Topic:  Non-hexagonal lattices from a two species interacting system Abstract: A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs, the two species appear alternately on a lattice.  A minimal two species periodic assembly

Title: Numerical simulations of macroscopic quantities for stochastic differential equations with alpha-stable processes Abstract: The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, $\alpha$-stable type L\'evy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and

Topic:  Fast Solutions of Large Linear Systems and Eigenvalue Problems by Exploring Structures Abstract: Solving large linear systems and eigenvalue problems remains to be the key computational tasks in scientific computing, data processing, and engineering simulations. Practical numerical problems often introduce various structures into the matrix representations. In this talk, we show the existence of

Title: Phase field method for geometric moving interface problems and their numerical approximations Abstract:  In this talk I shall first give a brief introduction to the phase field method for general geometric moving interface problems. The focus will be on presenting its idea, formulation,and relationship to other methods for moving interface problems such as the