Fuzzy spaces and new random matrix ensembles

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.Comment: 12 pages, 1 figure; version to appear in Phys. Rev.

Random matrix theory for CPA: Generalization of Wegner's nn--orbital model

We introduce a generalization of Wegner's $n$-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green's functions and the conductivity exactly in the limit $n\to\infty$. Our solution solves the CPA-equation of the $(n=1)$-Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.Comment: 3 pages, Rev-Te

The F-region trough: seasonal morphology and relation to interplanetary magnetic field

We present here the results of a statistical study of the ionospheric trough observed in 2003 by means of satellite tomography. We focus on the seasonal morphology of the trough occurrence and investigate the trough latitude, width and the horizontal gradients at the edges, at different magnetic local times, as well as their relations to geomagnetic activity and the interplanetary magnetic field. A seasonal effect is noticed in the diurnal variation of the trough latitude, indicating that summer clearly differs from the other seasons. In winter the troughs seem to follow the solar terminator. The width of the trough has a diurnal variation and it depends on the season, as well. The broadest troughs are observed in winter and the narrowest ones in summer. A discontinuity in the diurnal variation of the trough latitude is observed before noon. It is suggested that this is an indication of a difference between the generation mechanisms of morningside and eveningside troughs. The density gradients at the edges have a complex dependence on the latitude of the trough and on geomagnetic activity. The photoionization and the auroral precipitation are competing in the formation of the trough walls at different magnetic local times. An important finding is that the interplanetary magnetic field plays a role in the occurrence of the trough at different levels of geomagnetic activity. This is probably associated with the topology of the polar cap convection pattern, which depends on the directions of the IMF components <i>B<sub>y</sub></i> and <i>B<sub>z</sub></i>

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

Loop models, random matrices and planar algebras

We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map

Case Study About Resistance Projection Welding of Aluminized Steel Parts

Resistance projection welding is a non-polluting mechanized process used to obtain an assembly between similar or dissimilar metallic materials. The main advantages of this welding process are the possibility to achieve many different welded points at the same time and the long life of the electrodes compared to the spot-welding process. The paper analyses the effects of thin aluminium coating existing on mild steel parts of on the correct formation of welding points when assembling moulds for the manufacture of baking bread. From optical and electron microscopy analyses it resulted that some adjacent welded points show an interrupted fusion line, sprinkled with elongated islands of aluminium-rich compounds. The paper presents the effect of changing the values ​​of the welding parameters on the weld spot size, in correlation with the Al-rich inclusions that appear on the weld fusion zone. The best results have been obtained when the welding parameters values were the follows: electrode pressure of 2.6 bar, welding power of 19.18kVA and welding time of 7ms. The problems that occur when electric resistance welding of parts with aluminium coating have been highlighted, being useful for specialists who make products using this welding process

Segal-Bargmann-Fock modules of monogenic functions

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.Comment: 11 page

Summing free unitary random matrices

I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of CUE summands, I write them in terms of two "master equations," which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first sub-leading correction, for independent identically-distributed zero-drift unitary random matrices.Comment: 17 pages, 15 figure