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  • Articles  (38)
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  • stability  (20)
  • Turbulence  (18)
  • Springer  (38)
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  • 1995-1999  (38)
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  • 1999  (20)
  • 1997  (18)
  • Physics  (38)
  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    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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  • 9
    Electronic Resource
    Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004546215920
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  • 10
    Electronic Resource
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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 
    Details
    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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  • 11
    Electronic Resource
    Electronic Resource
    Optimization of Upstream Profiles in Modelled Flow Over Complex Terrain (1997)
    Springer
    Boundary layer meteorology 83 (1997), S. 285-309 
    Details
    ISSN: 1573-1472
    Keywords: Adjoint ; Data assimilation ; Turbulence ; Complex terrain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper describes an adjoint method for data assimilation intoupstream boundary conditions of numerical modelsusing optimal control theory. Mathematical formalisms are given along with the numerical implementation of the schemein a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solutionin a model of turbulent flow in complex terrain. To contrast thiswith other methods, two solutions for flow over an isolatedhill are calculated, one with an optimized upstream solution andone with a simple surface-layer formulation for the upstream solution.These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to producesolutions of flow in complex terrain that are substantively differentat the two solutions, with the optimized solution giving more accurate results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1000229609412
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  • 12
    Electronic Resource
    Electronic Resource
    Coherent eddies and temperature structure functions for three contrasting surfaces. Part II: Renewal model for sensible heat flux (1997)
    Springer
    Boundary layer meteorology 84 (1997), S. 125-147 
    Details
    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Renewal models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Sensible heat, latent heat, and other scalar fluxes cannot be measuredwithin short dense canopies, e.g., straw mulches, with standard approachessuch as eddy correlation, Bowen ratio-energy balance, aerodynamic, andvariance methods. However, recently developed surface renewal models, thatare based on the fact that most of the turbulent transfer within and abovecanopies is associated with large-scale coherent eddies, which are evidentas ramp patterns in scalar time series, offer a feasible solution. Wepresent a new air renewal model that calculates sensible heat flux atdifferent heights within and above a canopy from the average cubictemperature structure function, sampled at a moderate rate, and measuredaverage friction velocity. The model is calibrated and tested with datameasured above and within a Douglas-fir forest and above a straw mulch andbare soil. We show that the model describes half-hour variations ofsensible heat flux very well, both within the canopy and roughnesssublayers and in the inertial sublayer, for stable and unstable atmosphericconditions. The combined empirical coefficient that appears in the modelhas an apparently universal value of about 0.4 for all surfaces andheights, which makes application of the model particularly simple. Themodel is used to predict daytime and nighttime sensible heat flux profileswithin the straw mulch and within a small bare opening in the mulch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1000342918158
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  • 13
    Electronic Resource
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    Trajectory Curvature As A Selection Criterion For valid Lagrangian Stochastic Dispersion Models (1997)
    Springer
    Boundary layer meteorology 84 (1997), S. 411-425 
    Details
    ISSN: 1573-1472
    Keywords: Trajectories ; Turbulence ; Dispersion ; Diffusion ; Numerical models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce ‘spiralling trajectories,’ with an associated reduction in dispersion. We therefore investigate statistics of increments dθ ' to the orientation θ'= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. ‘Zero-spin’ models, having 〈 dθ'〉 = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1000474206967
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  • 14
    Electronic Resource
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    Turbulent mixing of reactive gases in the convective boundary layer (1997)
    Springer
    Boundary layer meteorology 85 (1997), S. 197-222 
    Details
    ISSN: 1573-1472
    Keywords: Turbulence ; Chemistry ; Closure ; Convective boundary layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯Θ, ¯w¯θ ¯θ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1000414710372
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  • 15
