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This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

Probability · Mathematics 2021-06-24 Sarath Yasodharan , Rajesh Sundaresan

The flow curve of various yield stress materials is singular as the strain rate vanishes, and can be characterized by the so-called Herschel-Bulkley exponent $n=1/\beta$. A mean-field approximation due to Hebraud and Lequeux (HL) assumes…

Soft Condensed Matter · Physics 2018-01-17 Jie Lin , Matthieu Wyart

We study the collision probability $p$ of particles advected by open flows displaying chaotic advection. We show that $p$ scales with the particle size $\delta$ as a power law whose coefficient is determined by the fractal dimensions of the…

Chaotic Dynamics · Physics 2012-01-27 Alessandro P. S. de Moura

Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…

Soft Condensed Matter · Physics 2016-04-20 Aaron Dörr , Steffen Hardt

We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…

Probability · Mathematics 2026-03-03 Angeliki Koutsimpela , Stefan Grosskinsky

Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…

General Mathematics · Mathematics 2025-11-12 Dimiter Prodanov

We are interested in a kinetic equation intended to describe the interactions of particles with their environment. We focus on the long time behaviour. We prove that the time derivative of the spatial density goes to 0 and exhibit the omega…

Analysis of PDEs · Mathematics 2019-04-10 Arthur Vavasseur

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…

Optimization and Control · Mathematics 2024-04-04 Cameron Davies

The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…

Chemical Physics · Physics 2009-10-31 Martin Z. Bazant , Howard A. Stone

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 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…

Analysis of PDEs · Mathematics 2023-11-27 Rupert L. Frank , Ryan W. Matzke

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven…

Statistical Mechanics · Physics 2009-11-10 E. Levine , D. Mukamel , G. M. Schutz

Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…

Condensed Matter · Physics 2009-10-22 H. Castella , X. Zotos

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…

Soft Condensed Matter · Physics 2016-05-02 Robert Großmann , Pawel Romanczuk , Markus Bär , Lutz Schimansky-Geier

The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…

Soft Condensed Matter · Physics 2009-11-10 D. S. Dean , A. Lefèvre

The transverse nuclear response to an electromagnetic probe which is limited to create (or destroyed) a particle-hole ($ph$) or delta-hole ($\Delta h$) pair is analyzed. Correlations of the random phase approximation (RPA) type and self…

Nuclear Theory · Physics 2009-10-31 E. Bauer

We consider a ballistic Mach-Zehnder interferometer for electrons propagating chirally in one dimension (such as in an integer Quantum Hall effect edge channel). In such a system, dephasing occurs when the finite range of the interaction…

Mesoscale and Nanoscale Physics · Physics 2009-03-12 Clemens Neuenhahn , Florian Marquardt

The $\alpha$-XY model generalizes, through the introduction of a power-law decaying potential, a well studied mean-field hamiltonian model with attractive long-range interactions. In the $\alpha$-model, the interaction between classical…

Statistical Mechanics · Physics 2007-05-23 Andrea Giansanti , Daniele Moroni , Alessandro Campa

We study the long range percolation model on $\mathbb{Z}$ where sites $i$ and $j$ are connected with probability $\beta |i-j|^{-s}$. Graph distances are now well understood for all exponents $s$ except in the case $s=2$ where the model…

Probability · Mathematics 2015-11-10 Jian Ding , Allan Sly

We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and…

Probability · Mathematics 2022-07-25 Noah Forman , Douglas Rizzolo , Quan Shi , Matthias Winkel