Title: Building a Stochastic Continuum Model for a Magnetic System

Abstract: Stochastic partial differential equations (SPDEs) naturally arise as continuum models for spatially-extended systems with thermal noise effects that are important to resolve, such as spontaneous magnetization flipping.  While finite difference approximations in space can be made at large enough spatial scales to assume independent noise in space, this assumption is clearly false in the continuum limit, leading to both undesirable modeling and mathematical properties.  I will provide some intuition for constructing continuum models that have both spatially correlated noise yet maintain sampling the physically relevant Gibbs distribution in time.  Applying this to a spin system model of a magnet, I will discuss some properties of the resulting dynamics.

Host: Karen Daniels