Wiener-Hopf method

Duduchava R., Wendland W. (1995) The Wiener-Hopf method for system of pseudodifferential equations with applications to crack problems. Integr. Eqs. and Oper. Theory 23, 294-335. 

The Mode III problem has received most attention essentially because it is the simplest case. Mode I and II problems are considerably more difficult, but have been considered in a limiting case by Atkinson (1979), and again using an exact, partly numerical application of the Wiener-Hopf method, by Popelar and Atkinson (1980). But the physical Importance of the Mode III problem is cast into doubt by experimental observations of Knauss (1970 b) indicating that such cracks do not grow rectilinearly, at least in brittle materials. 

The solution was first obtained independently by Wertheim [32] and Thiele [33] using Laplace transfonns. Subsequently, Baxter [34] obtained the same solutions by a Wiener-Hopf factorization teclmique. This method has been generalized to charged hard spheres. 

Noble, B., Methods Based on The Wiener-Hopf Technique for the Solution of Partial Differential Equations, London Chelsea Publishing, 1988. 

The Wiener-Hopf Technique An Alternative to the Singular Eigenfunction Method... 

The Landman-Montroll method, based on the Wiener-Hopf technique and requiring a knowledge of 9(0 in the physical region only [3]. 

Baxter discussed the Wiener-Hopf factorization of the inverse structure factor for disordered fluids [182]. He was able to split OZ2 Eq. (Ill) into a pair of equations, which provide a route to determine c (R. Dixon and Hutchinson complemented Baxter s developments by stating conditions for proper R values (in simulation work with cubic boxes / co T / 2) and proposed a highly accurate minimization method to solve Baxter s equations [183]. These R proper values will be denoted by R and termed zeros hereafter. As proven by the present author in extensive calculations [96,103,155], there is always (at least) one zero when physically significant functions are analyzed. By following this procedure (BDH), except for very low densities, one normally obtains more than one R [Pg.111]

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