University of Alberta

We introduce a 2x2 nonlinear nonlocal system. On the one hand, it models possible blow-up mechanism in the 3D Euler equations; On the other hand, it can be seen as a further step in the recent progress in understanding the role of nonlocal operators...

I will survey some recent results on several types of aggregation equations. These are continuum models used to describe the swarming phenomenon in biology. I will focus on mathematical issues related to the basic understanding of these equations...

Natural landscapes are often not homogeneous but show spatial variation in environmental conditions. Natural and human disturbances result in additional landscape fragmentation and heterogeneity. In this talk, I will consider (a) conditions under...

The zero Debye length asymptotic of the Schrodinger-Poisson system in Coulomb gauge for ill-prepared initial dada is studied. We prove that the Debye length to the current density defined by the solution of the Schrodinger-Poisson system in Coulomb...

Efficient algorithms have recently been developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are...

A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalised...

This talk outlines multiscale problems which combine techniques of model reduction and filtering. Multiple time scales occur in models throughout the sciences and engineering, where the rates of change of different variables differ by orders of...

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...

Morphogens (ligands) are molecular substances synthesized at some localized source and bound to cell surface receptors and other molecules as they are transported away from their source. The concentration gradients of different morphogen-receptor...