Abstract April 17, 2019
Speaker: Ibrahim Fatkullin, Dept. of Mathematics
Title: Mathematical models in condensed matter physics
A lot of phenomena in physics may be described and modeled (theoretically of computationally) using quite different mathematical frameworks. For example, to describe gas in a room, one may use probabilistic language of statistical mechanics, or formulate a large system of ODEs for particle dynamics, or employ a kinetic (e.g., Boltzmann) equation for the evolution of probability density of particles' velocities and locations, or one could use various hydrodynamic equations, such as Navier-Stokes or Euler PDEs. My primary interest is in connecting such different descriptions using various tools from probability theory, calculus of variations, and numerical analysis. I will outline a few outstanding problems in physics of liquid crystals and polymers and discuss a few ideas on how to approach them using all these different formalisms.