Prof. Dr.-Ing. Timon Rabczuk
Institute of Structural Mechanics
Bauhaus-Universtät Weimar

Computational Modeling of Vesicles Based on Isogeometric Analysis and Phase Fields

ABSTRACT: In this presentation, I will present a computational framework based on isogeometric analysis and phase field models for vesicles. Vesicles are small sac-like structures filled with fluid and enclosed by a lipid bilayer membrane. They play important roles in various essential cellular processes, including transporting molecules and proteins, cellular signaling, storing food, and enzymes. It provides a basic model of red blood cells as well. And apart from their roles in natural cells’ functions, vesicles have several applications in synthetic biology, for example, as drug delivery or for production of biomolecules. The fluid-vesicle interaction problem or a chemomechanical problem of a multicomponent vesicle in the presence or absence of fluid flows are prime examples of a moving boundary/interface problem. These problems are mathematically described by a set of partial differential equations (PDEs) posed on moving domains, another set of PDEs posed on a moving interface, and a set of boundary conditions on the moving interface which couples these PDEs. I will take advantage of the higher order continuity of isogeometric analysis and its high accuracy and efficiency for dynamic problems while we employ the flexibility of phase fields to track the fluid-vesicle interface through the solution of an additional differential equation. Finally, the presented method will be applied to a series of applications including the hydrodynamics of homogeneous vesicles and vesicle doublets and their deformation under electric fields.

BIOGRAPHY: Timon Rabczuk received his Dr.-Ing. (PhD) at University of Karlsruhe in January 2002. He then joined the computational mechanics group of Prof. Ted Belytschko at Northwestern University as a postdoctoral fellow before he went for another postdoctoral position at the Technical University of Munich in October 2005. In February 2007, Timon was appointed senior lecturer at the Department of Mechanical Engineering of the University of Canterbury, Christchurch, New Zealand before he joined the Bauhaus-Universität Weimar in February 2009. His major research direction is Computational Mechanics or Computational Sciences with a focus on developing computational methods for the solution of PDEs. One key application he is interested in is moving boundary/interface problems, which are also the topic of this presentation.