Related papers: Minimizers for an aggregation model with attractiv…
We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate…
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on $\Real^d$. Such equations arise in mathematical biology as models for organism group dynamics…
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the…
We introduce a generic and accessible implementation of an exact diagonalization method for studying few-fermion models. Our aim is to provide a testbed for the newcomers to the field as well as a stepping stone for trying out novel…
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…
Exhausters are families of compact, convex sets which provide minmax or maxmin representations of positively homogeneous functions and they are efficient tools for the study of nonsmooth function. Upper and lower exhausters of positively…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in $\mathbb{R}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is…
The settling of colloidal particles with short-ranged attractions is investigated via highly resolved immersed boundary simulations. At modest volume fractions, we show that inter-colloid attractions lead to clustering that reduces the…
The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication…
We propose that the behavior of asymmetric binary fluid mixtures with a large class of attractive or repulsive interparticle interactions can be understood by mapping onto effective non-additive hard-sphere models. The latter are best…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena. Even though some of these behaviors can be overcome in…
We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial…
We consider a nonlocal aggregation diffusion equation incorporating repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction. When the attractive interaction kernel is radially symmetric and strictly…
In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power \alpha of their distance…