A new geometric setting for classical field theories

A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.Comment: 22 page

Comparing Mean Field and Euclidean Matching Problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

Singular lagrangian systems and variational constrained mechanics on Lie algebroids

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve

A potential library for primary MFL pedagogy: the case of Young Pathfinders

As readers of this journal will know very well, 2010 will see all KS2 (ages 7-11) pupils in England entitled to learn a modern foreign language in normal curriculum time. This development of the commitment to primary language learning should provide an excellent opportunity and experience for pupils, whilst at the same time requiring some radical changes for many teachers, schools and much of the wider language learning community. Recent research has indicated general trends suggesting an increase in primary languages already, in anticipation of this development and even beforehand. One of the most recent studies indicates that 43% of primary children currently learn a foreign language at KS2, either in class or as an extra-curricular activity, although the extent of this learning varies considerably (Driscoll, Jones and Macrory, 2004). It has also been suggested (Muijs et al, 2005) that there are certain aspects of the process that will be particularly demanding if the challenge of providing this entitlement are to be met

The random link approximation for the Euclidean traveling salesman problem

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N ``cities''. We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive analytical predictions for these quantities using the random link approximation, where the lengths between cities are taken as independent random variables. From the ``cavity'' equations developed by Krauth, Mezard and Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3, numerical results show that the random link approximation is a good one, with a discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we argue that the approximation is exact up to O(1/d^2) and give a conjecture for beta_E(d), in terms of a power series in 1/d, specifying both leading and subleading coefficients.Comment: 29 pages, 6 figures; formatting and typos correcte

Perturbations in Bouncing Cosmological Models

I describe the features and general properties of bouncing models and the evolution of cosmological perturbations on such backgrounds. I will outline possible observational consequences of the existence of a bounce in the primordial Universe and I will make a comparison of these models with standard long inflationary scenarios.Comment: 9 pages, no figure

Dedicated front-end electronics for the next generation of linear collider electromagnetic calorimeter

This paper describes an R&D electronic program for the next generation of linear collider electromagnetic calorimeter. After a brief presentation of the requirements, a global scheme of the electronics is given. Then, we describe the three different building blocks developed in 0.35\mum CMOS technology: an amplifier, a comparator and finally the pipelined AD

Non-universal gaugino masses from non-singlet F-terms in non-minimal unified models

In phenomenological studies of low-energy supersymmetry, running gaugino masses are often taken to be equal near the scale of apparent gauge coupling unification. However, many known mechanisms can avoid this universality, even in models with unified gauge interactions. One example is an F-term vacuum expectation value that is a singlet under the Standard Model gauge group but transforms non-trivially in the symmetric product of two adjoint representations of a group that contains the Standard Model gauge group. Here, I compute the ratios of gaugino masses that follow from F-terms in non-singlet representations of SO(10) and E_6 and their sub-groups, extending well-known results for SU(5). The SO(10) results correct some long-standing errors in the literature.Comment: 13 page