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Asymptotic analysis of a system of algebraic equations arising in dislocation theory

Abstract:

The system of algebraic equations given by $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$ appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. We present a general analysis of systems of this type for a > 0 and n la...

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Publication date:
2010-01-01
URN:
uuid:fc3210d3-14ee-45a5-bded-5d22ab9871a2
Local pid:
oai:eprints.maths.ox.ac.uk:994

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