Liqun Cao

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...

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...

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...

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 introduce the background and motivation of Hamiltonian systems and symplectic geometry. The basic ideas and the key steps on developing symplectic geometric algorithms are presented. Applications of symplectic geometric methods for...

The heat transfer problem in composite materials has been investigated which contains the nano-scale interface. A molecular dynamics-continuum coupled model is developed to study the heat transport from the macro- to the micro-scales. The model...