Diffraction has been numerically modeled using a Monte Carlo statistical analysis. The Heisenberg uncertainty principle has been applied to attain this goal. Example solutions have been studied and are presented to illustrate the utility and accuracy of the technique.

The statistical technique of photon ray tracing, commonly known as the Monte Carlo Method, has been successfully used on numerous radiant transport problems. Because of its simplicity, the method can be applied to complex systems which are otherwise not amenable to a corrveñtional approach such as the solution of integral -differential equations. The primary limitation of the method is the wide ranging complementary techniques necessary in reducing the amount of computations in each analysis. This paper presents such a technique that can be used in the analysis of radiant interchange. Applied to an optical system, the method can be used to solve for image quality, system attenuation, off -axis energy rejection, and thermal radiation heat transfer. Results of three demonstrative examples are also presented.

Abstract. A simple analytical model is proposed which describes the region between a plane, cooled nonablating anode and an arc column normal to the anode The model takes an initial arc contraction into account due to the low temperature of the anode ("thermal pinch"). The resulting magnetic pinch effect leads to an entrainment of cold gas which determines via an energy balance the final shape of the arc in the anode region. The conservation equations are solved numerically for the anode region with a relaxation method, and results are presented based on atmospheric arcs in nitrogen. Finally, limitations of this model and necessary refinements are briefly discussed; possible extensions of the arc parameter range for future work are proposed.

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