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It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
We propose a model to study symmetric binary fluids, based in the mesoscopic molecular simulation technique known as multiparticle collision, where space and state variables are continuous while time is discrete. We include a repulsion rule…
We review all the calculations necessary for the construction of a Lyapunov like functional for nonlinear stability analysis of steady states in thermodynamically isolated/open systems composed of compressible heat conducting fluids.
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for…
We perform numerical experiments to study the Lyapunov spectra of dynamical systems associated with the Navier--Stokes (NS) equation in two spatial dimensions truncated over the Fourier basis. Recently new equations, called GNS equations,…
We show how the Lyapunov exponents of a dynamic system can in general be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive…
We compare dynamical nonequilibrium molecular dynamics and continuum simulations of the dynamics of relaxation of a fluid system characterized by a non uniform density profile. Results match quite well as long as the lengthscale of density…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
Dissipative particle dynamics (DPD) is a relatively new technique which has proved successful in the simulation of complex fluids. We caution that for the equilibrium achieved by the DPD simulation of a simple fluid the temperature depends…
The authors present a study of the non equilibrium statistical properties of a one dimensional hard-rod fluid dissipating energy via inelastic collisions and subject to the action of a Gaussian heat bath, simulating an external driving…
Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the…
We introduce and test via molecular simulation a simple model for predicting the manner in which interparticle interactions and thermodynamic conditions impact the single-particle free-volume distributions of equilibrium fluids. The model…
Thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations. For computationally intensive problems such as the simulation of biomolecules, we propose to average over…