Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size

Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field. Comparison with the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for "deep" clusters where value of the field on each site is much greater than the rms disorder.Comment: 15 pages, 6 figures, RevTe

Tunable transmission and harmonic generation in nonlinear metamaterials

We study the properties of a tunable nonlinear metamaterial operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators and wires where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We show that at higher powers the transmission of the metamaterial becomes power dependent, and we demonstrate experimentally power-dependent transmission properties and selective generation of higher harmonics.Comment: 3 page

Characterization of transport and magnetic properties in thin film La(0.67)(Ca(x)Sr(1-x))(0.33)MnO(3) mixtures

We have grown thin films of (100) oriented La_{0.67}(Ca_{x}Sr_{1-x})_{0.33}MnO_{3} on (100) NdGaO_{3} substrates by off-axis sputtering. We have looked at the changes in the resistivity and magnetoresistance of the samples as the Ca/Sr ratio was varied. We find that as the calcium fraction is decreased, the lattice match to the substrate decreases, and the films become more disordered, as observed in transport measurements and the variation in Curie and peak resistance temperatures. We find a correlation between the temperature independent and T^2 terms to the low temperature resistivity. The room temperature magnetoresistance exhibits a maximum as the peak temperature is increased by the substitution of Sr for Ca, and a change in the field dependence to the resistivity at room temperature is observed.Comment: 5 pages, 6 eps figures, to be published in Journal of Applied Physic

Tunable transmission and harmonic generation in nonlinear metamaterials

We study the properties of a tunable nonlinear metamaterial operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators and wires where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We show that at higher powers the transmission of the metamaterial becomes power dependent, and we demonstrate experimentally power-dependent transmission properties and selective generation of higher harmonics.This work has been supported by the Australian Research Council through the Discovery projects, by the Australian Academy of Science through a travel grant, and by the Air Force Office of Scientific Research AFOSR through the MURI program Grant No. F49620-03-1-0420

Maps and twists relating U(sl(2))U(sl(2)) and the nonstandard Uh(sl(2))U_{h}(sl(2)): unified construction

A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them, in so far as they can be explicitly constructed, enable us to translate results obtained in terms of one to the other cases. Here the role of the maps is studied in the context of construction of twist operators between the cocommutative and noncocommutative coproducts of the $U(sl(2))$ and $U_{h}(sl(2))$ algebras respectively. It is shown that a particular map called the `minimal twist map' implements the simplest twist given directly by the factorized form of the ${\cal R}_{h}$-matrix of Ballesteros-Herranz. For other maps the twist has an additional factor obtainable in terms of the similarity transformation relating the map in question to the minimal one. The series in powers of $h$ for the operator performing this transformation may be obtained up to some desired order, relatively easily. An explicit example is given for one particularly interesting case. Similarly the classical and the Jordanian antipode maps may be interrelated by a similarity transformation. For the `minimal twist map' the transforming operator is determined in a closed form.Comment: LaTeX, 13 page