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We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles…

Probability · Mathematics 2024-10-22 Patrick van Meurs , Mark A. Peletier , Thomas Slangen

We consider an SDE system for signed Coulomb particles moving in $\mathbb R^2$. Due to the singular Coulomb interaction force, collisions between particles of opposite sign will happen in finite time. Upon collision, the colliding particles…

Analysis of PDEs · Mathematics 2026-05-19 Patrick van Meurs , Yoan Tardy

We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…

Analysis of PDEs · Mathematics 2022-07-01 Patrick van Meurs , Mark A. Peletier , Norbert Pozar

In the recent trend of extending discrete-to-continuum limit passages for gradient flows of single-species particle systems with singular and nonlocal interactions to particles of opposite sign, any annihilation effect of particles with…

Analysis of PDEs · Mathematics 2019-01-01 Patrick van Meurs , Marco Morandotti

We study a physical system of $N$ interacting particles in $\mathbb{R}^d$, $d\geq1$, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as $N$ tends to…

Probability · Mathematics 2014-09-09 Djalil Chafaï , Nathael Gozlan , Pierre-André Zitt

In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…

Mathematical Physics · Physics 2021-03-18 Alessia Nota , Juan J. L. Velázquez , Raphael Winter

Recently we studied $N$ run-and-tumble particles in one dimension - which switch with rate $\gamma$ between driving velocities $\pm v_0$ - interacting via the long range 1D Coulomb potential (also called rank interaction), both in the…

Statistical Mechanics · Physics 2025-02-14 Léo Touzo , Pierre Le Doussal

We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…

Analysis of PDEs · Mathematics 2020-08-26 Marco Di Francesco , Antonio Esposito , Markus Schmidtchen

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…

Analysis of PDEs · Mathematics 2020-10-27 Masato Kimura , Patrick van Meurs

This paper considers the equilibrium positions of $n$ particles in one dimension. Two forces act on the particles; a nonlocal repulsive particle-interaction force and an external force which pushes them to an impenetrable barrier. While the…

Analysis of PDEs · Mathematics 2021-05-18 Patrick van Meurs

We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale…

Nuclear Theory · Physics 2019-10-23 C. H. Schmickler , H. -W. Hammer , A. G. Volosniev

We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…

Mathematical Physics · Physics 2012-06-01 V. A. Malyshev

We consider first-order conservative systems of particles with binary Coulomb interactions in the mean-field scaling regime in dimensions $d\geq 3$. We show that if at some time, the associated sequence of empirical measures converges in a…

Analysis of PDEs · Mathematics 2020-10-21 Matthew Rosenzweig

We consider hamiltonian $N$ particle system on the finite segment with nearest-neighbor Coulomb interaction and external force $F$. We study the fixed points of such system and show that the distances between neighbors are asymptotically,…

Mathematical Physics · Physics 2012-02-02 V. A. Malyshev

We study a model in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. Combining theoretical and numerical work we locate the line of…

Disordered Systems and Neural Networks · Physics 2009-11-10 Francesco Sciortino , Piero Tartaglia , Emanuela Zaccarelli

We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…

Analysis of PDEs · Mathematics 2019-07-22 Adriana Garroni , Patrick van Meurs , Mark A. Peletier , Lucia Scardia

For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…

Materials Science · Physics 2007-05-23 Xiao-Yin Pan , Viraht Sahni

In this paper we consider a system of $N$ particles on the real line evolving according to Newton's law, interacting through a singular (repulsive) force deriving from the potential $\frac{|x|^{1-\alpha}}{1-\alpha}$ with $\alpha \in…

Analysis of PDEs · Mathematics 2018-10-23 Samir Salem

Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…

Analysis of PDEs · Mathematics 2023-10-06 Michael Fischer , Laura Kanzler , Christian Schmeiser

In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…

Statistical Mechanics · Physics 2020-10-23 Avanish Kumar , Manas Kulkarni , Anupam Kundu
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