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Showing papers on "Dissipative system published in 2002"


Journal ArticleDOI
TL;DR: A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented in this paper, which elucidates the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics.
Abstract: A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field.

273 citations



Proceedings ArticleDOI
12 May 2002
TL;DR: A dissipative particle swarm optimization is developed according to the self-organization of dissipative structure where the negative entropy is introduced to construct an opening dissipative system that is far-from-equilibrium so as to driving the irreversible evolution process with better fitness.
Abstract: A dissipative particle swarm optimization is developed according to the self-organization of dissipative structure The negative entropy is introduced to construct an opening dissipative system that is far-from-equilibrium so as to driving the irreversible evolution process with better fitness The testing of two multimodal functions indicates it improves the performance effectively

265 citations


Journal ArticleDOI
TL;DR: In this paper, large-eddy simulations of spatially developing planar turbulent jets are performed using a compact finite-difference scheme of sixth-order and an advective upstream splitting method-based method of second-order accuracy.

264 citations


Journal ArticleDOI
TL;DR: In this paper, the steady state of an ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement, and the authors conjecture that this is a general mechanism for entangler creation in driven dissipative quantum systems.
Abstract: We model the behavior of an ion trap with all ions driven simultaneously and coupled collectively to a heat bath. The equations for this system are similar to the irreversible dynamics of a collective angular momentum system known as the Dicke model. We show how the steady state of the ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement. We calculate the entanglement of this steady state for two ions in the trap and in the case of more than two ions we calculate the entanglement between two ions by tracing over all the other ions. The entanglement in the steady state is a maximum for the parameter values corresponding roughly to a bifurcation of a fixed point in the corresponding semiclassical dynamics. We conjecture that this is a general mechanism for entanglement creation in driven dissipative quantum systems.

236 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered nonlinear systems of Timoshenko type in a one-dimensional bounded domain with a dissipative mechanism being present only in the equation for the rotation angle; it is a damping effect through heat conduction.

233 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the Navier-Stokes equations possess an exponentially attracting invariant measure, which is in fact the consequence of a more general ''Harris-like'' ergodic theorem applicable to many dissipative stochastic PDEs and processes with memory.
Abstract: We prove that the two dimensional Navier-Stokes equations possess an exponentially attracting invariant measure. This result is in fact the consequence of a more general ``Harris-like'' ergodic theorem applicable to many dissipative stochastic PDEs and stochastic processes with memory. A simple iterated map example is also presented to help build intuition and showcase the central ideas in a less encumbered setting. To analyze the iterated map, a general ``Doeblin-like'' theorem is proven. One of the main features of this paper is the novel coupling construction used to examine the ergodic theory of the non-Markovian processes.

197 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the path integral method yields the exact quantum theory of the Caldirola-Kanai Hamiltonian without violation of Heisenberg's uncertainty principle.

196 citations


Journal ArticleDOI
TL;DR: The Müller-Israel-Stewart second-order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultrarelativistic heavy-ion collisions.
Abstract: The Muller-Israel-Stewart second-order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultrarelativistic heavy-ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.

192 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method with special focus on the role played by the $H$ theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.
Abstract: In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics of complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one essential requirement is compliance with the second law of thermodynamics. In this Colloquium, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method, with special focus on the role played by the $H$ theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.

177 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations and find that the best overall performance is for integrators in which the velocity dependence of dissipative forces is taken into account, and particularly good performance is found for an approach in which velocities and dissipative force are determined self-consistently.
Abstract: We examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often studied in simulations. Specifically, we clarify the performance of integration schemes in hybrid models, which combine microscopic and mesoscale descriptions of different particles using both soft and hard interactions. We find that in all three model systems many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient. The artifacts are found to be strongest in systems, where interparticle interactions are soft and predominated by random and dissipative forces, while in systems governed by conservative interactions the artifacts are weaker. Our results suggest that the quality of any integration scheme employed is crucial in all cases where the role of random and dissipative forces is important, including hybrid models where the solvent is described in terms of soft potentials. Regarding the integration schemes, the best overall performance is found for integrators in which the velocity dependence of dissipative forces is taken into account, and particularly good performance is found for an approach in which velocities and dissipative forces are determined self-consistently. Remaining temperature deviations from the desired limit can be corrected by carrying out the self-consistent integration in conjunction with an auxiliary thermostat, in a manner that is similar in spirit to the well-known Nose–Hoover thermostat. Further, we show that conservative interactions can play a significant role in describing the transport properties of simple fluids, in contrast to approximations often made in deriving analytical theories. In general, our results illustrate the main problems associated with simulation methods in which dissipative forces are velocity dependent, and point to the need to develop new techniques to resolve these issues.

