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

© 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

Analytical determination of the Landau-Ginzburg parameters of (100) metal homoepitaxial systems

In the initial stages of homoepitaxial growth on the (100) surface of metals such as Ag, Fe, Cu, Ni, and Pd, where the clean surface does not reconstruct, two-dimensional islands with compact, near-square shapes are formed. In order to determine the phenomenological material parameters of the nonlinear and nonlocal Landau-Ginzburg theory, which describes the metal homoepitaxial systems mentioned above, an atomistic model for these systems is developed. Based on this model, we derive analytical relationships between the Landau-Ginzburg parameters A, B, C, and D, and the parameters of the homoepitaxial system (such as coverage, first-neighbour interaction energy, etc.). We find that the Landau-Ginzburg parameters of the system depend on the specific material as well as on the coverage of the surface. We then apply the method to the Ag/Ag(100) system. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200668.47.De Metallic surfaces, 61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling, 64.60.Qb Nucleation,