Computing and Mathematical Sciences Colloquium

Fluctuating hydrodynamic descriptions provide a promising approach for mesoscopic modelling and simulation of elastic structures that interact with a fluid when subject to thermal fluctuations.  This allows for capturing simultaneously such effects as the Brownian motion of spatially extended mechanical structures as well as their hydrodynamic coupling and responses to external flows.  Fluctuating hydrodynamics approaches handle the hydrodynamic equations directly allowing for spatially adaptive discretizations or domains having complex geometries.  However, this presents the challenge of numerically approximating a set of stiff stochastic partial differential equations (SPDEs) having non-classical solutions (distributions).  We introduce stochastic discretization procedures based on ideas from statistical mechanics and Ito calculus.   We show how efficient stochastic computational methods can be developed for viable fluctuating hydrodynamic simulations.   We demonstrate these methods in the context of applications including the simulation of particles within microfluidic devices and the rheological responses of soft materials.  We also survey current challenges and opportunities for fluctuating hydrodynamic approaches.

Biography: Paul J. Atzberger studied mathematics at the Courant Institute at New York University where he received his PhD in 2003. Subsequently, from 2003 - 2006 he was a postdoctoral fellow at Rensselaer Polytechnic Institute. He joined the faculty at the University of California Santa Barbara in 2006. His research is in the area of stochastic analysis and computational methods motivated by applications arising in the natural sciences and engineering.