Research activities

Our primary research objective is to develop rapid and accurate numerical algorithms and analytic techniques for devices and systems.  In the past, our main areas of research have encompassed electromagnetic field modeling, especially electric field propagation in waveguides and fibers, semiconductor physics with emphasis on optical and transport processes in heavily doped III-V semiconductors, underwater acoustics, numerical boundary conditions and wide-angle methods for parabolic partial differential equations.  From 2002-2014 our research additionally centered on polarization effects in optical communications with emphasis on time varying polarization-dependent component of the transit times of electric fields in optical fibers (polarization mode dispersion).  These were modeled by introducing an analogy between the probability density function of communication systems and the statistical mechanical density of states that led to new methods based on biased sampling for finding the bit-error-rate in optical fiber systems.
Since, however, in large-scale systems computing the physically significant outputs for even a single realization of the numerous underlying system variables often requires substantial resources, further optimization of  multicanonical and related biased sampling procedures is highly desirable.  This motivated us to examine foundational aspects of these procedures as well further refinements motivated by practical applications. Recently we have clarified subtle issues inherent in the transition matrix method reformulation of biased sampling and have introduced several novel strategies for mitigating these accuracy and efficiency problems. In particular, we have quantified the relationship between the accuracy of biased sampling procedures and the degree to which these methods evenly sample all accessible regions of state (configuration) space.  As well, my group has recently been examining related numerical modeling issues in statistical and fluid mechanics.