Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

An Axiom of Military Law : Applicability of National Criminal Law to Military Personnel and Associated Civilians Abroad

States regularly deploy elements of their armed forces abroad. When that happens, the military personnel concerned largely remain governed by the penal law of the State that they serve. This extraterritorial extension of national criminal law, which has been treated as axiomatic in domestic law and ignored by international law scholarship, is the subject of this dissertation. The first part of the study considers the ambit of national criminal law without any special regard to the armed forces. It explores the historical development of the currently prevailing system of territorial law and looks at the ambit that national legal systems claim today. Turning then to international law, the study debunks the oddly persistent belief that States enjoy a freedom to extend their laws to extraterritorial conduct as they please, and that they are in this respect constrained only by some specific prohibitions in international law. Six arguments historical, empirical, ideological, functional, doctrinal and systemic are advanced to support a contrary view: that States are prohibited from extending the reach of their legal systems abroad, unless they can rely on a permissive principle of international law for doing so. The second part of the study deals specifically with State jurisdiction in a military context, that is to say, as applied to military personnel in the strict sense (service members) and various civilians serving with or accompanying the forces (associated civilians). While the status of armed forces on foreign soil has transformed from one encapsulated in the customary concept of extraterritoriality to a modern regulation of immunities granted by treaties, elements of armed forces located abroad usually do enjoy some degree of insulation from the legal system of the host State. As a corollary, they should generally remain covered by the law of their own State. The extent of this extraterritorial extension of national law is revealed in a comparative review of national legislation, paying particular attention to recent legal reforms in the United States and the United Kingdom two states that have sought to extend the scope of their national law to cover the conduct of military contractor personnel. The principal argument of the dissertation is that applying national criminal law to service members and associated civilians abroad is distinct from other extraterritorial claims of jurisdiction (in particular, the nationality principle or the protective principle of jurisdiction). The service jurisdiction over the armed forces has a distinct aim: ensuring the coherence and indivisibility of the forces and maintaining discipline. Furthermore, the exercise of service jurisdiction seeks to reduce the chances of the State itself becoming internationally liable for the conduct of its service members and associated civilians. Critically, the legal system of the troop-deploying State, by extending its reach abroad, seeks to avoid accountability gaps that might result from immunities from host State law.

An online-implementable differential evolution tuned all-aspect guidance law

This paper proposes a differential evolution based method of improving the performance of conventional guidance laws at high heading errors, without resorting to techniques from optimal control theory, which are complicated and suffer from several limitations. The basic guidance law is augmented with a term that is a polynomial function of the heading error. The values of the coefficients of the polynomial are found by applying the differential evolution algorithm. The results are compared with the basic guidance law, and the all-aspect proportional navigation laws in the literature. A scheme for online implementation of the proposed law for application in practice is also given. (c) 2010 Elsevier Ltd. All rights reserved.

Deformation dynamics of SS-316 Between 1023-K TO 1223-K In The Framework of Cottrell-Stokes Law

Kocks' formalism for analysing steady state deformation data for the case where Cottrell-Stokes law is valid is extended to incorporate possible back stresses from solution and/or precipitation hardening, and dependence of pre-exponential factor on the applied stress. A simple graphical procedure for exploiting these equations is demonstrated by analyzing tensile steady state data for a type 316 austentic stainless steel for the temperature range 1023 to 1223 K. In this instance, the computed back stress values turned out to be negative, a physically meaningless result. This shows that for SS 316, deformation in this temperature regime can not be interpreted in terms of a mechanism that obeys Cottrell-Stokes law.