Non-Equilibrium Problems in Collisional Kinetic and Quantum Theory

题目：碰撞动力学和量子理论中的非平衡问题。本提案的目的是继续在与玻尔兹曼积分-微分方程和量子流体动力学模型相对应的碰撞动力学统计方程的解析和数值问题方面的广泛计划。将开发非线性分析的新工具，以及计算策略。所考虑的统计模型与能量耗散有关。一个例子是气体模型，其中粒子被表示为硬球体，碰撞是非弹性的。另一个物理场景是颗粒流。该项目考虑的尺度包括纳米科学中的尺度。

Abstract, DMS 0507038, I Gamba, University of TexasTitle: Non-equilibrium problems in collisional kinetic and quantum theory The aim of this proposal is to continue a broad program in analytical and numerical problems for collisional kinetic statistical equations corresponding to the Boltzmann integro-differential equation and quantum hydrodynamic models. New tools from non-linear analysis will be developed, as well as computational strategies.The statistical models considered relate to energy dissipation. An example is the model of a gas in which particles are represented as hard spheres and collisions are inelastic. Another physical scenario is granular flow. The scales considered in the project include those occurring in nano-science.