Non-equilibrium Collisional Transport in Nano and Mesoscale Modeling

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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.