On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects - magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can " create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU(N) gauge theory at any $N$.Comment: Some references and comments adde

A numerical analysis of the relation between CTOD and fatigue crack growth

El cálculo de la vida a fatiga durante la etapa de propagación de la grieta se suele realizar relacionando da/dN con ΔK. Sin embargo, la influencia que en estos análisis tiene el parámetro ΔK debe recaer en algún otro parámetro no lineal cercano al frente de la grieta, ya que estos son los que realmente controlan la velocidad de crecimiento de la grieta. El principal objetivo del presente artículo es intentar mejorar la comprensión del crecimiento de grieta en fatiga empleando el desplazamiento de apertura de la punta de la grieta (CTOD). Este parámetro no ha sido muy empleado en el problema del cierre de grieta y su propagación en fatiga, teniendo un gran potencial. Por este motivo, se ha realizado un análisis numérico para un amplio rango de cargas de amplitud constante en dos aleaciones de aluminio (6016-T4 y 6082-T6). Cuando no se considera el contacto entre los flancos de la grieta se puede observar una relación bien definida entre el valor máximo de CTOD y ΔK, lo cual indica que no existe influencia de la relación de cargas y valida la mecánica de la fractura elástica lineal. Se ha encontrado una relación lineal entre los valores de CTOD y ΔK al considerar una doble escala logarítmica. Los valores de CTOD cuando se considera el contacto se superpone a los resultados sin contacto, únicamente cuando se emplea el ΔK efectivo, lo cual valida el concepto del cierre de grieta. Se ha encontrado una relación lineal entre da/dN y CTOD cuando se considera una doble escala logarítmica para la aleación de aluminio 6082-T6.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A note on the Markoff condition and central words

We define Markoff words as certain factors appearing in bi-infinite words satisfying the Markoff condition. We prove that these words coincide with central words, yielding a new characterization of Christoffel words

Bidimensionality of Geometric Intersection Graphs

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the corresponding bodies is non-empty. For such graph classes and under natural restrictions on their maximum degree or subgraph exclusion, we prove that the relation between their treewidth and the maximum size of a grid minor is linear. These combinatorial results vastly extend the applicability of all the meta-algorithmic results of the bidimensionality theory to geometrically defined graph classes

An evaluation of location management procedures

This paper gives a comparative description of two scenarios for location management in a mobile telecommunications system. The first scenario uses fixed location and paging areas. Mobiles perform a location update as they enter a new location area. The second scenario uses a time-out based location updating scheme. Mobiles start their timer as they leave the paging area they are currently registered in. As the timer elapses, the mobile performs a location update. Both scenarios also differ in the way paging is performed. In the first scenario it is only necessary to page in the location area the mobile is currently registered in. In order to do this efficiently, the paging is done in a 2-step fashion: mobiles are paged first in the paging area in which they were registered in, and next in the entire location area they are registered in. In the second scenario the mobile is paged in multiple steps: first in the paging area it is registered in, next in a circle of paging areas surrounding that area, and so on, until the mobile is found, or the number of steps has reached a certain upper limit. Results comprise a quantitative and qualitative comparison of these scenarios, and guidelines for optimal applicatio

Backbone colorings for networks: tree and path backbones

We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\rightarrow \{1,2,\ldots\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. We study the cases where the backbone is either a spanning tree or a spanning path

Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult

We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem

Comment on Mott Scattering in strong Laser Field

The first differential cross section for Mott scattering of a Dirac-Volkov electron is reviewed. The expression (26) derived by Szymanowski et al. [Physical Review A {\bf 56}, 3846,(1997)] is corrected. In particular, we disagree with the expression of $(\frac{d\sigma}{d\Omega})$ they obtained and we give the exact coefficients multiplying the various Bessel functions appearing in the scattering differential cross section.Comment: 16 pages, LaTex, added reference for section 3, corrected some typosReport no: LPHEA 02-0

Connecting Terminals and 2-Disjoint Connected Subgraphs

Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that there are at most ${|V \setminus T| \choose |T|-2} \cdot 3^{\frac{|V \setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \leq n/3$ and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case $|T|=2$. We apply our enumeration algorithm to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time $O^*(1.7804^n)$, improving on the recent $O^*(1.933^n)$ algorithm of Cygan et al. 2012 LATIN paper.Comment: 13 pages, 1 figur

A numerical analysis of the plastic wake influence on plasticity induced crack closure

Fatigue crack closure has been studied by means of finite element method since long time ago. Most work has been performed considering bi-dimensional models. Lately, the use of threedimensional models has been extended. Nevertheless, the methodology employed has been taken from that developed for bi-dimensional cases. There are a great number of previous bi-dimensional studies which analyse different numerical parameters and optimise them. The current computational capabilities allow a comprehensive study of the influence of the different modelling parameters in a similar way to those studies carried out with bidimensional models, with the advantage, that the evolution along the thickness of the analysed parameters can be taken into consideration. In particular, one of the key issues is related to the plastic wake length which is developed during the previous loading cycles. This residual stresses have a great influence on the crack opening and closure values. As the numerical analysis are complex and computationally expensive, the length of the simulated wake is a critical parameter. In this work, a comprehensive study of the effect of the plastic wake in fatigue crack closure is made. On this purpose, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the simulated plastic wake length. The numerical analysis is made in terms of crack closure and opening values as in terms of the stress and strain fields near the crack front.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech