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A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions.… (More)

SUMMARY In this paper we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as 'bubble' shape functions. A series of simple test… (More)

A new method of evaluating overlap integrals involving orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. For a large class of polynomials and for sufficiently large orders, these coefficients can be written explicitly as Taylor series in terms of powers of = 1/n, where n is… (More)

The aim of this work is to model the evolution of the modal distribution of the electromagnetic field as it propagates along a randomly deformed multimode optical waveguide. When the number of guided modes becomes large we can regard the discrete set of modes as a quasi continuum. In some cases, nearest neighbor coupling predominates over other power… (More)

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