Related papers: Aggregation-Diffusion to Constrained Interaction: …
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…
This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and…
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…
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…
We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…
Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
High-quality power flow datasets are essential for training machine learning models in power systems. However, security and privacy concerns restrict access to real-world data, making statistically accurate and physically consistent…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the…
We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this scheme keeps the dissipation…
This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimum flow process, offers a potential generalization of…
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform…
We investigate transient clustering dynamics in nonlocal aggregation-diffusion systems from an energetic perspective. Starting from a stochastic interacting particle system, we study the associated macroscopic McKean-Vlasov equation on the…
We investigate the existence of ground states for a free energy functional on Cartan-Hadamard manifolds. The energy, which consists of an entropy and an interaction term, is associated to a macroscopic aggregation model that includes…
Magnetic fields and magnetic materials have promising microfluidic applications. For example, magnetic micro-convection can enhance mixing considerably. However, previous studies have not explained increased effective diffusion during this…
A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations…
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the…
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…