invariant systems, upper and lower bounds on RDMs, the existence of the thermodynamic limit of pressure, RDMs and correlation functions, an inequality comparing correlations with Fermi statistics to ones with Bose statistics, and inequalities which are important in the study of Bose-Einstein condensation and of superconductivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008516
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  • 17
    Electronic Resource
    Electronic Resource
    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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  • 18
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    Electronic Resource
    Renormalization of the Chapman–Enskog Expansion: Isothermal Fluid Flow and Rosenau Saturation (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 285-305 
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    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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  • 19
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    Classical Lattice-Gas Models of Quasicrystals (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 835-850 
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    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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  • 20
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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 
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    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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  • 21
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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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  • 22
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050557
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  • 23
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212907
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  • 24
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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 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF00194708
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    The breakup and atomization of a viscous liquid jet (1996)
    Springer
    Acta mechanica Sinica 12 (1996), S. 124-134 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02486791
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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 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02487763
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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 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02487196
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    The stability of viscous liquid jets in a swirling gas (1998)
    Springer
    Acta mechanica Sinica 14 (1998), S. 226-233 
    Details
    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 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02451459
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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)
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    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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    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)
    Springer
    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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    Behaviour of double emulsions in shear flows (1982)
    Springer
    Rheologica acta 21 (1982), S. 593-597 
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    ISSN: 1435-1528
    Keywords: Shear deformation ; stability ; heterogeneous drop ; liquid membrane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The stability behaviour of heterogeneous drops indicates that, for liquid-liquid dispersions, we may have to modify the stability criterion to incorporate either the rheological characteristics of the dispersion or its cohesion or both.
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    Rheology of coal suspensions (1983)
    Springer
    Rheologica acta 22 (1983), S. 500-504 
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    ISSN: 1435-1528
    Keywords: Coal suspension ; shear dependence ; solid phase concentration ; dispersing medium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Proper design of operations encountered in preparation, transport and employment of suspensions like coal slurries and coal-oil mixtures require an accurate knowledge of their rheological behaviour. Such concentrated suspensions generally exhibit non-Newtonian behaviour (shearthinning) which is more pronounced at higher coal concentrations. The nature of the dispersing medium influences the aggregation state of the disperse phase and, consequently, affects the stability and the rheology of the systems. In the present paper coal suspensions prepared with different dispersing media and covering a wide range in solid phase concentration are studied, by using a rotational coaxial cylinders viscometer. Different models have been taken into consideration for correlating experimental data. In particular, in order to describe the dependence of viscosity on shear rate and solid phase concentration, the suitability of the model suggested by Smith and Bruce is evaluated. Accordingly, the aggregation state of the disperse phase as well as its dependence on shear rate and dispersing medium can be estimated.
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    URL: http://dx.doi.org/10.1007/BF01462937
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    On stable spherical configurations of artificial protocells (1995)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00700439
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    Ising-like field theory (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 143-152 
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    ISSN: 1572-9613
    Keywords: Ising model ; field theory model ; stability ; pressure ; ultraviolet divergence ; infrared divergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A field theory model onR 2 in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in λ of the ground state energy, as λ→0, without using the cluster expansion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008483
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    Equal-time second-order moments of a harmonic oscillator with stochastic frequency and driving force (1980)
    Springer
    Journal of statistical physics 23 (1980), S. 755-765 
    Details
    ISSN: 1572-9613
    Keywords: Harmonic oscillator ; stochastic frequency ; stochastic differential equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using a simple matrix method, we have obtained exact second-order equilibrium moments for a linearly damped harmonic oscillator with a fluctuating frequency ω(t) and driven by a fluctuating forcef(t). We have assumed each of the fluctuating quantities to be delta-correlated. We demonstrate that the final answers are identical whetherf(t) and ω(t) are statistically independent or delta-correlated. We have also established the region of parameter space in which the oscillator is energetically stable. The results are shown to be completely determined by the coefficients of the first and second cumulants of the fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008517
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    A reaction-diffusion equation for a cyclic system with three components (1997)
    Springer
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181277
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  • 50
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    Small-Angle Neutron Scattering Studies of Vesicle Stability (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 461-470 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022517511951
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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 
    Details
    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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    Lagrange's theorem for a class of nonholonomic systems and its application (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 135-146 
    Details
    ISSN: 1573-2754
    Keywords: nonholonomic system ; Lagrange's theorem ; manifold ; stability ; Liapunov's direct method
    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 problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied in this paper. Based on Liapunov's direct method and the definition of stability. Lagrange's theorem of holonomic systems is extended to a class of nonholonomic conservative systems and dissipative systems, and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces. Two examples are finally given to illustrate the application of the theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02457681
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    The variational principle of thin shell in stability (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 1161-1169 
    Details
    ISSN: 1573-2754
    Keywords: shell ; stability ; critical load
    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 This paper gives the resultant forces and moments, strain energy and work of external forces on the basis of the deformation theory of flexible body. Therefore, in accordance with the principle of virtual displacement, the energy criterion of critical load is obtained and the equilibrium equation and boundary conditions of stability problem are derived.