    Electronic Resource
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    Simulation of meteorological fields over a land-water-land terrain and comparison with observations (1999)
    Springer
    Boundary layer meteorology 91 (1999), S. 227-257 
    Details
    ISSN: 1573-1472
    Keywords: Coastal boundary layer ; Initialisation ; Mesoscale model ; Sea model breeze ; Thermal internal boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A numerical two-dimensional-mesoscale model with a level 1.5 closure scheme for turbulence is described. The model is used to simulate the boundary layer over coastal complex terrain. Meteorological data available from the Øresund land-sea-land terrain experiment are used to study the performance of the model. The model could simulate generally observed complexities in the mean wind and temperature fields. Internal boundary layers over the water and land surfaces were identified by the height of lowest value in the turbulence kinetic energy profile and this showed good agreement with radiosonde (RS) observations. Some disagreements with the data were also noticed, especially near the surface. The wind speed was over-predicted. Attempts were made to improve the model performance by adopting different schemes for model initialisation. Results showed that initialisation with an early model start time and observed wind profile near the inflow boundary improved the performance. The wind speed over-prediction could be further minimised by using a more realistic objective initialisation scheme. The problem centred around the proper estimation of the turbulent diffusion coefficient K through the closure scheme. Despite using the most popular empirical relationships in the level 1.5 closure scheme, these differences persisted. While this needs further investigation, the present model can be used to supply wind fields for practical purposes such as air pollution calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001886009260
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  • 16
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    The Effects of Probe-Induced Flow Distortion on Velocity Covariances: Field Observations (1999)
    Springer
    Boundary layer meteorology 91 (1999), S. 483-493 
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    ISSN: 1573-1472
    Keywords: Turbulence ; Flow distortion ; Sonic anemometers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We carried out measurements to test a simple theory of the effect of probe-induced flow distortion on turbulence measurements. We used two three-component sonic anemometers mounted 1.8m apart at a height of 6.7 m. Behind one was a horizontal circular cylinder of radius 0.15 m and length 1.2 m, chosen to model two-dimensional probe-induced flow distortion in the limit where the scale of the turbulence is very large compared to the scale of the probe. The second sonic anemometer measured the undistorted flow. The measured flow-distortion effects on the Reynolds shearing stress and the variances of streamwise and vertical velocity agree well with the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001868030313
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  • 17
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    Turbulence in a Katabatic Flow (1999)
    Springer
    Boundary layer meteorology 92 (1999), S. 37-63 
    Details
    ISSN: 1573-1472
    Keywords: Energy balance ; Glacier ; Katabatic flow ; Stable boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Turbulence measurements performed in a stable boundary layer over the sloping ice surface of the Vatnajökull in Iceland are described. The boundary layer, in which katabatic forces are stronger than the large-scale forces, has a structure that closely resembles that of a stable boundary layer overlying a flat land surface, although there are some important differences. In order to compare the two situations the set-up of the instruments on an ice cap in Iceland was reproduced on a flat grass surface at Cabauw, the Netherlands. Wind speed and temperature gradients were calculated and combined with flux measurements made with a sonic anemometer in order to obtain the local stability functions φm and φh as a function of the local stability parameter z/L. Unlike the situation at Cabauw, where φm was linear as a function of z/L, in the katabatically forced boundary layer, the dependence of φm on stability was found to be non-linear and related to the height of the wind maximum. Thermal stratification and the depth of the stable boundary layer however seem to be rather similar under these two different forcing conditions. Furthermore, measurements on the ice were used to construct the energy balance. These showed good agreement between observed melt and components contributing to the energy balance: net radiation (supplying 55% of the energy), sensible heat flux (30%) and latent heat flux (15%). Local sources and sinks in the turbulent kinetic energy budget are summed and indicate a reasonable balance in near-neutral conditions but not in more stable situations. The standard deviation of the velocity fluctuations σu, σv, and σw, can be scaled satisfactorily with the local friction velocity u* and the standard deviation of the temperature fluctuation σθ with the local temperature scale θ*.
