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De Leon M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Vilarino S.,Centro Universitario Of La Defensa
International Journal of Geometric Methods in Modern Physics | Year: 2014

In this paper, we extend the geometric formalism of the Hamilton-Jacobi theory for time-dependent Mechanics to the case of classical field theories in the k-cosymplectic framework. © 2014 World Scientific Publishing Company. Source

Berselli L.C.,University of Pisa | Cordoba D.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Granero-Belinchon R.,University of California at Davis
Interfaces and Free Boundaries | Year: 2014

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R2 or a bounded strip S D Rx (-π/2, π/2). The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth. © European Mathematical Society 2014. Source

Colombo L.,University of Michigan | De Diego D.M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Journal of Geometric Mechanics | Year: 2014

In this paper, we describe a geometric setting for higher-order Lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner- Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Poincaré equations, optimal control of underactuated control systems whose configuration space is a Lie group are shown, among others, along the paper © American Institute of Mathematical Sciences. Source

Bernardi O.,University Paris - Sud | Rue J.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
European Journal of Combinatorics | Year: 2012

It is well-known that the triangulations of the disc with n+2 vertices on its boundary are counted by the nth Catalan number C(n)=1/n+1 ( 2n n). This paper deals with the generalisation of this problem to any compact surface S with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface S with n vertices on its boundary. More generally, we determine the asymptotic number of dissections of S{double-struck} when the faces are δ-gons with δ belonging to a set of admissible degrees δ⊆ δ {3, 4, 5,...}. We also give the limit laws for certain parameters of such dissections. © 2011 Elsevier Ltd. Source

Garcia-Fernandez M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Communications in Mathematical Physics | Year: 2014

This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the Ricci tensor of a generalized metric, inspired by the work of Coimbra, Strickland-Constable and Waldram. © 2014 Springer-Verlag Berlin Heidelberg. Source

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