~~ The Department of Mechanical and Industrial Engineering Presents
Dr. Paul J. Atzberger
Associate Professor of Mathematics
University of California, Santa Barbara
Topic: Mesoscale Methods for the Hydrodynamics of Microstructures: Applications in Soft Materials and Microfluidics
Abstract: Fluctuating hydrodynamic descriptions provide a promising approach for mesoscale simulations of elastic microstructures of soft materials and devices. The use of a fluctuating hydrodynamic description allows for capturing simultaneously such effects as the collective Brownian motion of hydrodynamically coupled microstructure as well as responses to external flows. The approach allows also for handling domains having arbitrary geometries and large systems through spatially adaptive discretizations. However, obtaining viable methods for simulations requires handling stochastic hydrodynamic equations (SPDEs) that are stiff in the sense of exhibiting a wide-range of dynamical time-scales and exhibit non-classical solutions (distributions). We show how viable stochastic spatial and temporal discretizations can be developed based on ideas from statistical mechanics and exponential time-step integration. We also perform stochastic mode analysis to obtain reduced descriptions tailored to specific physical regimes. We demonstrate for practical applications our computational methods for simulations of (i) particles within microfluidic devices, (ii) diffusion within lipid bilayer membranes, and (iii) the rheological responses of soft materials. We also discuss our open source software package Mango-Selm that aims to make our computational methods accessible to the wider scientific community.
Bio: Paul J. Atzberger is an Associate Professor of Mathematics at the University of California Santa Barbara. He studied mathematics at the Courant Institute at New York University where he received his PhD in 2003. Subsequently, he held a postdoctoral position at Rensselaer Polytechnic Institute from 2003 - 2006 before joining the faculty at the University of California Santa Barbara. Paul J. Atzberger is currently an Associate Professor at the University of California Santa Barbara in the Department of Mathematics with a courtesy appointment in Mechanical Engineering. His research concerns stochastic phenomena and related computational methods for applications arising in the natural sciences and engineering. His past research includes work in the areas of fluctuating hydrodynamics, fluid-structure interaction, soft materials and complex fluids, and microfluidic / nanofluidic devices.Website