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    URL: http://dx.doi.org/10.1023/A:1001744822857
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  • 18
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    Large-Scale Motions in the Marine Atmospheric Surface Layer (1999)
    Springer
    Boundary layer meteorology 92 (1999), S. 165-183 
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    ISSN: 1573-1472
    Keywords: Coherent structures ; Turbulence ; Surface layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Multi-level turbulent wind data from the Risø Air-Sea Experiments (RASEX) were used to examine the structure of large-scale motions in the marine atmospheric surface layer. The quadrant technique was used to identify flux events (ejections/sweeps). Ejections, which appear to occur in groups, are seen to occur first at the upper level, moving successively to lower levels with small time delays. A strong correlation between events at different heights suggests that they may all be part of a single large structure. Cross-correlation between velocity signals was used to estimate orientation of the structure using Taylor's hypothesis. The inclination of this structure is shallow (≃ 15°) near the surface and increases with height. Spatial representations of the fluctuating wind vectors show a structure that is strikingly similar to conceptual models of transverse vortices and shear layers seen in laboratory flows and direct numerical simulation (DNS) of low Reynolds number flows. Spatial visualization of velocity fluctuations during other time periods and conditions clearly shows the existence of shear layers, transverse vortices, plumes, and downdrafts of various sizes and strengths. A quantitative analysis shows an increase in the frequency of shear related events with increasing wind speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001837729368
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  • 19
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    Intercomparison of Three- and one-Dimensional Model Simulations and Aircraft Observations of Stratocumulus (1999)
    Springer
    Boundary layer meteorology 92 (1999), S. 453-487 
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    ISSN: 1573-1472
    Keywords: Closure models ; Drizzle ; Entrainment ; Large Eddy Simulation ; Observations ; Stratocumulus ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract As part of the EUropean Cloud REsolving Modelling (EUCREM) model intercomparison project we compared the properties and development of stratocumulus as revealed by actual observations and as derived from two types of models, namely three-dimensional Large Eddy Simulations (LES) and one-dimensional Single Column Models (SCMs). The turbulence, microphysical and radiation properties were obtained from observations made in solid stratocumulus during the third flight of the first 'Lagrangian' experiment of the Atlantic Stratocumulus Transition Experiment (ASTEX). The goal of the intercomparison was to study the turbulence and microphysical properties of a stratocumulus layer with specified initial and boundary conditions. The LES models predict an entrainment velocity which is significantly larger than estimated from observations. Because the observed value contains a large experimental uncertainty no definitive conclusions can be drawn from this. The LES modelled buoyancy flux agrees rather well with the observed values, which indicates that the intensity of the convection is modelled correctly. From LES it was concluded that the inclusion of drizzle had a small influence (about 10%) on the buoyancy flux. All SCMs predict a solid stratocumulus layer with the correct liquid water profile. However, the buoyancy flux profile is poorly represented in these models. From the comparison with observations it is clear that there is considerable uncertainty in the parametrization of drizzle in both SCM and LES.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1002006919256
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  • 20
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487196
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  • 21
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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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    URL: http://dx.doi.org/10.1007/BF02452490
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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 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02459172
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    Some dynamical properties of a viscoelastic cylindrical shell (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 233-240 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463847
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    Characterisation and Simulation of the Multiscaling Properties of the Energy-Containing Scales of Horizontal Surface-Layer Winds (1999)
    Springer
    Boundary layer meteorology 90 (1999), S. 21-46 
    Details
    ISSN: 1573-1472
    Keywords: Atmospheric surface layer ; Longitudinal velocity fluctuations ; Multifractals ; Spectra ; Statistical analysis ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The multiscaling statistics of atmospheric surface-layer winds at low wavenumbers above farmland and in the lee of a mountain range were examined using a hot-wire and lightweight cup anemometer. It was found that the horizontal velocity spectra could be broken into high and low-wavenumber regimes according to the parameters given by this analysis. The low-wavenumber end of the spectrum possessed a spectral slope parameter that varied between values of 0.8 and 1.35 at the farmland site during the period of the experiment, and the high-wavenumber end – corresponding to the inertial range – possessed a spectral slope slightly greater than -5/3. The larger values for this parameter for the low-wavenumber end appeared to coincide with unstable conditions. In the lee of the mountain range, the low-wavenumber spectral slope parameter was larger still, at 1.45. The low-wavenumber signals over farmland were much less intermittent than inertial-range signals, but in the lee of the mountain range the intermittency increased. From this analysis, it was shown that the statistical properties of the recorded wind signal could be reproduced using a bounded random multiplicative cascade. The model was successfully used to simulate the wind velocity field directly, rather than simulating the energy dissipation field. Since the spectral slope parameter for low wavenumbers appeared to be a function of atmospheric stability, the method presented is a simple way of generating wind signals characteristic of a variety of atmospheric conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001749126625
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    Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness (1999)
    Springer
    Boundary layer meteorology 92 (1999), S. 99-121 
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    ISSN: 1573-1472
    Keywords: Displacement height ; Ice surface roughness ; Katabatic flow ; Stable boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z0/h = 0.5λ with λ the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.
