On the role of higher order deformation gradients in necking, spinodal decomposition and neuron firing

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© 2017 Elsevier Ltd This is a modest contribution in memory of Gérard Maugin-a contemporary French scholar of Paris who inspired many young scientists in Greece and maintained special ties with Aristotle University and Thessaloniki. It introduces three particular areas of research in nonlinear science that he defined in collaboration with the third author and presents preliminary one-dimensional results mainly due to previous work of the first author. These pertain to the phenomena of necking in cold drawing, spinodal decomposition in diffusive phase transformations and energy transfer in neuronal microtubules. The common ingredient in all three is the introduction of higher order gradients of deformation in a variational formalism, in order to describe solitary waves and pattern formation that emerge from uniform states when the system enters its nonconvex free energy regime.

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Mechanics Research Communications