New Structured Matrix Methods for Real and Complex Polynomial Root-finding

We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular numerical approximation of the real roots of a polynomial. Our analysis and experiments show efficiency of the resulting algorithms.Comment: 18 page

Heat conduction in deformable Frenkel-Kontorova lattices: thermal conductivity and negative differential thermal resistance

Heat conduction through the Frenkel-Kontorova (FK) lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance (NDTR).Comment: 15 pages, 7 figure

Generalized conductance sum rule in atomic break junctions

When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels (valence orbitals of the junction atom) undergo strong variations. We propose a microscopic explanation of this phenomenon, based on Coulomb correlation effects between electrons in valence orbitals of the junction atom. The resulting approximate conductance quantization is closely related to the Friedel sum rule.Comment: 4 pages, 1 figure, appears in Proceedings of the NATO Advanced Research Workshop ``Size dependent magnetic scattering'', Pecs, Hungary, May 28 - June 1, 200

Direct Separation of Short Range Order in Intermixed Nanocrystalline and Amorphous Phases

Diffraction anomalous fine-structure (DAFS) and extended x-ray absorption fine-structure (EXAFS) measurements were combined to determine short range order (SRO) about a single atomic type in a sample of mixed amorphous and nanocrystalline phases of germanium. EXAFS yields information about the SRO of all Ge atoms in the sample, while DAFS determines the SRO of only the ordered fraction. We determine that the first-shell distance distribution is bimodal; the nanocrystalline distance is the same as the bulk crystal, to within 0.01(2)   Å, but the mean amorphous Ge-Ge bond length is expanded by 0.076(19)   Å. This approach can be applied to many systems of mixed amorphous and nanocrystalline phases

On the Stability and Structural Dynamics of Metal Nanowires

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals that metal nanocylinders with certain magic conductance values G=1, 3, 6, 12, 17, 23, 34, 42, 51, 67, 78, 96, ... times the conductance quantum are exceptionally stable. A nonlinear dynamical simulation of nanowire structural evolution reveals a universal equilibrium shape consisting of a magic cylinder suspended between unduloidal contacts. The lifetimes of these metastable structures are also computed.Comment: 8 pages, 6 figure

Current Animal Models of Postoperative Spine Infection and Potential Future Advances.

Implant related infection following spine surgery is a devastating complication for patients and can potentially lead to significant neurological compromise, disability, morbidity, and even mortality. This paper provides an overview of the existing animal models of postoperative spine infection and highlights the strengths and weaknesses of each model. In addition, there is discussion regarding potential modifications to these animal models to better evaluate preventative and treatment strategies for this challenging complication. Current models are effective in simulating surgical procedures but fail to evaluate infection longitudinally using multiple techniques. Potential future modifications to these models include using advanced imaging technologies to evaluate infection, use of bioluminescent bacterial species, and testing of novel treatment strategies against multiple bacterial strains. There is potential to establish a postoperative spine infection model using smaller animals, such as mice, as these would be a more cost-effective screening tool for potential therapeutic interventions