By Leroy A. MacColl (ed.)
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Extra resources for Applied Probability
Y'. " It will be required shortly in our discussion of diffraction by smooth bodies. 236). 17. The Surface Eiconal Equation and Surface Rays In preparation for our study of diffraction by smooth bodies we consider now the initial value problem for the eiconal equation on a surface. We are concerned with a function 8 defined only on a surface S, and with initial values prescribed on a curve 44 Joseph B. Keller and Robert M. Lewis which lies on that surface. Let X = X ( r 1 , r2) be a parametric equation for the regular surface S.
Then we can confine our attention to a plane normal to the edges. In this plane let the screen lie on the y-axis of a rectangular co-ordinate system with the edges of the slit at x = 0 and y = ±a. Let the incident field be the plane wave ui = eik(xcosa-ysina) . 212) Each edge is hit by one ray which produces singly-diffracted rays leaving the edge in all directions in the normal plane. Two singly-diffracted rays, one from each edge, pass through any point P other than an edge. 209). 13. 13. 213) can be improved by adding to it the leading term of the doublydiffracted field u~(P), which consists of the sum of two terms corresponding to the two doubly-diffracted rays passing through P.
Are infinite there. However, the limit id, introduced in Subsection 1. 7, is finite. 204) The proportionality factor D will be called a diffraction coefficient. 158). In general, diffraction coefficients, unlike reflection and transmission coefficients, cannot be obtained so simply 36 Joseph B. Keller and Robert M. 11. from the prescribed boundary conditions. Instead they can be obtained either from the solution of canonical problems or by boundary layer methods . The latter methods for > 0.
Applied Probability by Leroy A. MacColl (ed.)