We consider a two-dimensional transport equation subject to small diffusive perturbations. The transport equation is given by a Hamiltonian flow near a compact and connected heteroclinic cycle. We investigate approximately harmonic functions corresponding to the generator of the perturbed transport equation. In particular, we investigate such functions in the boundary layer near the heteroclini...

On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined, infinitesimal isometries do not exist in general. The complete prolongation of the Killing equation is a PDE on the bundle of 1-jets of vector fields. Restricted to a curve, it becomes an ODE that generalizes the Jacobi equation. A solution of this ODE is call...

Solute mass transport in porous media is strongly correlated with pore fluid flow. The analysis of solute transport is an effective means for studying medium heterogeneities. In this study, we discuss the effects of heterogeneity on the tracer transport. Assuming steady fluid flow, we have simulated tracer transport in various permeability heterogeneities. The results show that the tracer distr...

Rui M. R. de Bastos SUPERPOSITION RENDERING: Increased Realism for Interactive Walkthroughs (Under the direction of Dr. Frederick P. Brooks, Jr.) The light transport equation, conventionally known as the rendering equation in a slightly different form, is an implicit integral equation, which represents the interactions of light with matter and the distribution of light in a scene. This research...

Rui M. R. de Bastos SUPERPOSITION RENDERING: Increased Realism for Interactive Walkthroughs (Under the direction of Dr. Frederick P. Brooks, Jr.) The light transport equation, conventionally known as the rendering equation in a slightly different form, is an implicit integral equation, which represents the interactions of light with matter and the distribution of light in a scene. This research...

In the field of laser generated high energy density physics, hydrodynamics is considered to be a very popular approach of continuum description of plasma. Radiation, as another physical phenomenon, takes its significant part in energy transport [1] and [2]. This multiphysics context can be found e.g. in Tokamaks and Inertial Confinement Fusion systems and a great effort has been engaged to simu...

-The finite element response matrix method has been applied to the solution of the neutron transport equation. This method has previously been applied to the neutron diffusion equation for coarse mesh reactor analysis with excellent results. As with the diffusion equation implementation, the transport method employs a local-global projection technique to allow treatment of internal heterogeneit...