Non-equilibrium Collisional Transport in Nano and Mesoscale Modeling

建议：0204568PI：艾琳·甘巴研究所：得克萨斯大学奥斯汀分校题目：纳米和介观模型中的非平衡碰撞输运这个研究项目涉及纳米和介观尺度下的统计力学和输运理论的几个方程。特别令人感兴趣的是动力学碰撞输运的积分微分方程组(如玻尔兹曼方程)和带电粒子输运的积分微分方程组和偏微分方程组(量子流体力学-泊松方程)。我们的目标是通过证明存在性和稳定性定理以及通过数值模拟潜在的物理问题来严格分析这些方程。该项目需要开发和应用非线性分析的新工具，以及设计新的计算策略，将从量子水平到动力学水平再到流体水平的不同模型联系起来。该研究计划在几个领域都有应用。我们提到了颗粒状物质的快速流动，这是由非弹性粒子碰撞传输的统计模型来描述的，以及电子纳米器件建模，其中通道长度是纳米量级的，量子隧道效应是重要的。这项研究的结果有望导致确定性计算工具的设计，这些工具可以应用于高度非均匀介质中的多尺度现象的模拟，例如在湍流颗粒流问题和电子或生物纳米器件模拟中。

Proposal: 0204568PI: Irene GambaInstitution: University of Texas at AustinTitle: Non-equilibrium collisional transport in nano and mesoscale modelingThis research project is concerned with several equations of statistical mechanics and transport theory at the nano- and mesoscale. Of particular interest are integrodifferential equations for kinetic collisional transport (like the Boltzmann equation) and systems of integrodifferential and partial-differential equations for transport of charged particles (quantum hydrodynamic-Poisson equations). The goal is to rigorously analyze these equations by proving existence and stability theorems and by numerically simulating the underlying physical problems. The project requires the development and application of new tools from nonlinear analysis, as well as the design of new computational strategies linking the different models from the quantum level to the kinetic level to the fluid level.This research program has applications in several areas. We mention the rapid flow of granular materials, which is described by statistical models for collisional transport of inelastic particles, and electronic nanodevice modeling, where channel lengths are of the order of nanometers and quantum tunneling effects are important. The results of this research are expected to lead to the design of deterministic computational tools that can be applied to the simulation of multiscale phenomena in highly heterogeneous media, for example in turbulent granular flow problems and electronic or biological nanodevice modeling.