Related papers: Congested aggregation via Newtonian interaction
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
A numerical analysis of upwind type schemes for the nonlinear nonlocal aggregation equation is provided. In this approach, the aggregation equation is interpreted as a conservative transport equation driven by a nonlocal nonlinear velocity…
We study the impact of attractive self-interactions on the nonequilibrium dynamics of relativistic quantum fields with large occupancies at low momenta. Our primary focus is on Bose-Einstein condensation and nonthermal fixed points in such…
We develop the long-time analysis for gradient flow equations in metric spaces. In particular, we consider two notions of solutions for metric gradient flows, namely energy and generalized solutions. While the former concept coincides with…
We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest in many contexts in multi-population modelling. We prove…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
The small-scale velocity gradient is connected to fundamental properties of turbulence at the large scales. By neglecting the viscous and nonlocal pressure Hessian terms, we derive a restricted Euler model for the turbulent flow along an…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, interacting through lubrication forces and pairwise repulsive forces. The repulsion arises from the assumption that each particle is surrounded…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
In the Master's thesis of the author, we investigate certain aspects of gravitational physics that emerge from stochastic toy models of holographic gauge theories. We begin by reviewing field theory thermodynamics, black hole thermodynamics…
We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and…
We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model. Basic properties of the model…
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential equations known as aggregation-diffusion equations.…
We consider a nonlinear degenerate convection-diffusion equation with inhomogeneous convection and prove that its entropy solutions in the sense of Kru\v{z}kov are obtained as the - a posteriori unique - limit points of the JKO variational…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…
Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewicz inequalities in this context), are known to provide global…