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    URL: http://dx.doi.org/10.1023/A:1001899015849
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    AN EVALUATION OF SEVERAL TURBULENCE SCHEMES FOR THE PREDICTION OF MEAN AND TURBULENT FIELDS IN COMPLEX TERRAIN (1997)
    Springer
    Boundary layer meteorology 83 (1997), S. 43-73 
    Details
    ISSN: 1573-1472
    Keywords: Model evaluation ; Mesoscale ; Turbulence ; Dispersion ; Convective boundary layer ; Complex terrain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A prognostic three-dimensional mesoscale model has been developed andused in one- and two-dimensional modes to evaluate ten local turbulenceclosure schemes. The schemes ranged from first-order to the two-equationprognostic schemes. Predictions by the models were compared for aone-dimensional convective boundary layer using mixed layer scaling andmeasurements to interpret the results. Two-dimensional simulations were alsoperformed for a sea-breeze flow and for flow over a hill. The results showedthat for all of the models considered, minor differences were produced in themean meteorological fields and in the vertical scalar fluxes, but majordifferences were apparent in the velocity variances and dissipation rate.Predicted tracer concentrations were very sensitive to the turbulence modelformulation for dispersion from a point source in the convective boundarylayer, particularly for the prediction of maximum concentrations. Predictedtracer concentrations from a surface volume source for the two-dimensionalsimulations were similar for all models, although the degree of mixing in themorning growth period produced some differences. Generally, good results forthe mean meteorological fields can be obtained with first-order schemes, evenif they underpredict the magnitude of turbulence in the convective boundarylayer, and reasonable tracer concentrations can also be obtained with thesemodels provided near-source effects are not important. The two-equationprognostic models performed best for the prediction of turbulence in theconvective boundary layer.
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    URL: http://dx.doi.org/10.1023/A:1000217722421
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    Non-local mixing of momentum in the convective boundary layer (1997)
    Springer
    Boundary layer meteorology 84 (1997), S. 1-22 
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    ISSN: 1573-1472
    Keywords: Large-eddy simulation ; Turbulence ; Non-local closure ; Convective boundary layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Recently Frech and Mahrt proposed a closure scheme which includes alarge-scale stress term to represent the effects of non-local momentummixing in the convective boundary layer. Here large-eddy simulation (LES)datasets are used to evaluate the performance of this scheme across a rangeof stabilities between neutral and highly convective conditions, and as afunction of baroclinity. Generally the inclusion of the non-local term inthe closure model leads to results in better agreement with LES, althoughsome modifications to the model formulation are suggested.
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    URL: http://dx.doi.org/10.1023/A:1000388830859
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    A Three-Dimensional Correlation/Spectral Model for Turbulent Velocities in a Convective Boundary Layer (1997)
    Springer
    Boundary layer meteorology 85 (1997), S. 35-52 
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    ISSN: 1573-1472
    Keywords: Turbulence ; Atmospheric convective boundary layer ; Correlation function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKármán's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.
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    URL: http://dx.doi.org/10.1023/A:1000418709945
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    Steps, Waves and Turbulence in the Stably Stratified Planetary Boundary Layer (1999)
    Springer
    Boundary layer meteorology 90 (1999), S. 397-421 
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    ISSN: 1573-1472
    Keywords: Gravity waves ; Planetary boundary layer ; Turbulence ; Wind structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The stably-stratified planetary boundary layer contains small-vertical-scale, step-like structures, waves on a multitude of scales, large horizontal eddies and small-scale turbulence, all of which constantly interact with, and modify, one another. Current knowledge of how the various components act in the vicinity of the step-like structures is surveyed. It is concluded that packets of internal waves are the main conduit for interaction within and across the boundary layer, and low-intensity critical-level absorption at the fringes of their spectrum probably maintains the step-like structures. Further investigation of the processes requires intensive observations of the four-dimensional structure of the region, but such an investigation will need a new generation of high-resolution sensing systems.
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    URL: http://dx.doi.org/10.1023/A:1001709029773
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    Nonlocal Turbulent Mixing Based on Convective Adjustment Concepts (Ntac) (1999)
    Springer
    Boundary layer meteorology 92 (1999), S. 263-291 
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    ISSN: 1573-1472
    Keywords: Convective adjustment ; Turbulence ; Mixing ; Nonlocal mixing ; Parameterization ; Numerical weather prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A nonlocal turbulent mixing parameterization is introduced in this study and denoted by the acronym NTAC, which stands for Nonlocal parameterization of Turbulent mixing using convective Adjustment Concepts. NTAC uses the average value of quantities in the turbulent domain in much the same way that local convective adjustment schemes use the average potential temperature. Averages are determined in the region with non-convective turbulence using information from the two end layers (denoted by TLA, Two Layer Average), while all layers contribute to the average in regions with convective turbulence (denoted by CLA, Convective Layer Average). The NTAC parameterization estimates the mixing percentage and uses this percentage as a mixing coefficient. These percentages are determined from a simplified turbulent kinetic energy equation. The scheme is versatile, conservative, and when programmed efficiently the proposed parameterization is a computationally acceptable nonlocal procedure that can be used in many existing numerical weather prediction forecast models. Numerical weather forecast model simulations using the NTAC parameterization and traditional K-theory are compared against radiosonde data. The accuracy of the proposed NTAC parameterization is found to be competitive with K theory. The greatest improvement of the NTAC over K-theory occurs during the daytime and early nighttime hours when (dry) convective activity is high. Also, areal cloud coverage is increased by the NTAC parameterization. Our findings show that the greatest nonlocal vertical mixing occurs between the layer nearest the earth's surface and the remaining layers making up the planetary boundary layer.
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    URL: http://dx.doi.org/10.1023/A:1002029909587
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    Multiresolution Flux Decomposition (1997)
    Springer
    Boundary layer meteorology 83 (1997), S. 117-137 
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    ISSN: 1573-1472
    Keywords: Reynolds averaging ; Turbulence ; Time series ; Cospectra ; Sampling error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Geophysical variables are orthogonally decomposed by averaging timeseries using different averaging lengths, referred to as a (Haar)multiresolution decomposition. This simple and economic decomposition isassociated with cospectra that formally satisfy Reynolds averaging rules foreach averaging length. The multiresolution decomposition provides a naturalestimate of the random error in estimating a mean turbulent flux. The Fourierand multiresolution decompositions are compared using aircraft data fromBOREAS.
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    URL: http://dx.doi.org/10.1023/A:1000210427798
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    Coherent eddies and temperature structure functions for three contrasting surfaces. Part I: Ramp model with finite microfront time (1997)
    Springer
    Boundary layer meteorology 84 (1997), S. 99-124 
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    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Structure functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Air temperature time series within and above canopies reveal ramp patternsassociated with coherent eddies that are responsible for most of thevertical transport of sensible heat. Van Atta used a simple step-changeramp model to analyse the coherent part of air temperature structurefunctions. However, his ocean data, and our own measurements for aDouglas-fir forest, straw mulch, and bare soil, reveal that even withoutlinearization his model cannot account for the observed decrease of thecubic structure function for small time lag. We found that a ramp model inwhich the rapid change at the end of the ramp occurs in a finite microfronttime can describe this decrease very well, and predict at least relativemagnitudes of microfront times between different surfaces. Averagerecurrence time for ramps, determined by analysis of the cubic structurefunction with the new ramp model, agreed well with values determined usingthe Mexican Hat wavelet transform, except at lower levels within theforest. Ramp frequency above the forest and mulch scaled very well withwind speed at the canopy top divided by canopy height. Within the forest,ramp frequency did not vary systematically with height. This is inaccordance with the idea that large-scale canopy turbulence is mostlygenerated by instability of the mean canopy wind profile, similar to aplane mixing layer. The straw mulch and bare soil experiments uniquelyextend measurements of temperature structure functions and ramp frequencyto the smallest scales possible in the field.
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    URL: http://dx.doi.org/10.1023/A:1000338817250
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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 
    Details
    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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    Stability of viscoelastic flow around periodic arrays of cylinders (1997)
    Springer
    Rheologica acta 36 (1997), S. 367-383 
    Details
    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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    A reaction-diffusion equation for a cyclic system with three components (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1145-1164 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF02181277
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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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    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.
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    URL: http://dx.doi.org/10.1023/A:1007423306486
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