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    URL: http://dx.doi.org/10.1007/BF02466986
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    Codimension two bifurcations and hopf bifurcations of an impacting vibrating system (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 65-75 
    Details
    ISSN: 1573-2754
    Keywords: impacting vibration ; stability ; codimension two bifurcation
    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 Bifurcation problems of a spring-mass system vibrating against an infinite large plane are studied in this paper. It is shown that there exist phenomena of codimension two bifurcations when the ratios of frequencies are in the neigborhood of the same special values and the coefficient of restitution approach unity. By theory of normal forms, we reduce Poincare maps to normal forms, and find flip bifurcations, Hopf bifurcations of fixed points and that of period two points. The theoretical solutions are verified by numerical computations.
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    URL: http://dx.doi.org/10.1007/BF00131296
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    On the boundedness and the stability results for the solution of certain fourth order differential equations via the intrinsic method (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 1039-1049 
    Details
    ISSN: 1573-2754
    Keywords: nonlinear differential equations of the fourth order ; Lyapunov function ; stability ; boundedness ; intrinsic method
    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, we first present constructing a Lyapunov function for (1.1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡0, and the boundedness result of the solutions of (1.1) for case p≠0. These results improve several well-known results.
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    URL: http://dx.doi.org/10.1007/BF00119951
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    Equilibrium stability of generalized Birkhoff's autonomous system (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 564-567 
    Details
    ISSN: 1573-2754
    Keywords: generalized Birkhoff's system ; equilibrium state ; 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, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and then the linear approximate method and direct method of stability in equilibrium state are studied. Some results on equilibrium of generalized Birkhoff's autonomous system are obtained on the basis of Lyapunov's thorem. Last, the application of the results is illustrated with an example.
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    URL: http://dx.doi.org/10.1007/BF02463754
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    Remarks on the Instability of an Incompressible and Isotropic Hyperelastic, Thick-Walled Cylindrical Tube (1997)
    Springer
    Journal of elasticity 48 (1997), S. 218-239 
    Details
    ISSN: 1573-2681
    Keywords: stability ; nonlinear elasticity ; Mooney-Rivlin material ; incompressible material ; thick-walled tube
    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 problem of instability of a hyperelastic, thick-walled cylindrical tube was first studied by Wilkes [1] in 1955. The solution was formulated within the framework of the theory of small deformations superimposed on large homogeneous deformations for the general class of incompressible, isotropic materials; and results for axially symmetrical buckling were obtained for the neo-Hookean material. The solution involves a certain quadratic equation whose characteristic roots depend on the material response functions. For the neo-Hookean material these roots always are positive. In fact, here we show for the more general Mooney–Rivlin material that these roots always are positive, provided the empirical inequalities hold. In a recent study [2] of this problem for a class of internally constrained compressible materials, it is observed that these characteristic roots may be real-valued, pure imaginary, or complex-valued. The similarity of the analytical structure of the two problems, however, is most striking; and this similarity leads one to question possible complex-valued solutions for the incompressible case. Some remarks on this issue will be presented and some new results will be reported, including additional results for both the neo-Hookean and Mooney–Rivlin materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007423306486
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    On the Stability of Thermoelastic Materials (1998)
    Springer
    Journal of elasticity 53 (1998), S. 199-213 
    Details
    ISSN: 1573-2681
    Keywords: thermoelasticity ; stability ; strong ellipticity.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A notion of material stability is introduced and discussed in the setting of nonlinear thermoelasticity. Necessary and sufficient conditions are established for the stability of a general thermoelastic material. The adiabatic theory and the theory that accounts for heat conduction are considered separately.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007513631783
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    Stability of elastic bodies with nonmonotone multivalued boundary conditions of the quasidifferential type (1995)
    Springer
    Journal of elasticity 41 (1995), S. 137-149 
    Details
    ISSN: 1573-2681
    Keywords: stability ; eigenvalue inequalities ; nonsmooth eigenvalue problems ; 35A15 ; 35R35 ; 73K20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Necessary conditions for the stability of elastic bodies subjected to nonmonotone multivalued boundary conditions are derived. These conditions are assumed to be derived from nonconvex and nonsmooth, quasidifferentiable energy functions. A ‘difference convex’ approximation of the potential energy function is written based on an appropriate quasidifferential formulation. Under appropriate assumptions for the convex and the concave parts we prove the existence of at least one nontrivial solution to the nonlinear eigenvalue problem.
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    URL: http://dx.doi.org/10.1007/BF00042511
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