Related papers: The Mirrors Model : Macroscopic Diffusion Without …
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
We analyze the classical dynamics of a system composed of a one-dimensional cavity with a perfect, fixed mirror and a movable mirror with non-zero transparency interacting with a monochromatic laser. The movable mirror can deviate far from…
We study the stationary non-local equation which corresponds to the energy functional of a one-dimensional Ising spin system, in which particles interact via a Kac potential. The boundary conditions share the same sign and both lie above…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the…
Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively…
Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
We consider an interacting particle system in the interval $[1,N]$ with reservoirs at the boundaries. While the dynamics in the channel is the simple symmetric exclusion process, the reservoirs are also particle systems which interact with…
In an attempt to merge the microscopic with the macroscopic worlds, we present a brief study about a force which depends on the Planck force and on the coupling constant that in turn depends on the size of a particle in a particular…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…
We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…