Related papers: On perturbation around closed exclusion processes
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We derive a formula for the quasi-potential of one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of…
We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can…
We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS)…
We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutators method of Mourre. We also obtain the limiting absorption…
The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334-368, 2008] for linear transport equations in kinetic and diffusive regimes. We prove that the…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
Motor proteins are key players in intracellular transport processes and biological motion. Theoretical modeling of these systems has been achieved by the use of step processes on one-dimensional lattices. After a comprehensive introduction…
Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to…
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
The totally asymmetric simple exclusion process along with particle adsorption and evaporation kinetics is a model of boundary-induced nonequilibrium phase transition. In the continuum limit, the average particle density across the system…
We investigate the effect of adsorption-desorption phenomenon of ions in an asymmetric electrolytic cell at open circuit conditions. Our approach is based on the Poisson-Nernst-Planck theory for electrolytes and the kinetic model of…
Suppose that an infinite lattice gas of constant density $n_0$, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius $R$. Employing the macroscopic fluctuation…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…