Energy dependence of the quark masses and mixings

The one loop Renormalization Group Equations for the Yukawa couplings of quarks are solved. From the solution we find the explicit energy dependence on $t=\ln E/\mu$ of the evolution of the {\em down} quark masses $q=d,s,b$ from the grand unification scale down to the top quark mass $m_{t}$. These results together with the earlier published evolution of the {\em up} quark masses completes the pattern of the evolution of the quark masses. We also find the energy dependence of the absolute values of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $|V_{ij}|$. The interesting property of the evolution of the CKM matrix and the ratios of the quark masses: $m_{u,c}/m_{t}$ and $m_{d,s}/m_{b}$ is that they all depend on $t$ through only one function of energy $h(t)$.Comment: Talk presented at the IX Mexican School on Particles and Fields, August 9-19, Metepec, Pue., Mexico. To be published in the AIP Conference Proceedings. 5 pages and 1 eps figure included in the tex

Electronic structure of the ferromagnetic superconductor UCoGe from first principles

The superconductor UCoGe is analyzed with electronic structure calculations using Linearized Augmented Plane Wave method based on Density Functional Theory. Ferromagnetic and antiferromagnetic calculations with and without correlations (via LDA+U) were done. In this compound the Fermi level is situated in a region where the main contribution to DOS comes from the U-5f orbital. The magnetic moment is mainly due to the Co-3d orbital with a small contribution from the U-5f orbital. The possibility of fully non-collinear magnetism in this compound seems to be ruled out. These results are compared with the isostructural compound URhGe, in this case the magnetism comes mostly from the U-5f orbital

Class of PPT bound entangled states associated to almost any set of pure entangled states

We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition nor by the realignment criterion, i.e. by any permutational criterion in the bipartite setting. In the range in which the states are Positive under Partial Transposition (PPT), they are not distillable; on the other hand, the states in the considered class are provably distillable as soon as they are Nonpositive under Partial Transposition (NPT). The states are associated to any set of more than two pure states. The analysis is extended to the multipartite setting. By an opportune selection of the set of multipartite pure states, it is possible to construct mixed states which are PPT with respect to any choice of bipartite cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we show that every $k$-positive but not completely positive map is associated to a family of nondecomposable maps.Comment: 12 pages, 3 figures. To appear in Phys. Rev.

Large Time Existence for Thin Vibrating Plates

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as $h\to 0$ is either the nonlinear von K\'arm\'an plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation

Discrete model for laser driven etching and microstructuring of metallic surfaces

We present a unidimensional discrete solid-on-solid model evolving in time using a kinetic Monte Carlo method to simulate micro-structuring of kerfs on metallic surfaces by means of laser-induced jet-chemical etching. The precise control of the passivation layer achieved by this technique is responsible for the high resolution of the structures. However, within a certain range of experimental parameters, the microstructuring of kerfs on stainless steel surfaces with a solution of $\mathrm{H}_3\mathrm{PO}_4$ shows periodic ripples, which are considered to originate from an intrinsic dynamics. The model mimics a few of the various physical and chemical processes involved and within certain parameter ranges reproduces some morphological aspects of the structures, in particular ripple regimes. We analyze the range of values of laser beam power for the appearance of ripples in both experimental and simulated kerfs. The discrete model is an extension of one that has been used previously in the context of ion sputtering and is related to a noisy version of the Kuramoto-Sivashinsky equation used extensively in the field of pattern formation.Comment: Revised version. Etching probability distribution and new simulations adde

The loss of anisotropy in MgB2 with Sc substitution and its relationship with the critical temperature

The electrical conductivity anisotropy of the sigma-bands is calculated for the (Mg,Sc)B2 system using a virtual crystal model. Our results reveal that anisotropy drops with relatively little scandium content (< 30%); this behaviour coincides with the lowering of Tc and the reduction of the Kohn anomaly. This anisotropy loss is also found in the Al and C doped systems. In this work it is argued that the anisotropy, or 2D character, of the sigma-bands is an important parameter for the understanding of the high Tc found in MgB2

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Introduction: Tricksters, humour and activism

This special issue, entitled ‘The Trickster Activist in Global Humour and Comedy’, investigates the relevance of the concept of the trickster for explaining activist expressions that emanate from comedians, or that appear in comedy and humour more generally. Comedy has traditionally been viewed as an aesthetic or entertainment medium. It has often been charged with encouraging stereotype and the affirmation of mainstream audience beliefs. Despite this, we argue, there have been moments in recent history where comedians have given their performances an increased level of social and political consciousness that resonates with the public at large, or with sections of the public. Comedians, we argue, are able to reach this level of social commentary due to their potential to become tricksters. Paradoxically, the mythical trickster is a liminal entity, one that is adept at destruction as well as creation, or at conservativism as well radicalism. The articles in this issue explore the complexity of the trickster concept, showing some of the polysemy involved in the social activism enabled by comedy and humour

Geometrical organization of solutions to random linear Boolean equations

The random XORSAT problem deals with large random linear systems of Boolean variables. The difficulty of such problems is controlled by the ratio of number of equations to number of variables. It is known that in some range of values of this parameter, the space of solutions breaks into many disconnected clusters. Here we study precisely the corresponding geometrical organization. In particular, the distribution of distances between these clusters is computed by the cavity method. This allows to study the `x-satisfiability' threshold, the critical density of equations where there exist two solutions at a given distance.Comment: 20 page