Fluctuation effects in disordered Peierls systems

We review the density of states and related quantities of quasi one-dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The low-energy behavior of non-interacting fermions which are subject to a static random backscattering potential will be described by the fluctuating gap model (FGM). Recently, the FGM has also been used to explain the pseudogap phenomenon in high-$T_c$ superconductors. After an elementary introduction to the FGM in the context of commensurate and incommensurate Peierls chains, we develop a non-perturbative method which allows for a simultaneous calculation of the density of states (DOS) and the inverse localization length. First, we recover all known results in the limits of zero and infinite correlation lengths of the random potential. Then, we attack the problem of finite correlation lengths. While a complex order parameter, which describes incommensurate Peierls chains, leads to a suppression of the DOS, i.e. a pseudogap, the DOS exhibits a singularity at the Fermi energy if the order parameter is real and therefore refers to a commensurate system. We confirm these results by calculating the DOS and the inverse localization length for finite correlation lengths and Gaussian statistics of the backscattering potential with unprecedented accuracy numerically. Finally, we consider the case of classical phase fluctuations which apply to low temperatures where amplitude fluctuations are frozen out. In this physically important regime, which is also characterized by finite correlation lengths, we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.Comment: 60 pages, 16 figure

Novel Modifications of Parallel Jacobi Algorithms

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.Comment: Accepted for publication in Numerical Algorithm

Systems and methods for supplemental weather information presentation on a display

An embodiment of the supplemental weather display system presents supplemental weather information on a display in a craft. An exemplary embodiment receives the supplemental weather information from a remote source, determines a location of the supplemental weather information relative to the craft, receives weather information from an on-board radar system, and integrates the supplemental weather information with the weather information received from the on-board radar system

Supporting Pet Ownership of Vulnerable Populations

Peace of Mind Dog Rescue (POMDR) is a program that provides supplies and support to vulnerable populations to help with the care of their pets. This program is very successful at partnering with organizations and individuals for fundraising and to obtain supplies, but it frequently has a large inventory that needs to be distributed where it is needed most. There is a need to identify if outreach to vulnerable populations could be improved, resulting in a more efficient use of the programs resources. This capstone project focused on active marketing and outreach throughout Monterey county through multiple tabling events in front of discounted spay and neuter buses. POMDR supplies distributed included free flea treatment, dog food, leashes, harnesses, collars, and dog beds. Additional to supplies, business cards and brochures describing the services provided at POMDR were also handed out. Findings and recommendations are that outreach via partnering with discount spay programs to vulnerable populations who may need additional supplies and services was successful and resulted in distribution of a good amount of flea medication and harnesses. Surprisingly, dog beds were not as popular. Repeat usage of the program is expected based on feedback from clients. Future outreach is recommended