Bifurcations in the Regularized Ericksen Bar Model |
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Authors: | M Grinfeld G J Lord |
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Institution: | (1) Department of Mathematics, The University of Strathclyde, Glasgow, G1 1XH, UK;(2) Department of Mathematics and Maxwell Institute, Heriot-Watt University, Edinburgh, EH14 4AS, UK |
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Abstract: | We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary
conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods,
the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller’s conjecture
(Müller, Calc. Var. 1:169–204, 1993) concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of
the primary branch connections that occur in this problem. We give a reformulation of Müller’s conjecture and suggest two
further conjectures based on the local analysis and numerical observations. We conclude by analysing a “loop” structure that
characterizes (k,3k) bifurcations.
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Keywords: | Microstructure Lyapunov– Schmidt analysis Ericksen bar model |
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