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The dynamics of line singularities in three different physical systems are considered, namely vortices in an inviscid fluid, vortices in a type-II superconductor, and dislocations in an elastic crystal. When the core of the singularity can be re[...]texto impreso
We consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x[...]texto impreso
We shall prove that the celebrated Renyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropie[...]texto impreso
Putnis, Andrew ; Pina Martínez, Carlos Manuel ; Astilleros García-Monge, José Manuel ; Fernández-Díaz, Lourdes ; Prieto Rubio, Manuel | Royal Society of London | 2003The study of nucleation and growth mechanisms of salts from aqueous solutions, as a function of supersaturation, is described using both macroscopic and microscopic experiments. In situ observations in a fluid cell in an atomic force microscope [...]texto impreso
Oleaga Apadula, Gerardo Enrique ; Herrero, Miguel A. ; Velázquez, J.J. L. | Royal Society of London | 2004-02-08Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle psi not equal 0 at their junction, examples can be[...]texto impreso
Herrero, Miguel A. ; Oleaga Apadula, Gerardo Enrique ; Velázquez, J.J. L. | Royal Society of London | 2004Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle psi not equal 0 at their junction, examples can be[...]texto impreso
We first establish some general results connecting real and complex Lie algebras ofirst-order diferential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order diferential operators in R^2 .[...]
