Showing papers on "Dissipative system published in 1997"
Book•
04 Dec 1997
TL;DR: 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states.
Abstract: 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states Appendices Selected bibliography Index 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states Appendices Selected bibliography Index
732 citations
TL;DR: In this paper, a simple new zonal boundary condition has been proposed based upon the addition of dissipative and convective terms to the compressible Navier Stokes equations, which is based upon a simple addition of convective and dissipative terms.
Abstract: A simple new zonal boundary condition has been proposed. It is based upon the addition of dissipative and convective terms to the compressible Navier Stokes equations
374 citations
TL;DR: In this paper, the algebraically simplest example of a dissipative chaotic flow, x + A x − x 2 + x = 0, was found for third-order, autonomous ODEs with one dependent variable.
251 citations
TL;DR: In this article, a generalization of DPD that incorporates an internal energy and a temperature variable for each particle is presented, which can be viewed as a simplified solver of the fluctuating hydrodynamic equations and opens up the possibility of studying thermal processes in complex fluids with mesoscopic simulation technique.
Abstract: Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature variable for each particle. The dissipation induced by the dissipative forces between particles is invested in raising the internal energy of the particles. Thermal conduction occurs by means of (inverse) temperature differences. The model can be viewed as a simplified solver of the fluctuating hydrodynamic equations and opens up the possibility of studying thermal processes in complex fluids with a mesoscopic simulation technique.
251 citations
TL;DR: In this article, a review of the microcanonical approach to thermodynamics is presented, with a focus on hot nuclei, hot atomic clusters, and gravitating systems, and their applications in physics.
232 citations
TL;DR: In this paper, a fast explicit symplectic-reversible integrators for multiple rigid body molecular simulations is described, which uses a reduction to Euler equations for the free rigid body, together with a symplectic splitting technique.
Abstract: Rigid body molecular models possess symplectic structure and time-reversal symmetry. Standard numerical integration methods destroy both properties, introducing nonphysical dynamical behavior such as numerically induced dissipative states and drift in the energy during long term simulations. This article describes the construction, implementation, and practical application of fast explicit symplectic-reversible integrators for multiple rigid body molecular simulations. These methods use a reduction to Euler equations for the free rigid body, together with a symplectic splitting technique. In every time step, the orientational dynamics of each rigid body is integrated by a sequence of planar rotations. Besides preserving the symplectic and reversible structures of the flow, this scheme accurately conserves the total angular momentum of a system of interacting rigid bodies. Excellent energy conservation can be obtained relative to traditional methods, especially in long-time simulations. The method is implemented in a research code, ORIENT, and compared with a quaternion/extrapolation scheme for the TIP4P model of water. Our experiments show that the symplectic-reversible scheme is far superior to the more traditional quaternion method.
232 citations
TL;DR: In this paper, a generalization of DPD that incorporates an internal energy and a temperature variable for each particle is presented, which can be viewed as a simplified solver of the fluctuating hydrodynamic equations and opens up the possibility of studying thermal processes in complex fluids with mesoscopic simulation technique.
Abstract: Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature variable for each particle. The dissipation induced by the dissipative forces between particles is invested in raising the internal energy of the particles. Thermal conduction occurs by means of (inverse) temperature differences. The model can be viewed as a simplified solver of the fluctuating hydrodynamic equations and opens up the possibility of studying thermal processes in complex fluids with a mesoscopic simulation technique.
230 citations
TL;DR: In this paper, the dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation, where the Liouville operator and associated binary scattering operators are defined as the generators for time evolution in phase space.
Abstract: The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.
180 citations
TL;DR: In this paper, it was shown that in general there is no exact dissipative Liouville operator that describes the dynamics of the oscillator for arbitrary initial bath preparations, and that there are approximate Liouve operator independent of the initial bath preparation describing the long-time dynamics under appropriate conditions.
Abstract: Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact nonstationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long-time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude, and weak coupling cases. The connection with earlier work is discussed.
163 citations
TL;DR: In this paper, a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level is presented. But the choice of time step and imposition of boundary conditions are discussed.
Abstract: We report on details of a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level. We develop frame-invariant and linear viscous interactions between pairs of translating and rotating spheres in a form suitable for computation. We report an o(N) method for generating Brownian forces correlated with a pair resistance tensor and show how explicit finite difference schemes lead naturally to an algorithm with Brownian motion and an estimate of the Brownian stress. We justify the algorithm by appeal to the second-order Langevin equation. We discuss the choice of time step and imposition of boundary conditions. We assess a model of this kind as an approximation for colloid spheres concentrated in a fluid medium under shear flow. It is noted that the algorithm is also that required for simulation, in the diffusive limit, of a technique known as dissipative particle dynamics. We report on structural effects in Brownian sphere colloids and their sensitivity to the model details. We argue that the approximation has heuristic value in the study of the rheology in concentrated colloid systems. Its predictions for the rheology of suspensions are in semi-quantitative agreement with experiment.
