Past Events

The size effects at micro/nano-scale are first discussed. The scale invariance and the applications in mathematical modeling at nano-scale is then presented. An important concept such as the scale gap is introduced and we particularly discuss the...

We first discuss the scale invariance and electromagnetic modeling at nano-scale. For 3D time-harmonic Maxwell’s equations and 3D time-dependent Maxwell’s equations in composite materials, we presented the multi-scale asymptotic expansions and...

Multi-scale asymptotic methods are investigated for the parabolic equation with rapidly oscillating coefficients arising from heat transfer in composite or porous media. For the dual-phase-lag heat transfer model in composite media, we first applied...

In recent years, multi-scale modeling and computation have been widely used in the study of complex problems arising from science and engineering. The first lecture begins with an introduction of homogenization and main idea of multi-scale methods...

"Think analog, act digital" is a motto that is relevant to scientific computing and algorithm design in a variety of disciplines, including numerical analysis, image/signal processing, and computer graphics. Here, we will argue that cardinal splines...

Turbulence and other complex flows are often characterized by their transport and mixing properties. Turbulence can greatly enhance molecular viscosity for the transport of momentum, and molecular diffusion coefficients for the transport of heat...

Simple random walk is well understood. However, if we condition a random walk not to intersect itself, so that it is a self-avoiding walk, then it is much more difficult to analyze and many of the important mathematical problems remain unsolved. This...