Rigidity for C1C^1 actions on the interval arising from hyperbolicity I: solvable groups

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed point at the interior, then the action is topologically conjugated to that of an affine group. Moreover, in case of non-Abelian image, we show a rigidity result concerning the multipliers of the homotheties, despite the fact that the conjugacy is not necessarily smooth. Some consequences for non-solvable groups are proposed. In particular, we give new proofs/examples yielding the existence of finitely-generated, locally-indicable groups with no faithful action by $C^1$ diffeomorphisms of the interval.Comment: A more detailed proof of Proposition 4.15 adde

Explosive synchronization in weighted complex networks

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and non linear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states

La Policia dins la comunitat : la interacció policial en les societats complexes

Malgrat la seva implantació social, la policia és una institució poc estudiada. Aquesta és, a les societats complexes, una agència fonamental en la gestió de problemes i conflictes. La quantitat i diversitat del treball que realitza en fan un element bàsic de la vida en societat. L'impacte i les conseqüències del fenomen de la immigració a la societat actual alteren de forma significativa les estructures socials i demogràfiques tradicionals. La implantació de noves formes culturals, derivades d'aquest fenomen, fa incidència en la diversitat social i també en el treball policial. Les persones immigrants formen part de la societat i no estan —o no haurien d'estar— al marge del treball de la policia.Despite its social establishment, the Police are an institution not very studied. The Police represents in sophisticated societies an essential agency for the management of problems and conflicts. The amount and diversity of tasks done by the Police makes this institution a basic element of the society. The impact and consequences of the immigration phenomenon in the actual society are changing in a significant way the traditional social and demographic framework. The introduction of new cultural forms, as a result of this phenomenon, has a bearing on the social diversity and also on the daily Police actions. Immigrants are part of the society and they are not —and should not be— left out by the Police.A pesar de su implantación social, la policía es una institución poco estudiada. Ésta es, en las sociedades complejas, una agencia fundamental en la gestión de problemas y conflictos. La cantidad y diversidad del trabajo que realiza hacen de ella un elemento básico de la vida en sociedad. El impacto y las consecuencias del fenómeno de la inmigración en la sociedad actual alteran de forma significativa las estructuras sociales y demográficas tradicionales. La implantación de nuevas formas culturales, derivadas de este fenómeno, incide en la diversidad social y también en el trabajo policial. Las personas inmigrantes forman parte de la sociedad y no están —o no deberían de estar— al margen del trabajo de la policía

A family of well-balanced WENO and TENO schemes for atmospheric flows

We herein present a novel methodology to construct very high order well-balanced schemes for the computation of the Euler equations with gravitational source term, with application to numerical weather prediction (NWP). The proposed method is based on augmented Riemann solvers, which allow preserving the exact equilibrium between fluxes and source terms at cell interfaces. In particular, the augmented HLL solver (HLLS) is considered. Different spatial reconstruction methods can be used to ensure a high order of accuracy in space (e.g. WENO, TENO, linear reconstruction), being the TENO reconstruction the preferred method in this work. To the knowledge of the authors, the TENO method has not been applied to NWP before, although it has been extensively used by the computational fluid dynamics community in recent years. Therefore, we offer a thorough assessment of the TENO method to evidence its suitability for NWP considering some benchmark cases which involve inertia and gravity waves as well as convective processes. The TENO method offers an enhanced behavior when dealing with turbulent flows and underresolved solutions, where the traditional WENO scheme proves to be more diffusive. The proposed methodology, based on the HLLS solver in combination with a very high-order discretization, allows carrying out the simulation of meso- and micro-scale atmospheric flows in an implicit Large Eddy Simulation manner. Due to the HLLS solver, the isothermal, adiabatic and constant Brunt-Väisälä frequency hydrostatic equilibrium states are preserved with machine accuracy