Structural Design and Analysis of a Rigidizable Space Shuttle Experiment

AFIT is in the process of designing a Space Shuttle experiment designated as the Rigidized Inflatable Get-Away-Special Experiment (RIGEX) to study the effects of microgravity on the deployment of rigidizable composite structures. Once in space, the experiment will inflate and rigidize three composite structures and perform a vibration analysis on each by exciting the tubes using piezoelectric patches and collecting data via an accelerometer. This paper presents the structural and vibration analysis of the RIGEX assembly and inflatable composite tubes using ABAQUS Finite Element Analysis (FEA) software. Comparison of the analysis has been carried out with Eigenvalue/Eigenvector experimentation by means of ping testing. This FEA analysis has been used to verify the natural frequency and structural integrity of the RIGEX support assemblies. The ABAQUS FEA results correlated to within 20% of experimental values

Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems

Shared-memory parallelization (SMP) strategies for density matrix renormalization group (DMRG) algorithms enable the treatment of complex systems in solid state physics. We present two different approaches by which parallelization of the standard DMRG algorithm can be accomplished in an efficient way. The methods are illustrated with DMRG calculations of the two-dimensional Hubbard model and the one-dimensional Holstein-Hubbard model on contemporary SMP architectures. The parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential DMRG calculations.Comment: 18 pages, 9 figure

Gap to Transition Temperature Ratio in Density Wave Ordering: a Dynamical Mean Field Study

We use the dynamical mean-field method to determine the origin of the large ratio of the zero temperature gap to the transition temperature observed in most charge density wave materials. The method is useful because it allows an exact treatment of thermal fluctuations. We establish the relation of the dynamical mean-field results to conventional diagrammatics and thereby determine that in the physically relevant regime the origin of the large ratio is a strong inelastic scattering.Comment: 4 figure

On Quantum Groups in the Hubbard Model with Phonons

The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum symmetry only for D = 1 and that terms of higher order in the fermionic operators in addition to phonons are required for a quantum symmetric hamiltonian. The condition for quantum symmetry is "half filling" and there is no local electron-phonon coupling. A discussion of Quantum symmetries in general is given in a formalism that should be readily accessible to non Hopf-algebraists.Comment: latex, 17 page

Hall resistance in the hopping regime, a "Hall Insulator"?

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.Comment: Late

Landauer Theory, Inelastic Scattering and Electron Transport in Molecular Wires

In this paper we address the topic of inelastic electron scattering in mesoscopic quantum transport. For systems where only elastic scattering is present, Landauer theory provides an adequate description of transport that relates the electronic current to single-particle transmission and reflection probabilities. A formalism proposed recently by Bonca and Trugman facilitates the calculation of the one-electron transmission and reflection probabilities for inelastic processes in mesoscopic conductors connected to one-dimensional ideal leads. Building on their work, we have developed a self-consistent procedure for the evaluation of the non-equilibrium electron distributions in ideal leads connecting such mesoscopic conductors to electron reservoirs at finite temperatures and voltages. We evaluate the net electronic current flowing through the mesoscopic device by utilizing these non-equilibrium distributions. Our approach is a generalization of Landauer theory that takes account of the Pauli exclusion principle for the various competing elastic and inelastic processes while satisfying the requirement of particle conservation. As an application we examine the influence of elastic and inelastic scattering on conduction through a two site molecular wire with longitudinal phonons using the Su-Schrieffer-Heeger model of electron-phonon coupling.Comment: 25 pages, 8 figure

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

Effects of dimensionality and anisotropy on the Holstein polaron

We apply weak-coupling perturbation theory and strong-coupling perturbation theory to the Holstein molecular crystal model in order to elucidate the effects of anisotropy on polaron properties in D dimensions. The ground state energy is considered as a primary criterion through which to study the effects of anisotropy on the self-trapping transition, the self-trapping line associated with this transition, and the adiabatic critical point. The effects of dimensionality and anisotropy on electron-phonon correlations and polaronic mass enhancement are studied, with particular attention given to the polaron radius and the characteristics of quasi-1D and quasi-2D structures. Perturbative results are confirmed by selected comparisons with variational calculations and quantum Monte Carlo data

A Review of Rare Pion and Muon Decays

After a decade of no measurements of pion and muon rare decays, PIBETA, a new experimental program is producing its first results. We report on a new experimental study of the pion beta decay, Pi(+) -> Pi(0) e(+) Nu, the Pi(e2 gamma) radiative decay, Pi(+) -> e(+) Nu Gamma, and muon radiative decay, Mu -> e Nu Gamma. The new results represent four- to six-fold improvements in precision over the previous measurements. Excellent agreement with Standard Model predictions is observed in all channels except for one kinematic region of the Pi(e2 gamma) radiative decay involving energetic photons and lower-energy positrons.Comment: 10 pages, 6 figures, 2 tables, invited talk presented at MESON 2004, 8th Int'l. Workshop on Meson Production, Properties and Interaction, Krakow, Poland 4-8 June 200