Arbitrary bi-dimensional finite strain crack propagation

In the past two decades numerous numerical procedures for crack propagation have been developed. Lately, enrichment methods (either local, such as SDA or global, such as XFEM) have been applied with success to simple problems, typically involving some intersections. For arbitrary finite strain propagation, numerous difficulties are encountered: modeling of intersection and coalescence, step size dependence and the presence of distorted finite elements. In order to overcome these difficulties, an approach fully capable of dealing with multiple advancing cracks and self-contact is presented (see Fig.1). This approach makes use of a coupled Arbitrary Lagrangian-Eulerian method (ALE) and local tip remeshing. This is substantially less costly than a full remeshing while retaining its full versatility. Compared to full remeshing, angle measures and crack paths are superior. A consistent continuationbased linear control is used to force the critical tip to be exactly critical, while moving around the candidate set. The critical crack front is identified and propagated when one of the following criteria reaches a material limiting value: (i) the stress intensity factor; or (ii) the element-ahead tip stress. These are the control equations. The ability to solve crack intersection and coalescence problems is shown. Additionally, the independence from crack tip and step size and the absence of blade and dagger-shaped finite elements is observed. Classic benchmarks are computed leading to excellent crack path and load-deflection results, where convergence rate is quadratic

An SU(5)⊗\otimesZ_{13} Grand Unification Model

We propose an SU(5) grand unified model with an invisible axion and the unification of the three coupling constants which is in agreement with the values, at $M_Z$, of $\alpha$, $\alpha_s$, and $\sin^2\theta_W$. A discrete, anomalous, $Z_{13}$ symmetry implies that the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian protecting, at the same time, the invisible axion against possible semi-classical gravity effects. Although the unification scale is of the order of the Peccei-Quinn scale the proton is stabilized by the fact that in this model the standard model fields form the SU(5) multiplets completed by new exotic fields and, also, because it is protected by the $Z_{13}$ symmetry.Comment: 14 pages, more typos correcte

Classical instability of Kerr-AdS black holes and the issue of final state

It is now established that small Kerr-Anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its endpoint state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to co-exist in equilibrium with a certain amount of outside radiation.Comment: 11 pages, RevTex4. v2: small typos corrected. Version to appear in Phys. Rev.

Two-dimensional individual clustering model

10 pagesInternational audienceThis paper is devoted to study a model of individual clustering with two specific reproduction rates in two space dimensions. Given q > 2 and an initial condition in W 1,q (Ω), the local existence and uniqueness of solution have been shown in [6]. In this paper we give a detailed proof of existence of global solution