Journal ArticleDOI
TL;DR: In this paper, the velocity power spectrum in the inertial range is predicted to be Ek ~ k-1.74, which is the same as the Larson law in the dissipative range.
Abstract: The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range, such turbulence obeys the Kolmogorov law, while in the dissipative range, it behaves as Burgers turbulence developing shock singularities. On the base of the She-Leveque analytical model, we then predict the velocity power spectrum in the inertial range to be Ek ~ k-1.74. This result agrees well with recent numerical findings by Padoan & Nordlund and reproduces the observational Larson law u ~ l0.74...0.76. The application of the model to more general dissipative structures with higher fractal dimensionality is discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations and find that many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient.
Abstract: We examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often studied in simulations. Specifically we clarify the performance of integration schemes in hybrid models, which combine microscopic and meso-scale descriptions of different particles using both soft and hard interactions. We find that in all three model systems many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient. The artifacts are found to be strongest in systems, where interparticle interactions are soft and predominated by random and dissipative forces, while in systems governed by conservative interactions the artifacts are weaker. Our results suggest that the quality of any integration scheme employed is crucial in all cases where the role of random and dissipative forces is important, including hybrid models where the solvent is described in terms of soft potentials.

Journal ArticleDOI
TL;DR: A new framework for a variational principle invokes a coercive form that results in a criterion for self-organizing relaxation of a two-fluid plasma that is a stable equilibrium independent of the direct effects of dissipation.
Abstract: Self-organization of an ordered structure occurs in a plasma under rather restrictive conditions. A new framework for a variational principle invokes a coercive form that results in a criterion for self-organizing relaxation of a two-fluid plasma. The constraints (constants of motion of the ideal model) are adjusted, through a weakly dissipative process, so that the relaxed state, under well-defined conditions, is a stable equilibrium independent of the direct effects of dissipation.

Journal ArticleDOI
TL;DR: Numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature, are studied.
Abstract: We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers.

Journal ArticleDOI
TL;DR: In this article, the energy conservation on the material points is investigated and found to depend strongly on the version of the algorithm used, and the dissipative algorithm is a better choice in general, as the damping is consistent with the accuracy of the solution.

Journal ArticleDOI
TL;DR: In this article, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables in particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the volume is increased.
Abstract: Continuum thermomechanics hinges on the concept of a representative volume element (RVE), which is well defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) statistically representative volume containing a very large (mathematically infinite) set of microscale elements (eg, grains) Response of finite domains of material, however, displays statistical scatter and is dependent on the scale and boundary conditions In order to accomplish stochastic homogenization of material response, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables In particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the material volume is increased These functionals are linked to their duals via Legendre transforms either in the spaces of ensemble average velocities or ensemble-average dissipative forces In the limit of infinite volumes (RVE limit (ii) above) all the functionals become deterministic, and classical Legendre transforms of deterministic thermomechanics hold As an application, stochastic continuum damage mechanics of elastic-brittle solids is developed ©2002 ASME

Journal ArticleDOI
TL;DR: In this paper, a set of three-dimensional constitutive equations are proposed for modeling the nonlinear dissipative response of soft tissue, which are phenomenological in nature and they model a number of physical features that have been observed in soft tissue.

Journal ArticleDOI
TL;DR: In this article, the photoinduced dynamics at a conical intersection (the so-called system) which is weakly coupled to a thermal environment (the bath) are investigated.
Abstract: Redfield theory is applied to investigate the photoinduced dynamics at a conical intersection (the so-called system) which is weakly coupled to a thermal environment (the so-called bath). The dynamics of the system is described by a two-state three-mode model Hamiltonian, chosen to represent the S1(nπ*)–S2(ππ*) conical intersection in pyrazine. Dissipative effects are introduced through a bilinear coupling of the system vibrational modes with a harmonic bath, which represents the remaining vibrational degrees of freedom of the molecule and/or interactions with a condensed-phase environment. The Redfield equations for the reduced density matrix are solved numerically without further approximations. From the reduced density matrix the time evolutions of electronic-state populations and vibrational coherences are obtained, as well as time-dependent probability densities of individual vibrational modes. The results provide a visualization of the essential features of the ultrafast (time scale of 10 fs) intern...

