Last-passage Monte Carlo algorithm for mutual capacitance.

We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and terminate on its surface. However, this algorithm does not seem to generalize to mutual capacitance problems. The last-passage algorithm, in a sense, is the time reversal of the first-passage algorithm; it involves averages over particles that initiate on an absorbing surface, leave that surface, and diffuse away to infinity. To validate this algorithm, we calculate the mutual capacitance matrix of the circular-disk parallel-plate capacitor and compare with the known numerical results. Good agreement is obtained.

Generalized ISAR--part I: an optimal method for imaging large naval vessels.

We describe a generalized inverse synthetic aperture radar (ISAR) process that performs well under a wide variety of conditions common to the naval ISAR tests of large vessels. In particular, the generalized ISAR process performs well in the presence of moderate intensity ship roll. The process maps localized scatterers onto peaks on the ISAR plot. However, in a generalized ISAR plot, each of the two coordinates of a peak is a fixed linear combination of the three ship coordinates of the scatterer causing the peak. Combining this process with interferometry will then provide high-accuracy three-dimensional location of the important scatterers on a ship. We show that ISAR can be performed in the presence of simultaneous roll and aspect change, provided the two Doppler rates are not too close in magnitude. We derive the equations needed for generalized ISAR, both roll driven and aspect driven, and test them against simulations performed in a variety of conditions, including large roll amplitudes.

Generalized ISAR--part II: interferometric techniques for three-dimensional location of scatterers.

This paper is the second part of a study dedicated to optimizing diagnostic inverse synthetic aperture radar (ISAR) studies of large naval vessels. The method developed here provides accurate determination of the position of important radio-frequency scatterers by combining accurate knowledge of ship position and orientation with specialized signal processing. The method allows for the simultaneous presence of substantial Doppler returns from both change of roll angle and change of aspect angle by introducing generalized ISAR ates. The first paper provides two modes of interpreting ISAR plots, one valid when roll Doppler is dominant, the other valid when the aspect angle Doppler is dominant. Here, we provide, for each type of ISAR plot technique, a corresponding interferometric ISAR (InSAR) technique. The former, aspect-angle dominated InSAR, is a generalization of standard InSAR; the latter, roll-angle dominated InSAR, seems to be new to this work. Both methods are shown to be efficient at identifying localized scatterers under simulation conditions.

Edge distribution method for solving elliptic boundary value problems with boundary singularities.

Elliptic boundary value problems are difficult to treat in the vicinity of singularities, i.e., edges and corners, of the boundary. The concentration of electrical charge on the edges and corners of a conductor is perhaps the simplest example of such problems. Here we provide a rapid method for accurate treatment of these problems. It utilizes a Green's-function-based implementation of last-passage Monte Carlo diffusion methods. This is combined with a diffusion algorithm for the scaling of solutions to the Laplace equation near a corner singularity to yield the solution of a benchmark problem: the charge distribution near the edge and corner of a conducting cube.

First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface.

Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best first-passage diffusion algorithm) in solving the classical problem of computing the charge distribution on a conducting disk held at unit voltage. All three algorithms show detailed agreement with the known analytic solution to this problem.