Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models

We use a numerical implementation of the strong disorder renormalization group (RG) method to study the low-energy fixed points of random Heisenberg and tight-binding models on different types of fractal lattices. For the Heisenberg model new types of infinite disorder and strong disorder fixed points are found. For the tight-binding model we add an orbital magnetic field and use both diagonal and off-diagonal disorder. For this model besides the gap spectra we study also the fraction of frozen sites, the correlation function, the persistent current and the two-terminal current. The lattices with an even number of sites around each elementary plaquette show a dominant $\phi_0=h/e$ periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant $\phi_0/2$ periodicity at vanishing diagonal disorder, with a positive weak localization-like magnetoconductance at infinite disorder fixed points. The magnetoconductance with both diagonal and off-diagonal disorder depends on the symmetry of the distribution of on-site energies.Comment: 19 pages, 20 figure

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression

Model for Anisotropic Directed Percolation

We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio $\mu$ between the axes of a semi-ellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in 2D is an invariant equal to 2.8 independently of $\mu$. This result suggests that Sinai's theorem proposed originally for isotropic percolation is also valid for anisotropic directed percolation problems. The new invariant also yields a constant fractal dimension $D_{f} \sim 1.71$ for all $\mu$, which is the same value found in isotropic directed percolation (i.e., $\mu = 1$).Comment: RevTeX, 9 pages, 3 figures. To appear in Phys.Rev.

Out of equilibrium electronic transport properties of a misfit cobaltite thin film

We report on transport measurements in a thin film of the 2D misfit Cobaltite $Ca_{3}Co_{4}O_{9}$. Dc magnetoresistance measurements obey the modified variable range hopping law expected for a soft Coulomb gap. When the sample is cooled down, we observe large telegraphic-like fluctuations. At low temperature, these slow fluctuations have non Gaussian statistics, and are stable under a large magnetic field. These results suggest that the low temperature state is a glassy electronic state. Resistance relaxation and memory effects of pure magnetic origin are also observed, but without aging phenomena. This indicates that these magnetic effects are not glassy-like and are not directly coupled to the electronic part.Comment: accepted in Phys Rev B, Brief report

LOX/hydrocarbon rocket engine analytical design methodology development and validation. Volume 2: Appendices

This final report includes a discussion of the work accomplished during the period from Dec. 1988 through Nov. 1991. The objective of the program was to assemble existing performance and combustion stability models into a usable design methodology capable of designing and analyzing high-performance and stable LOX/hydrocarbon booster engines. The methodology was then used to design a validation engine. The capabilities and validity of the methodology were demonstrated using this engine in an extensive hot fire test program. The engine used LOX/RP-1 propellants and was tested over a range of mixture ratios, chamber pressures, and acoustic damping device configurations. This volume contains time domain and frequency domain stability plots which indicate the pressure perturbation amplitudes and frequencies from approximately 30 tests of a 50K thrust rocket engine using LOX/RP-1 propellants over a range of chamber pressures from 240 to 1750 psia with mixture ratios of from 1.2 to 7.5. The data is from test configurations which used both bitune and monotune acoustic cavities and from tests with no acoustic cavities. The engine had a length of 14 inches and a contraction ratio of 2.0 using a 7.68 inch diameter injector. The data was taken from both stable and unstable tests. All combustion instabilities were spontaneous in the first tangential mode. Although stability bombs were used and generated overpressures of approximately 20 percent, no tests were driven unstable by the bombs. The stability instrumentation included six high-frequency Kistler transducers in the combustion chamber, a high-frequency Kistler transducer in each propellant manifold, and tri-axial accelerometers. Performance data is presented, both characteristic velocity efficiencies and energy release efficiencies, for those tests of sufficient duration to record steady state values

Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames

We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.Comment: New title and introductio