Journal ArticleDOI
TL;DR: In this paper, the authors considered the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation.
Abstract: In this paper, we consider the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation. Using path integral method, we compute exactly the probability density function of the power (averaged over a time interval of length τ) injected (and dissipated) by the random force into a Brownian particle driven by a Langevin equation. The resulting distribution, as well as the associated large deviation function, display strong asymmetry, whose origin is explained. Connections with the so-called “Fluctuation Theorem” are thereafter discussed. Finally, considering Langevin equations with a pinning potential, we show that the large deviation function associated with the injected power is completely insensitive to the presence of a potential.

Journal ArticleDOI
TL;DR: In this article, the static and dynamic behavior of well localized solitary solutions of a three-component reaction-diffusion model in two-and three-dimensional space is investigated, where the field equations are reduced to a set of ordinary differential equations describing rather well the dynamical behaviour of isolated and interacting dissipative solitons using their center coordinates and amplitudes of certain propagator modes.

Journal ArticleDOI
TL;DR: The structural and dynamical properties of three-dimensional isotropic complex plasmas are investigated kinetically within the framework of a dissipative Yukawa model and a modified Coulomb coupling parameter is proposed whose value alone determines the location of the complex plasma melting line.
Abstract: The structural and dynamical properties of three-dimensional isotropic complex plasmas are investigated kinetically within the framework of a dissipative Yukawa model. A modified Coulomb coupling parameter is proposed whose value alone determines the location of the complex plasma melting line. This implies that the phase transition has a universal scaling at the kinetic level. In detail, our molecular dynamics investigations show that the system dynamics is universal (but different) in the limits of high as well as low-frictional dissipation, while in the intermediate case it depends considerably on the dissipation rate. Issues such as the influence of the interaction strength on the single particle diffusion constant and the applicability of dynamical criteria for freezing are discussed.

Journal ArticleDOI
TL;DR: Solitary waves are experimentally studied in a monolayer hexagonal dust lattice which is formed from monodisperse plastic microspheres and levitated in the sheath of an rf discharge and it is found that the product of thesoliton amplitude and the square of the soliton width is constant as the solitons propagates.
Abstract: Solitary waves are experimentally studied in a monolayer hexagonal dust lattice which is formed from monodisperse plastic microspheres and levitated in the sheath of an rf discharge. It is found that the product of the soliton amplitude and the square of the soliton width is constant as the soliton propagates. The analytical theory describing the experiment is based on the equations of motion written for a linear chain. It takes into account damping, dispersion, and nonlinearity. The numerical simulation of a linear chain produces double solitons like those observed in the experiment.

Journal ArticleDOI
TL;DR: In this article, the method of l-trajectories is used to study the large-time behavior of nonlinear evolutionary systems, where solutions suffer from lack of regularity or when the leading elliptic operator is nonlinear.

Book ChapterDOI
05 Aug 2002
TL;DR: In this article, the authors discuss the effects of entanglement between a quantum system and its environment on the system degree of freedom and the quantum superposition of quantum states in a process referred to as decoherence.
Abstract: The coupling of a system to its environment is a recurrent subject in this collection of lecture notes. The consequences of such a coupling are threefold. First of all, energy may irreversibly be transferred from the system to the environment thereby giving rise to the phenomenon of dissipation. In addition, the fluctuating force exerted by the environment on the system causes fluctuations of the system degree of freedom which manifest itself for example as Brownian motion. While these two effects occur both for classical as well as quantum systems, there exists a third phenomenon which is specific to the quantum world. As a consequence of the entanglement between system and environmental degrees of freedom a coherent superposition of quantum states may be destroyed in a process referred to as decoherence. This effect is of major concern if one wants to implement a quantum computer. Therefore, decoherence is discussed in detail in Chap. 5.

