Related papers: Free boundary problems in PDEs and particle system…
The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being…
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…
Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used…
We discuss the effects of open boundary conditions and boundary induced drift on condensation phenomena in the pair-factorized steady states transport process, a versatile model for stochastic transport with tunable nearest-neighbour…
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
The effects of the propagation of particles which have a finite life-time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source…
We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially completely disordered quantum systems, comparable to the systems which are sometimes referred to as Lifshitz…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem on a non-smooth domain, are…
The totally asymmetric simple exclusion process (TASEP) is a well studied example of far-from-equilibrium dynamics. Here, we consider a TASEP with open boundaries but impose a global constraint on the total number of particles. In other…
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each…
A multi-component lattice Boltzmann model recently introduced (R. Benzi et al. Phys. Rev. Lett 102, 026002 (2009)) to describe some dynamical behaviors of soft-flowing materials is theoretically analyzed. Equilibrium and transport…