Existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition

We give necessary and sufficient conditions on body and traction forces for the existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition.     

Growth conditions and regularity,a counterexample

It is shown that the so-called growth conditions are necessary for the local regularity of minimizers.This paper has been written while the author was visiting the Mathematisches Institut der Universität Bonn under the support of the Sonderforschungsberich 256.     

A Simple Generalized Excitability Model Mimicking Salient Features of Neuron Dynamics

A generalization of the FitzHugh—Nagumo model for excitability is provided to account for salient features of Inferior Olive neurons. The base state is a limit cycle and excitability appears as spiking over peaks of the oscillations. The response of the model to various types of external stimulus is also presented. In particular, we show the relevance of an appropriate balance between amplitude and duration of the stimulus.     

Ground states of simple bodies that may undergo brittle fractures

Equilibrium states of elastic-brittle solids that may suffer nucleation of cracks in finite deformation setting are analyzed. Crack patterns are described in terms of appropriate Radon measures, namely curvature varifolds with boundary. A new form of the energy is presented: it includes terms associated with the curvature of margins and tips of possible cracks. Existence of minima of the energy is established in classes of pairs of deformation and families of varifolds. Configurational balances in weak form are determined with reference to generic curvature varifolds with boundary. They include non-standard terms associated with the curvatures involved in the energy. Pointwise balances of configurational actions are also evaluated in a special case: new pointwise balances at the tips and along the margins of the crack pattern emerge.     

Nonlinear elliptic systems with quadratic growth

We consider nonlinear elliptic systems div (A(x,u)·Du)=f(x,u,Du) with a right-hand side of quadratic growth |f(x,u,p)|a|p|²+b Under suitable assumptions we show that every solution of such system is regular, except possibly on a closed set, whose codimension is greater that two.     

Density results for the <Emphasis Type="Italic">W</Emphasis><Superscript>1/2</Superscript> energy of maps into a manifold

We show that maps from Bⁿ to a smooth compact boundaryless manifold which are smooth out of a singular set of dimension n−2 are dense for the strong topology in W^1/2(Bⁿ,). We also prove that for n≥2 smooth maps from Bⁿ to are dense in W^1/2(Bⁿ,) if and only if π₁()=0, i.e. the first homotopy group of is trivial.     

Excitons and plasmons in wide gaps: Solid rare gases

We develop a model macroscopic response function that describes the electronic response in wide gap insulators. The parameters entering the model, which consists of two coupled oscillators, are fixed by electrostatics. Application is made to both valence and core transitions in solid rare gases. We obtain exciton and plasmon energies in agreement with the available experimental data.