Related papers: Classifying minimum energy states for interacting …
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a range of exponents corresponding to mild…
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
We consider a non-local interaction energy over bounded densities of fixed mass $m$. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when…
We consider minimizers of the N-particle interaction potential energy and briefly review numerical methods used to calculate them. We consider simple pair potentials which are repulsive at short distances and attractive at long distances,…
The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as…
In a 1979 paper, Ventevogel and Nijboer showed that classical point particles interacting via the pair potential $\phi(x)=\left(1+x^4\right)^{-1}$ are not equally spaced in their ground states in one dimension when the particle density is…
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than…
We consider a class of nonlocal shape optimization problems for sets of fixed mass where the energy functional is given by an attractive/repulsive interaction potential in power-law form. We find that the existence of minimizers of this…
We study a two parameter family of energy minimization problems for interaction energies $\mathcal{E}_{\alpha,\beta}$ with attractive-repulsive potential $W_{\alpha,\beta}$. We develop a concavity principle, which allows us to provide a…
Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types…
We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
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…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive-attractive potentials of power-law type in one dimension. We prove that sum of two Dirac masses is the unique local minimizer under the…
We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low--density (Boltzmann--Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann…
In this paper we consider the minimizers of the interaction energies with the power-law interaction potentials $W({\bf x}) = \frac{|{\bf x}|^a}{a} - \frac{|{\bf x}|^b}{b}$ in $d$ dimensions. For odd $d$ with $(a,b)=(3,2-d)$ and even $d$…