Related papers: A Hamiltonian interacting particle system for comp…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow…
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the…
The Hamiltonian of mean force (HMF) provides the standard starting point for strong-coupling thermodynamics, yet explicit operator forms are known only in restricted settings. We present a quenched density framework that uses the…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
The dynamics and the thermodynamics of particles/spins interacting via long-range forces display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian system of…
These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays,…
We discuss the transport of a tracer particle through the Bose Einstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean field models. The microscopic model is based on three…
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics…
We derive a minimal port-Hamiltonian formulation of a general class of interacting particle systems driven by alignment and potential-based force dynamics which include the Cucker-Smale model with potential interaction and the second order…
Fluids with shear-rate-dependent viscosity form a special class of non-Newtonian fluids that play a crucial role in continuum dynamics. We consider a compressible barotropic flow of such fluids, governed by a generalized Navier-Stokes…