Related papers: Hydrodynamic and hydrostatic limit for a generaliz…
We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above…
We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in…
We study the hydrodynamic limit for a periodic $1$-dimensional exclusion process with a dynamical constraint, which prevents a particle at site $x$ from jumping to site $x\pm1$ unless site $x\mp1$ is occupied. This process with degenerate…
The mechanical force from light -- radiation pressure -- provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a…
We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin…
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena…
We study the hydrodynamic limit for the isothermal dynamics of an anharmonic chain under hyperbolic space-time scaling under varying tension. The temperature is kept constant by a contact with a heat bath, realised via a stochastic…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
We consider the dynamics of a class of spin systems with unbounded spins interacting with local mean field interactions. We proof convergence of the empirical measure to the solution of a McKean-Vlasov equation in the hydrodynamic limit and…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
We analyze the generalized symmetric exclusion process, which allows at most $\alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $\theta\in\mathbb R$. We prove that the…
We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is…
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…
We prove that the hydrodynamic limit of a zero-range process evolving in graphs approximating the Sierpinski gasket is given by a nonlinear heat equation. We also prove existence and uniqueness of the hydrodynamic equation by considering a…
The electrostatic interaction between colloidal particles trapped at the interface between two immiscible electrolyte solutions is studied in the limit of small inter-particle distances. Within an appropriate model exact analytic…
Using duality techniques, we derive the hydrodynamic limit for one-dimensional, boundary-driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary, for which the classical entropy method fails.
We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their…
Hydrodynamic interactions (HIs), namely solvent mediated long-range interactions between dispersed particles, play a crucial role in the assembly and dynamics of many active systems, from swimming bacteria to swarms of propelling…