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We provide a quantitative asymptotic analysis for the nonlinear Vlasov--Poisson--Fokker--Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often…

Analysis of PDEs · Mathematics 2021-03-24 José A. Carrillo , Young-Pil Choi , Yingping Peng

The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…

Probability · Mathematics 2021-03-30 Michele Coghi , Benjamin Gess

The dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a…

Pattern Formation and Solitons · Physics 2009-11-11 B. Meulenbroek , U. Ebert , L. Schaefer

We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier-Stokes) equation and describing the motion of a suspension of rigid rods in gravity. A reciprocal coupling leads to the formation of…

Fluid Dynamics · Physics 2015-10-13 Christiane Helzel , Athanasios E. Tzavaras

We study self-propelled particles with velocity reversal interacting by uniaxial (nematic) alignment within a coarse-grained hydrodynamic theory. Combining analytical and numerical continuation techniques, we show that the physics of this…

Statistical Mechanics · Physics 2016-11-30 Robert Großmann , Fernando Peruani , Markus Bär

We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary…

One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…

Chaotic Dynamics · Physics 2013-05-30 François Gay-Balmaz , Vakhtang Putkaradze

Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…

Pattern Formation and Solitons · Physics 2026-04-14 David Pinto-Ramos

We consider solutions of the Navier-Stokes equations in $3d$ with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth…

Analysis of PDEs · Mathematics 2022-05-18 Jacob Bedrossian , Pierre Germain , Benjamin Harrop-Griffiths

The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…

Analysis of PDEs · Mathematics 2025-08-25 Leonid Berlyand , Spencer Dang , Pierre-Emmanuel Jabin , Mykhailo Potomkin

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

We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck equation coupled with the compressible isentropic Navier-Stokes system through a drag force…

Analysis of PDEs · Mathematics 2020-06-18 Young-Pil Choi , Jinwook Jung

We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an 'equivalent-rod' theory from…

Soft Condensed Matter · Physics 2024-11-14 Michael Gomez , Eric Lauga

We consider fluid flows for which the linearized Navier-Stokes operator is strongly non-normal. The responses of such flows to external perturbations are spanned by a generically very large number of non-orthogonal eigenmodes. They are…

Fluid Dynamics · Physics 2025-07-11 Yves-Marie Ducimetière , François Gallaire

In this work we study the homogenization for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening and general non-associative monotone plastic flows. The constitutive equations in the models we study are…

Analysis of PDEs · Mathematics 2016-10-11 Sergiy Nesenenko

There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between…

Statistical Mechanics · Physics 2026-03-25 Tara Steinhöfel , Horst-Holger Boltz , Thomas Ihle

We develop a bonded-particle model for magneto-elastic rods that unifies large deformations, contact, and long-range magnetic interactions within a single discrete-element framework. The rod is discretized into orientable particles…

Soft Condensed Matter · Physics 2026-03-31 Gabriel Alkuino , Joel T. Clemmer , Christian D. Santangelo , Teng Zhang

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…

Numerical Analysis · Mathematics 2020-10-29 Chak Shing Lee , François Hamon , Nicola Castelletto , Panayot S. Vassilevski , Joshua White

We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…

Soft Condensed Matter · Physics 2014-03-11 Marcelo A. Dias , Basile Audoly

We consider the dynamics of the system of self propelling particles modeled via the Vicsek algorithm in continuum time limit. It is shown that the alignment process for the velocities can be subdivided into two regimes: "fast" kinetic and…

Statistical Mechanics · Physics 2010-11-03 V. L. Kulinskii , A. A. Chepizhko