Journal ArticleDOI
TL;DR: In this paper, the authors re-examined the stability of viscous resistive magnetized Couette flow with the emphasis on flows that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradient of angular velocity and specific angular momentum.
Abstract: Axisymmetric stability of viscous resistive magnetized Couette flow is re-examined, with the emphasis on flows that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum. In this regime, magnetorotational instabilities (MRI) may occur. Previous work has focused on the Rayleigh-unstable regime. To prepare for an experimental study of MRI, which is of intense astrophysical interest, we solve for global linear modes in a wide gap with realistic dissipation coefficients. Exchange of stability appears to occur through marginal modes. Velocity eigenfunctions of marginal modes are nearly singular at conducting boundaries, but magnetic eigenfunctions are smooth and obey a fourth-order differential equation in the inviscid limit. The viscous marginal system is of tenth order; an eighth-order approximation previously used for Rayleigh-unstable modes does not permit MRI. Peak growth rates are insensitive to boundary conditions. They are predicted with surprising accuracy by WKB methods even for the largest-scale mode. We conclude that MRI is achievable under plausible experimental conditions using easy-to-handle liquid metals such as gallium.

Journal ArticleDOI
TL;DR: In this paper, the receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analyzed and its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions.
Abstract: The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given

Journal ArticleDOI
TL;DR: In this article, the authors examined the feasibility of convection-dominated black hole accretion models by explicitly calculating the leading-order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows.
Abstract: The principles underlying a proposed class of black hole accretion models are examined. The flows are generally referred to as "convection-dominated" and are characterized by inward transport of angular momentum by thermal convection and outward viscous transport, vanishing mass accretion, and vanishing local energy dissipation. In this paper, we examine the viability of these ideas by explicitly calculating the leading-order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows. The modes are destabilized by the generalized magnetorotational instability, including the effects of angular velocity and entropy gradients. It is explicitly shown that modes that would be stable in the absence of a destabilizing entropy gradient transport angular momentum outward. There are no inward-transporting modes at all, unless the magnitude of the (imaginary) Brunt-Vaisala frequency is comparable to the epicyclic frequency, a condition requiring substantial levels of dissipation. When inward-transporting modes do exist, they appear at long wavelengths, unencumbered by magnetic tension. Moreover, very general thermodynamic principles prohibit the complete recovery of irreversible dissipative energy losses, a central feature of convection-dominated models. Dissipationless flow is incompatible with the increasing inward entropy gradient needed for the existence of inward-transporting modes. Indeed, under steady conditions, dissipation of the free energy of differential rotation inevitably requires outward angular momentum transport. Our results are in good agreement with global MHD simulations, which find significant levels of outward transport and energy dissipation, whether or not destabilizing entropy gradients are present.

Journal ArticleDOI
01 Apr 2002-EPL
TL;DR: In this article, Baldassarri et al. used Monte Carlo simulations of the spatially homogeneous Boltzmann equation for inelastic Maxwell molecules, and obtained a transcendental equation from which the exponents, appearing in the power law tails, can be calculated.
Abstract: Monte Carlo simulations of the spatially homogeneous Boltzmann equation for inelastic Maxwell molecules, performed by Baldassarri et al. (cond-mat/0111066), have shown that general classes of initial distributions evolve for large times into a singular nonlinear scaling solution with a power law tail. By applying an asymptotic analysis we derive these results from the nonlinear Boltzmann equation, and obtain a transcendental equation from which the exponents, appearing in the power law tails, can be calculated. The dynamics of this model describes a dissipative flow in v-space, which drives the system to an attractor, the nonlinear scaling solution, with a constant negative rate of irreversible entropy production, given by − ¼(1 − α2), where α is the coefficient of restitution.

Journal ArticleDOI
TL;DR: Atomic resolution of both conservative and dissipative forces are established by lateral force microscopy, presenting the resolution of atomic defects.
Abstract: Friction is caused by dissipative lateral forces that act between macroscopic objects. An improved understanding of friction is therefore expected from measurements of dissipative lateral forces acting between individual atoms. Here we establish atomic resolution of both conservative and dissipative forces by lateral force microscopy, presenting the resolution of atomic defects. The interaction between a single-tip atom that is oscillated parallel to an Si(111)-(7 × 7) surface is measured. A dissipation energy of up to 4 eV per oscillation cycle is found. The dissipation is explained by a “plucking action of one atom on to the other” as described by G. A. Tomlinson in 1929 [Tomlinson, G. A. (1929) Phil. Mag. 7, 905–939].