Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities

We consider the stationary states of a chain of $n$ anharmonic coupled oscillators, whose deterministic hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature $T_\ell$ and $T_r$ and subject to constant forces $τ_\ell$ and $τ_r$. If the forces differ $τ_\ell \neq τ_r$ the center of mass of the system will move of a speed $V_s$ inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity…

具有随机速度的行人流模型：微观和宏观方法

A pedestrian flow model with stochastic velocities: microscopic and macroscopic approaches

本文研究了一种随机模型层次结构用于行人流动，从微观的社会力模型出发，推导出一种守恒型宏观模型，并引入了新的问题导向的闭合函数。

Hydrodynamic limit for the velocity flip model

We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state modified by a correction term.

关于功转化为热：微观模型与宏观方程

On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations

本文研究钉扎谐振链在随机速度翻转与周期力作用下的功热转换，推导出流体动力学极限下温度分布的热方程，并扩展到高维、非钉扎及非谐情形。

Ballistic and superdiffusive scales in macroscopic evolution of a chain of oscillators

We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the system has only three conserved quantities: volume, momentum and energy. We show the existence of two space--time scales on which the en- ergy of the system evolves. On the hyperbolic scale (t$ε$--1,x$ε$--1) the limits of the conserved quantities satisfy a Euler system of equa- tions, while the thermal part of the energy macroscopic profile re- mains stationa…

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.