Modeling and Computation Seminar

The Modeling & Computation Seminar is held on Thursdays at 12:30 PM, in Mathematics 402.

Fall 2008

August

08/28
Organizational meeting.

September

09/04
Raymond E. Goldstein
Department of Applied Mathematics and Theoretical Physics
University of Cambridge

Fluid Dynamics and the Evolution of Biological Complexity

One of the most fundamental issues in evolutionary biology is the nature of transitions from single cell organisms to multicellular ones, with accompanying cellular differentiation and specialization. Not surprisingly for microscopic life in fluid environments, many of the relevant physical considerations involve diffusion and mixing, for the efficient exchange of nutrients and metabolites with the environment is one of the most basic features of life. In this talk I will describe a synthesis of theoretical and experimental work that attempts to answer some basic questions about issues of transport important to multicellular life, using various model organisms to study the high Peclet number regime in which advection strongly dominates diffusion. Topics to be addressed include metabolic dynamics, phototaxis and flagellar synchronization in the colonial alga Volvox, the microfluidics of cytoplasmic streaming in the aquatic plant Chara, and dynamics of the vacuolar membrane in the terrestrial plant Arabidopsis. Emphasis will be placed on outstanding open problems in applied mathematics arising from these investigations.

09/11
Matthew West
College of Engineering
University of Illinois, Urbana-Champaign

Optimal Mixing in Microfluidic Channels and the Cutoff Phenomenon

We present an optimization framework for designing fast-mixing microfluidic channels, based on approximate Markov Chain models of the mixing process. Using this, we obtain two optimized channel designs, one surface-etched and one 3D structure, both of which perform better than existing mixing channels. The approximate Markov Chain models of mixing and microfluidic experimental results both show the super-exponential mixing rates characteristic of mixing by chaotic maps. We present numerical and analytical evidence that suggests that this is in fact a cutoff phenomenon in the sense of Diaconis, and that such phenomena are widespread in chaotic map mixing.

09/18
Jinjie Liu
Department of Mathematics
The University of Arizona

Nonorthogonal Overlapping Yee FDTD Method with Application to Optical Force Computation

We propose a new overlapping Yee (OY) method for solving time-domain Maxwell's equations on nonorthogonal grids. The proposed method is a direct extension of the Finite-Difference Time-Domain (FDTD) method to irregular grids. The OY algorithm is stable and maintains second-order accuracy of the original FDTD method, and it overcomes the late-time instability of the previous FDTD algorithms on nonorthogonal grids. Applications including scattering problems and optical force computation will be presented to illustrate the accuracy, stability, convergence, and efficiency of the OY method.

09/25
Ildar Gabitov
Department of Mathematics
The University of Arizona

Stochastic Pulse-Switching in a Degenerate Resonant Optical Medium

We studied the statistical properties of Maxwell-Bloch soliton solutions describing optical pulses propagating through a three-level disordered atomic medium.

October

10/02
Yong Zeng
Department of Mathematics
The University of Arizona

A Classical Model of Second-Harmonic Generation from Metal-Based Metamaterials

We developed a classical electron-gas model, which is well known in Plasma Physics as cold plasma wave equation, to interpret recent experiments regarding second-harmonic generation from metal nanoparticles. By employing a three-dimensional finite-difference time-domain approach, we numerically investigate the dependence of second-harmonic generation on the geometrical symmetry, plasmonic resonance, and polarization of the incident fundamental-frequency wave.