## Radiowave Propagation Techniques

We are interested in developing propagation prediction techniques in various environments such as Rough Surface, Indoor and Outdoor Wireless Communications, Tunnels, Uneven Terrain, Inhomogeneous atmosphere, etc. The goal is to come up with efficient methodologies to make reasonably accurate predictions.

## Stochastic Methods for Wave Propagation

Some of the topics we are exploring in this connection are stochastic formulation of Parabolic Wave Equation, Wave and Telegraph Equations and Material Boundaries, Absorbing Boundaries, etc. More recently we have been developing stochastic based techniques for estimating wildlife location coordinates using time-series of power measurements from nano-tages attached to the animal body. The pinging signal is received via various towers erected along the coastal Atlantic region.The actual measured trajectories (dot-dashed line) and the trajectories predicted by the movement model (solid line) coupled with the Kalman filter are shown in the figure below. Observation time is shown in the color map.

## Computational and Theoretical Electromagnetics

We are studying the use of Feynman-Kac type stochastic representations in determining the electromagnetic field within plasmonic nanomaterials. The methodology allows the solution to be obtained at selected points wihtout having to compute the field globally at all interior points. Furthermore, the methodology leads to complete parallelization. Comparison is shown below between the exact solution and the solution obtained by the stochastic representation for fields inside a plasmonic nanosphere excited by an external vertical electric dipole. Excellent agreement is seen both for the magnitude and phase of the fields even with the use of only a few realizations in the stochastic representation.