Acousto-optic imaging in diffuse media is a dual wave-sensing technique in which an acoustic field interacts with multiply scattered laser light. The acoustic field causes a phase modulation in the optical field emanating from the interaction region, and this phase-modulated optical field carries with it information about the local optomechanical properties of the media. We report on the use of...

Statistical continuum approach is used to predict effective conductivity of anisotropic random porous heterogeneous media using twopoint correlation functions. Probability functions play a critical role in describing the statistical distribution of different constituents in a heterogeneous media. In this study a three-dimensional two-point correlation function is utilized to characterize the an...

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion ...

We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. Well-posedness that is global in time in the two dimensional case and local in time in the three dimensional case are established. Several blow-up criterions in the three dimensional case are provided as well.

The paper shows how established two-dimensional multi-media technologies were used to develop robust prototypes which were then observed in use by children. Results from these phases have been used to guide the current phase of work. This involves the construction of a three-dimensional shared VE using the experimental Deva Virtual Reality system.

We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equat...

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction-diffusion equations with spatially periodic diffusive fluxes. The result connects wave pinning phenomena in lattice differential equations and in reaction-diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, wher...