162 citations
TL;DR: In this article, the authors considered a system of balance laws compatible with an entropy principle and convex entropy density, and they defined the concept of principal subsystem associated with the system and proved that the 2 − 2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law.
Abstract: We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2
N
−2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases.
TL;DR: In this paper, two different Markovian approaches to the quantum dynamics of a periodically driven harmonic oscillator with dissipation were studied, and an improved master equation was achieved by treating the entire driven system within the Floquet formalism and coupling the reservoir as a whole.
Abstract: Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain the periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a nonunitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures.
TL;DR: In this article, the relaxation theory of an ideal magnetofluid is developed for a multispecie magnet ofluid, and its invariants are the self-helicities, one for each specie.
Abstract: The relaxation theory of an ideal magnetofluid is developed for a multispecie magnetofluid. Its invariants are the self-helicities, one for each specie. Their ``local'' invariance in the ideal case follows from the helicity transport equation. The global forms of the self-helicities are investigated for a two-fluid (ion and electron), and their ruggedness in a weakly dissipative system is defended by cascade and selective decay arguments. In general the two-fluid theory predicts relaxed states with finite pressure and sheared flows. The familiar single-fluid relaxation theory, which admits only force-free states, is a reduced case of the present more general theory.
TL;DR: In this paper, the authors address the issue of spatially localized periodic oscillations in coupled networks and deduce existence of discrete breathers in networks where each site has an equilibrium and some sites have a limit cycle and in Hamiltonian networks without requiring local anharmonicity.
Abstract: We address the issue of spatially localized periodic oscillations in coupled networks - so-called discrete breathers - in a general context. This context is concerned with general conditions which allow continuation of periodic solutions of vector fields. One advantage of our approach is to encompass in the same mathematical framework the cases of conservative and dissipative systems. An essential feature is that we allow the period to vary. In particular, we deduce existence of discrete breathers in networks where each site has an equilibrium and some sites have a limit cycle, and in Hamiltonian networks without requiring local anharmonicity. The latter case is dealt with by considering the persistence of families of periodic solutions in the more general context of systems with an integral, not just Hamiltonian ones.
TL;DR: In this article, a transport theory for collective motion of an atomic nucleus is developed, which may be considered as a typical representative of a self-bound micro-system, where collective variables are introduced as shape parameters, self-consistency with respect to the nucleonic degrees of freedom has been implemented at various important stages.
TL;DR: This work shows that the long-time behavior of the projection of the exact solutions to the Navier-Stokes equations and other dissipative evolution equations on the finite-dimensional space of interpolant polynomials determines theLong-time Behavior of the solution itself provided that the spatial mesh is fine enough.
Abstract: We show that the long-time behavior of the projection of the exact solutions to the Navier-Stokes equations and other dissipative evolution equations on the finite-dimensional space of interpolant polynomials determines the long-time behavior of the solution itself provided that the spatial mesh is fine enough. We also provide an explicit estimate on the size of the mesh. Moreover, we show that if the evolution equation has an inertial manifold, then the dynamics of the evolution equation is equivalent to the dynamics of the projection of the solutions on the finite-dimensional space spanned by the approximating polynomials. Our results suggest that certain numerical schemes may capture the essential dynamics of the underlying evolution equation.
TL;DR: In this paper, a Fortran program is described which calculates the reduced density matrix of a one-dimensional quantum mechanical continuous or discrete system coupled to a harmonic dissipative environment, based on Feynman's path integral formulation of time-dependent quantum mechanics.
TL;DR: In this article, a thermodynamically consistent theory of gradient-regularized plasticity with coupling to isotropic damage is presented, which describes the successive development of the localization zone that is pertinent to the softening regime due to excessive damage close to failure.
TL;DR: In this article, the authors used the algorithm for dissipative particle dynamics (DPD) as a starting point for proving an H-theorem for the free energy and deriving hydrodynamic equations.
Abstract: The algorithm for Dissipative Particle Dynamics (DPD), as modified by Espanol and Warren, is used as a starting point for proving an H-theorem for the free energy and deriving hydrodynamic equations. Equilibrium and transport properties of the DPD fluid are explicitly calculated in terms of the system parameters for the continuous time version of the model.
TL;DR: In this paper, the Dirichlet boundary conditions were considered for coupled nonlinear oscillators with external periodic forces and it was shown that synchronization occurs provided that the coupling is dissipative and the coupling coefficients are sufficiently large.
Book•
15 Oct 1997
TL;DR: In this article, a strategy for Structural-Acoustic problems is proposed for solving structural-acoustic problems, based on Variational Formulations of Variational Variational Functions for the Master Structure.
