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.

A computer study of the miscibility limits of Pd-Cu-Si

Metallic glasses are of interest because of their mechanical properties. They are ductile as well as brittle. This is true of Pd77.5Cu6Si16.5, a ternary glassy alloy. Actually, the most stable metallic glasses are those which are alloys of noble or transition metals A general formula is postulated as T70–80G30-20where T stands for one or several 3d transition elements, and includes the metalloid glass formers. Another general formula is A3B to A5B where B is a metalloid. A computer method utilising the MIGAP computer program of Kaufman is used to calculate the miscibility gap over a range of temperatures. The precipitation of a secondary crystalline phase is postulated around 1500K. This could produce a dispersed phase composite with interesting high temperature-strength properties.

A computer study of the miscibility limits of Sb-Te-Bi

The quaternary system Sb1bTe1bBi1bSe with small amounts of suitable dopants is of interest for the manufacture of thermoelectric modules which exhibit the Peltier and Seebeck effects. This property could be useful in the production of energy from the thermoelectric effect. Other substances are bismuth telluride (Bi2Te3) and Sb1bTe1bBi and compounds such as ZnIn2Se4. In the present paper the application of computer programs such as MIGAP of Kaufman is used to indicate the stability of the ternary limits of Sb1bTe1bBi within the temperature ranges of interest, namely 273 K to 300 K.

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.

Computer estimation of the Cd---Hg---Te phase diagram

The compounds CdHgTe and its constituent binaries CdTe, HgTe, and CdHg are semiconductors which are used in thermal, infrared, nuclear, thermoelectric and other photo sensitive devices. The compound CdHgTe has a Sphaleritic structure of possible type A1IIB1IIC6VI. The TERCP program of Kaufman is used to estimate the stable regions of the ternary phase diagram using available thermodynamic data. It was found that there was little variation in stochiometry with temperature. The compositions were calculated for temperatures ranging from 325K to 100K and the compositional limits were Cd13−20Hg12−01Te75−79, Hg varying most. By comparison with a similar compound, Cd In2Te4 of forbidden band width. 88 to .90 e.V., similar properties are postulated for Cd1Hg1Te6 with applications in the infra red region of the spectrum at 300K where this composition is given by TERCP at the limit of stability.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.