Related papers: The gradient flow approach to hydrodynamic limits …
In \cite{J} M. Jara has presented a method, reducing the proof of the hydrodynamic limit of symmetric exclusion processes to an homogenization problem, as unified approach to recent works on the field as \cite{N}, \cite{F1}, \cite{F2} and…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be…
In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach…
We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…
Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of three different…
We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling…
This paper concerns with the hydrodynamic limit of the Kob-Andersen model, an interacting particle system that has been introduced by physicists in order to explain glassy behavior, and widely studies since. We will see that the density…
We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is…
We show that any positive, continuous, and bounded function can be realised as the diffusion coefficient of an evolution equation associated with a gradient interacting particle system. The proof relies on the construction of an appropriate…
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the…
We study the hydrodynamic limit for three gradient spin models: generalized Kipnis-Marchioro-Presutti (KMP), its discrete version and a family of harmonic models, under symmetric and nearest-neighbor interactions. These three models share…
We introduce the transportation-annihilation distance $W_p^\sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a…
The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a…
We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter $m$, a Generalized Brownian Energy Process, and the…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
We examine the behavior of a single impurity particle embedded within a Totally Asymmetric Simple Exclusion Process (TASEP). By analyzing the impurity's dynamics, characterized by two arbitrary hopping parameters $ \alpha $ and $\beta$, we…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
We consider the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system…