Symmetry of uniaxial global Landau-de Gennes minimizers in the\ud theory of nematic liquid crystals

We extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solutions) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures

Una experiència universitària saludable i noviolenta

Des del 1962, el Doctor Héctor Abad Gómez, Professor de la Universitat d’Antioquia i Defensor dels Drets Humans, posava de manifest el fet de que la violència havia de ser considerada com el principal problema de Salut Pública, deia: “la violència és només un símptoma de mals socials profunds, com ara la injustícia, la pobresa, la mala distribució de la riquesa, la ignorància o el fanatisme. Provar d’acabar amb la violència amb “una altra violència” és com pretendre curar una malaltia amb una altra malaltia.” i animava a investigar més sobre aquest assumpte i als governs els demanava que busquessin una solució.Desde 1962, el Doctor Héctor Abad Gómez, Profesor de la Universidad de Antioquia y Defensor de los Derechos Humanos, llamaba la atención sobre el hecho de que la violencia debía ser considerada el principal problema de Salud Publica, decía: “la violencia es solo un síntoma de males sociales profundos, tales como la injusticia, la pobreza, la mala distribución de las riquezas, la ignorancia o el fanatismo. Tratar de acabar la violencia con “otra violencia” es como pretender curar una enfermedad con otra enfermedad.” e invitaba a investigar mas sobre el asunto y a los gobiernos a buscar una solución

Determination of the zero-order fringe position in digital speckle pattern interferometry

A method for determining the position of the zero-order fringe in a metrological experiment with digital speckle pattern interferometry is proposed. It is based on an averaging procedure with shifted images obtained before and after a load is applied. This technique is a complement to the phase-shifting methods. Experimental examples are shown

Γ-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity

The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-014-0820-3Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (Arch Rational Mech Anal 197:619–655, 2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The expression of the functional involves a volume integral and two surface integrals, and this fact makes the problem numerically intractable. In this paper we propose an approximation (in the sense of Γ-convergence) by functionals involving only volume integrals, which makes a numerical approximation by finite elements feasible. This approximation has some similarities to the Modica–Mortola approximation of the perimeter and the Ambrosio–Tortorelli approximation of the Mumford–Shah functional, but with the added difficulties typical of nonlinear elasticity, in which the deformation is assumed to be one-to-one and orientation-preservingD. Henao gratefully acknowledges the Chilean Ministry of Education’s support through the FONDE-CYT Iniciación project no. 11110011. C. Mora-Corral has been supported by Project MTM2011-28198 of the Spanish Ministry of Economy and Competitivity, the ERC Starting grant no. 307179, the “Ramón y Cajal” programme and the European Social Fund. X. Xu acknowledges the funding by NSFC 1100126