Abstract: A Strategy for Structural-Acoustic Problems. Basic Notions on Variational Formulations. Linearized Vibrations of Conservative Structures and Structural Modes. Dissipative Constitutive Equation for the Master Structure. Master Structure Frequency Response Function. Calculation of the Master Structure Frequency Response function in the LF Range. Calculation of the Master Structure Frequency Response Function in the MF Range. Reduced Model in the MF Range. Response to Deterministic and Random Excitations. Linear Acoustic Equations. Internal Acoustic Fluid Formulation for the LF and MF Ranges. External Acoustic Fluid: Boundary Integral Formulation for the LF and MF Ranges. Structural-Acoustic Master System in the LF Range. Structural-Acoustic Master System in the MF Range. Fuzzy Structure Theory. Appendix: Mathematical Notations. References. Subject Index. Symbol Index.
TL;DR: In this paper, the authors investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description.
Abstract: We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, equivalent to the usual density perturbations, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viscous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases. A companion paper uses the general formalism to analyze damping of density perturbations before last scattering.
TL;DR: In this paper, the authors reported experimental observation of a localized structure, which is of a new type for dissipative systems, appearing as a solitary vortex pair (diwhirl) in Couette flow with highly elastic polymer solutions.
Abstract: We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex pair (``diwhirl'') in Couette flow with highly elastic polymer solutions. In contrast to the usual solitons the diwhirls are stationary. It is also a new object in fluid dynamics---a pair of vortices that build a single entity. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect.
TL;DR: In this article, a fully nonlinear, diffusive, and weakly dispersive wave equation is derived for describing gravity surface wave propagation in a shallow porous medium, where Darcy's flow is assumed in a homogeneous and isotropic porous medium.
Abstract: A fully nonlinear, diffusive, and weakly dispersive wave equation is derived for describing gravity surface wave propagation in a shallow porous medium. Darcy's flow is assumed in a homogeneous and isotropic porous medium. In deriving the general equation, the depth of the porous medium is assumed to be small in comparison with the horizontal length scale, i.e. O(μ2) =O(h0/L)2[Lt ]1. The order of magnitude of accuracy of the general equation is O(μ4). Simplified governing equations are also obtained for the situation where the magnitude of the free-surface fluctuations is also small, O(e)=O(a/h0)[Lt ]1, and is of the same order of magnitude as O(μ2). The resulting equation is of O(μ4, e2) and is equivalent to the Boussinesq equations for water waves. Because of the dissipative nature of the porous medium flow, the damping rate of the surface wave is of the same order magnitude as the wavenumber. The tide-induced groundwater fluctuations are investigated by using the newly derived equation. Perturbation solutions as well as numerical solutions are obtained. These solutions compare very well with experimental data. The interactions between a solitary wave and a rectangular porous breakwater are then examined by solving the Boussinesq equations and the newly derived equations together. Numerical solutions for transmitted waves for different porous breakwaters are obtained and compared with experimental data. Excellent agreement is observed.
TL;DR: In this article, the authors considered the Cauchy problem of coupled dissipative Klein-Gordon-Schrodinger equations in R 3 and proved the existence of the maximal attractor.
TL;DR: In this article, a numerical study using the multi-state quantum Fokker-Planck equation for a colored Gaussian-Markovian noise bath, which was expressed as a hierarchy of kinetic equations, was performed.
Abstract: Quantum coherence and its dephasing by coupling to a dissipative environment play an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions in the condensed phase. We have discussed nonlinear optical processes on a multi-state one-dimensional system with Morse potential surfaces in a dissipative environment. This was based on a numerical study using the multi-state quantum Fokker–Planck equation for a colored Gaussian–Markovian noise bath, which was expressed as a hierarchy of kinetic equations. This equation can treat strong system-bath interactions at a low temperature heat bath, where quantum effects play a major role. The approach applies to linear absorption measurements as well as four-wave mixing including pump-probe spectroscopy. Laser induced photodissociation and predissociation have been studied for the potential surfaces of Cs2. We have calculated nuclear wave packets in Wigner representation and their monitoring by femtosecond pump-probe spectroscopy for various displacements of potentials and heat-bath parameters. Numerical calculations of probe absorption spectra for strong pump pulse are also presented and discussed. The results show dynamical Stark splitting, but, in contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperature their peaks have different heights even when the pump pulse is on resonance.
TL;DR: In this paper, the authors established global well-posedness for the initial value problem associated to the so-called Benney-Lin equation, a Korteweg-de Vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics.
TL;DR: In this paper, an exact Navier-Stokes equation is derived for the linear evolution of the surface of a viscous fluid, and this equation becomes local and of second order in an interesting limit.
Abstract: We derive an exact equation which is nonlocal in time for the linear evolution of the surface of a viscous fluid, and show that this equation becomes local and of second order in an interesting limit. We use our local equation to study Faraday's instability in a strongly dissipative regime and find a new scenario which is the analog of the Rayleigh-Taylor instability. Analytic and numerical calculations are presented for the threshold of the forcing and for the most unstable mode with impressive agreement with experiments and numerical work on the exact Navier-Stokes equations.