The Goldman bracket characterizes homeomorphisms

We show that a homotopy equivalence between compact, connected, oriented surfaces with non-empty boundary is homotopic to a homeomorphism if and only if it commutes with the Goldman bracket. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Raman spectra of alkali halides

In this article, we present a comparative study of the Raman spectra of alkali halides in relation to the lattice dynamics ofBorn andRaman. It is shown that the experimentally observed limit of the second-order spectra in almost all the cases can be explained well by the Lyddane-Sachs-Teller relation. It is also seen, while, an explanation of the second-order Raman spectrum of a crystal of diamond or zinc blende structure requires the frequencies from the critical points,W, Gamma, X andL inBorn's analysis, the frequencies fromGamma, X andL alone are sufficient and necessary for an interpretation of the same onRaman's model. Some similarities in the determination of the long wave properties of crystals like elastic constants and limiting frequencies of the lattice vibrations in the symmetry directions in both the models are pointed out.

Phase-field elasticity model based on mechanical jump conditions

Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition