Related papers: A hydrodynamic limit for chemotaxis in a given het…
The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve…
Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the same class of infinite interacting…
This thesis deals with the study of properties and interactions of light mesons. Specifically, we focus on hadronic decay and scattering processes, which are dominated by effects of the strong interaction in the low-energy regime. A…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
Biological systems like ciliated microorganisms are capable to respond to the external chemical gradients, a process known as chemotaxis which has been studied here using the chiral squirmer model. This theoretical model considers the…
In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the…
The accumulation of self-propelled particles on repulsive barriers is a widely observed feature in active matter. Despite being implicated in a broad range of biological processes, from biofilm formation to cytoskeletal movement, wetting of…
We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…
Living cells are capable of interacting with their environments in a variety of ways, including cell signalling, adhesion, and directed motion. These behaviours are often mediated by receptor molecules embedded in the cell membrane, which…
We consider a chemotaxis-fluid system involving nonlinear cell diffusion of porous medium type, signal consumption by cells, and rather general, possibly matrix-valued, chemotactic sensitivities. It is shown that if the corresponding…
We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the…
Phase stability, and the limits thereof, are a central concern of materials thermodynamics. However, the temperature limits of equilibrium liquid stability in chemical systems have only been widely characterized under constant (typically…
We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in…
The article presents new model of equilibrium in open chemical systems suggesting a linear dependence of the reaction shift from equilibrium in presence of the external thermodynamic force. Basic equation of this model contains traditional…
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for…
In this chapter, we illustrate recently obtained thermodynamic bounds for a number of enzymatic networks by focusing on simple examples of unicyclic or multi-cyclic networks. We also derive complementary relations which constrain the…