Annual Report 2008.pdf - SAMSI

eflections, and then build the interface conditions into the numerical fluxes. This method allows
the resolution of high frequency waves without numerically resolving the small wave lengths,
and capture the correct transmissions and reflections at the interface. Moreover, we extend the
method to include diffraction, and quantum barriers. Applications to semiclassical limit of linear
Schrodinger equation, geometrical optics, elastic waves, and semiconductor device modeling,
will be discussed.
Ping Lin
University of Dundee (and National University of Singapore)
Division of Mathematics
matlinp@nus.edu.sg
“An Energy Law Perserving C0 Finite Element Scheme for a Phase Field Model of Two-phase
Flows”
In this talk we will study Allen-Cahn and Cahn-Hilliard phase field models for two phase flow
computation. The phase field model shares the advantage of the level set method, VOF method,
etc. as an Eulerian method and changes the Lagrangian description of the interface motion into
Eulerian description. It may be seen as a PDE based regularization of the sharp interface model
and has the advantage of including other physics, such as nonNewtonian fluids, polymers and
liquid crystals. A very good feature of the method is: it preserves the profile across the interface
due to its energy law which may not be easily done in other interface models. So it is desirable
that the energy law is at least approximately preserved in designing numerical methods. We
present a C0 finite element based modified midpoint scheme for the Allen-Cahn model and show
that the discrete energy law is accurately preserved. But when we apply the same idea to the
Cahn-Hilliard model under a C0 finite element setting oscillation near the interface occurs. It
seems that this is due to the modified midpoint scheme is not of stiff decay. Thus we present a
modified backward Euler scheme which approximately preserves the energy law. Numerical
examples show that it indeed works very well.
Ray Luo
University of California, Irvine
Department of Molecular Biology and Biochemistry
rluo@uci.edu
“Scaling in Biomolecular Solvation: Are Proteins Large?”
Implicit solvents have become increasingly popular in biomolecular simulations. However their
wide applications have revealed many limitations, such as improper balance of secondary
structures, over population of salt-bridge interactions, and stability of proteins in molecular
dynamics. These well-known limitations of implicit solvents show that more developments are
still needed to fully establish the applications of implicit solvents in biomolecular simulations.
We have initiated efforts to quantitatively and rigorously address how well implicit solvents can
approximate explicit solvents. We have studied whether implicit solvents break down when
scaling from small organic molecules to typical-sized biomacromolecules. We have analyzed
implicit solvents in the context of molecular dynamics simulations on simple systems such as
dipeptides and peptides where conformational sampling is less challenging. We have found