On the role of higher order deformation gradients in necking, spinodal decomposition and neuron firing. (October 2018) - Petsos, G.; Konstantinidis, A.; Aifantis, E.C.
Highlights: Τhree areas of research in nonlinear science are considered that G. Maugin defined in collaboration with the third author. Necking in cold drawing, spinodal decomposition in diffusive phase transformations and energy transfer in neuronal microtubules. In all three the common ingredient is the introduction of higher order gradients of deformation in a variational formalism. Abstract: 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.