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We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
A dynamical theory for the organization and dissipation of a current in a non-equilibrium fluid near equilibrium is presented. This is based on the Lyapunov exponents of the phase space of the system.
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
We use molecular dynamics simulations to study the evaporation of particle-laden droplets on a heated surface. The droplets are composed of a Lennard-Jones fluid containing rigid particles which are spherical sections of an atomic lattice,…
Humans can easily describe, imagine, and, crucially, predict a wide variety of behaviors of liquids--splashing, squirting, gushing, sloshing, soaking, dripping, draining, trickling, pooling, and pouring--despite tremendous variability in…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
We report an ab-initio simulation of liquid Indium in a wide range of pressures and temperatures. We calculate equation of state, thermal expansion and compressibility coefficients. The structure of the system is analyzed by radial…
We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy…
Molecular dynamics is a powerful tool to investigate the properties of fluid systems. However, a correct interpretation of the results of simulations is required. In particular, some simulations show appearance of large voids in liquids,…
Physics students now have access to interactive molecular dynamics simulations that can model and animate the motions of hundreds of particles, such as noble gas atoms, that attract each other weakly at short distances but repel strongly…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
Molecular Dynamics simulations are becoming a powerful tool for examining and predicting atomic and molecular processes in various environment. The present review shows how, in the fields of plasma physics, chemistry and interactions with…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…