Related papers: Congested aggregation via Newtonian interaction
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might oscillate in a rapid way, but fulfills a certain Lipschitz…
We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up…
Stein Variational Gradient Descent (SVGD) is a deterministic interacting-particle method for sampling from a target probability measure given access to its score function. In the mean-field and continuous-time limit, it is known that the…
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…
We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in…
We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
The effect of concentration-dependent switching of the non-equilibrium depletion interaction between obstacles in a gas flow of interacting Brownian particles is presented. When increasing bath fraction exceeds half-filling, the…
We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
We introduce a notion of viscosity solutions for a nonlinear degenerate diffusion equation with a drift potential. We show that our notion of solutions coincide with the weak solutions defined via integration by parts. As an application of…
We study the Wasserstein projection of a compactly supported probability measure onto the class of measures whose density ratio is bounded, and we place this projection in a broader program connecting generative modeling, optimal transport,…
A scheme for the solution of fluid-structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid…
We consider the properties of a one dimensional fluid of brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat-bath. Direct interactions among the particles are represented as binary, instantaneous…
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion…
We consider systems of $n$ parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the…
We study the interactions between two negatively charged macroscopic surfaces confining positive counterions. A density-functional approach is introduced which, besides the usual mean-field interactions, takes into account the correlations…
The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…
For free energies of the form \[ F(\mu) = E(\mu) + \sigma\int_\Omega \mu\log\mu\,dx, \quad \sigma > 0, \] we study the Wasserstein gradient flow, a continuity equation also known as mean-field Langevin dynamics, around a stationary state…