Annual Report 2008.pdf - SAMSI

Knut Solna
University of California-Irvine
Department of Mathematics
ksolna@math.uci.edu
“Effective Transport Equations and Enhanced Backscattering in Random Waveguides” (with
Josselin Garnier)
Sheldon Wang
New Jersey Institute of Technology
Mathematical Sciences Department
xwang@njit.edu
“On Finite Element Modeling of Random Media”
Yimin Xiao
Michigan State University and SAMSI
Department of Statistics
xiaoyimi@stt.msu.edu
“Gaussian and Stable Random Fields: Dependence Structure and Fractal Properties”
Isotropic and anisotropic random fields arise naturally in probability theory, statistics and have
been applied in a wide range of scientific areas. Examples include fractional Brownian motion,
solutions to stochastic heat and wave equations driven by Gaussian or stable noises, various
spatiotemporal processes and many more. We provide general methods for studying the
dependence structure, sample path regularity, and fractal properties of Gaussian and stable
random fields.
Ke Xu
University of North Carolina-Chapel Hill
Department of Mathematics
xuke@email.unc.edu
“On the Correspondence Between Creeping Flows of Viscous and Viscoelastic Fluids”
From the wealth of exact solutions for Stokes flow of simple viscous fluids [Pozrikidis, Oxford
University Press, Oxford, 1997, 222-311], the classical “viscous-viscoelastic correspondence”
between creeping flows of viscous and linear viscoelastic materials yields exact viscoelastic
creeping flow solutions. The correspondence is valid for an arbitrary prescribed source: of force,
flow, displacement or stress; local or nonlocal; steady or oscillatory. Two special
Stokes singularities, extended to viscoelasticity in this way, form the basis of
modern microrheology [Mason and Weitz, Phys. Rev. Lett. 74 (1995), 1250-1253]: the Stokeslet
(for a stationary point source of force) and the solution for a driven sphere. We amplify these