Related papers: Dynamics of some constrained lattices
We investigate the dynamics of elastic capsules suspended in two-dimensional active nematic fluids using lattice Boltzmann simulations. The capsules, modeled as flexible membranes enclosing active internal regions, exhibit a rich variety of…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear…
We present a 1D effective model for the evolution of a cigar-shaped Bose-Einstein condensate in time dependent potentials whose radial component is harmonic. We apply this model to investigate the dynamics and expansion of condensates in 1D…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
The paper contains a development of the previously proposed generalized lattice model (GLM). In contrast to usual lattice models, the difference of the specific atomic volumes of the components is taken in account in GLM. In addition to…
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…
Granular materials such as sand, powders, and food grains are ubiquitous in civil engineering, geoscience, agriculture, and medicine. While the influence of friction between the grains on the static structure of these systems is well…
3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via…
We begin a systematic investigation of quench dynamics in higher-dimensional lattice systems considering the case of non-interacting fermions with conserved particle number. We prepare the system in a translational-invariant non-equilibrium…
A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically…
We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
We implement molecular dynamics simulations in canonical ensemble to study the effect of confinement on a $2d$ crystal of point particles interacting with an inverse power law potential proportional to $r^{-12}$ in a narrow channel. This…
We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…
A large class of two-dimensional free-surface hydrodynamical systems is determined that can be self-consistently reduced by the condition that the velocity profile has a constant shear. The reduced systems turn out to be Hamiltonian, and so…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo…