Topological quantization and degeneracy in Josephson-junction arrays

We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed.Comment: To appear in Phys. Rev.

Using MathML to Represent Units of Measurement for Improved Ontology Alignment

Ontologies provide a formal description of concepts and their relationships in a knowledge domain. The goal of ontology alignment is to identify semantically matching concepts and relationships across independently developed ontologies that purport to describe the same knowledge. In order to handle the widest possible class of ontologies, many alignment algorithms rely on terminological and structural meth- ods, but the often fuzzy nature of concepts complicates the matching process. However, one area that should provide clear matching solutions due to its mathematical nature, is units of measurement. Several on- tologies for units of measurement are available, but there has been no attempt to align them, notwithstanding the obvious importance for tech- nical interoperability. We propose a general strategy to map these (and similar) ontologies by introducing MathML to accurately capture the semantic description of concepts specified therein. We provide mapping results for three ontologies, and show that our approach improves on lexical comparisons.Comment: Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, Englan

Spin-dependent (magneto)transport through a ring due to spin-orbit interaction

Electron transport through a one-dimensional ring connected with two external leads, in the presence of spin-orbit interaction (SOI) of strength \alpha and a perpendicular magnetic field is studied. Applying Griffith's boundary conditions we derive analytic expressions for the reflection and transmission coefficients of the corresponding one-electron scattering problem. We generalize earlier conductance results by Nitta et al. [Appl. Phys. Lett. 75, 695 (1999)] and investigate the influence of \alpha, temperature, and a weak magnetic field on the conductance. Varying \alpha and temperature changes the position of the minima and maxima of the magnetic-field dependent conductance, and it may even convert a maximum into a minimum and vice versa.Comment: 19 pages, 9 figure

Analysis of Strong-Coupling Parameters for Superfluid 3He

Superfluid $^{3}$He experiments show strong deviation from the weak-coupling limit of the Ginzburg-Landau theory, and this discrepancy grows with increasing pressure. Strong-coupling contributions to the quasiparticle interactions are known to account for this effect and they are manifest in the five $\beta$-coefficients of the fourth order Ginzburg-Landau free energy terms. The Ginzburg-Landau free energy also has a coefficient $g_{z}$ to include magnetic field coupling to the order parameter. From NMR susceptibility experiments, we find the deviation of $g_{z}$ from its weak-coupling value to be negligible at all pressures. New results for the pressure dependence of four different combinations of $\beta$-coefficients, $\beta$_{345}, $\beta$_{12}, $\beta$_{245}, and $\beta$_{5} are calculated and comparison is made with theory.Comment: 6 pages, 2 figures, 1 table. Manuscript prepared for QFS200

Magnetoresistance of UPt3

We have performed measurements of the temperature dependence of the magnetoresistance up to 9 T in bulk single crystals of UPt3 with the magnetic field along the b axis, the easy magnetization axis. We have confirmed previous results for transverse magnetoresistance with the current along the c axis, and report measurements of the longitudinal magnetoresistance with the current along the b axis. The presence of a linear term in both cases indicates broken orientational symmetry associated with magnetic order. With the current along the c axis the linear term appears near 5 K, increasing rapidly with decreasing temperature. For current along the b axis the linear contribution is negative.Comment: 6 pages, 3 figures, submitted to Quantum Fluids and Solids Conference (QFS 2006

Conductance of tubular nanowires with disorder

We calculate the conductance of tubular-shaped nanowires having many potential scatterers at random positions. Our approach is based on the scattering matrix formalism and our results analyzed within the scaling theory of disordered conductors. When increasing the energy the conductance for a big enough number of impurities in the tube manifests a systematic evolution from the localized to the metallic regimes. Nevertheless, a conspicuous drop in conductance is predicted whenever a new transverse channel is open. Comparison with the semiclassical calculation leading to purely ohmic behavior is made.Comment: 8 pages, 5 figure

A convex polynomial that is not sos-convex

A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)= M^T(x) M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is easy to see that sos-convexity is a sufficient condition for convexity of $p(x)$. Moreover, the problem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefinite program, which can be solved efficiently. Motivated by this computational tractability, it has been recently speculated whether sos-convexity is also a necessary condition for convexity of polynomials. In this paper, we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos-convex. Interestingly, our example is found with software using sum of squares programming techniques and the duality theory of semidefinite optimization. As a byproduct of our numerical procedure, we obtain a simple method for searching over a restricted family of nonnegative polynomials that are not sums of squares.Comment: 15 page

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

Salvage logging changes the taxonomic, phylogenetic and functional successional trajectories of forest bird communities

1.Salvage logging following natural disturbances may alter the natural successional trajectories of biological communities by affecting the occurrences of species, functional groups and evolutionary lineages. However, few studies have examined whether dissimilarities between bird communities of salvaged and unsalvaged forests are more pronounced for rare species, functional groups and evolutionary lineages than for their more common counterparts. 2. We compiled data on breeding bird assemblages from nine study areas in North America, Europe and Asia, covering a 17‐year period following wildfire or windstorm disturbances and subsequent salvage logging. We tested whether dissimilarities based on non‐shared species, functional groups and evolutionary lineages (a) decreased or increased over time and (b) the responses of rare, common and dominant species varied, by using a unified statistical framework based on Hill numbers and null models. 3. We found that dissimilarities between bird communities caused by salvage logging persisted over time for rare, common and dominant species, evolutionary lineages and for rare functional groups. Dissimilarities of common and dominant functional groups increased 14 years post disturbance. 4. Salvage logging led to significantly larger dissimilarities than expected by chance. Functional dissimilarities between salvaged and unsalvaged sites were lower compared to taxonomic and phylogenetic dissimilarities. In general, dissimilarities were highest for rare, followed by common and dominant species. 5. Synthesis and applications. Our research demonstrates that salvage logging did not decrease dissimilarities of bird communities over time and taxonomic, functional and phylogenetic dissimilarities persisted for over a decade. We recommend resource managers and decision makers to reserve portions of disturbed forest to enable unmanaged post‐disturbance succession of bird communities, particularly to conserve rare species found in unsalvaged disturbed forests

Salvage logging changes the taxonomic, phylogenetic and functional successional trajectories of forest bird communities

1. Salvage logging following natural disturbances may alter the natural successional trajectories of biological communities by affecting the occurrences of species, functional groups and evolutionary lineages. However, few studies have examined whether dissimilarities between bird communities of salvaged and unsalvaged forests are more pronounced for rare species, functional groups and evolutionary lineages than for their more common counterparts. 2. We compiled data on breeding bird assemblages from nine study areas in North America, Europe and Asia, covering a 17-year period following wildfire or windstorm disturbances and subsequent salvage logging. We tested whether dissimilarities based on non-shared species, functional groups and evolutionary lineages (a) decreased or increased over time and (b) the responses of rare, common and dominant species varied, by using a unified statistical framework based on Hill numbers and null models. 3. We found that dissimilarities between bird communities caused by salvage logging persisted over time for rare, common and dominant species, evolutionary lineages and for rare functional groups. Dissimilarities of common and dominant functional groups increased 14 years post disturbance. 4. Salvage logging led to significantly larger dissimilarities than expected by chance. Functional dissimilarities between salvaged and unsalvaged sites were lower compared to taxonomic and phylogenetic dissimilarities. In general, dissimilarities were highest for rare, followed by common and dominant species. 5. Synthesis and applications. Our research demonstrates that salvage logging did not decrease dissimilarities of bird communities over time and taxonomic, functional and phylogenetic dissimilarities persisted for over a decade. We recommend resource managers and decision makers to reserve portions of disturbed forest to enable unmanaged post-disturbance succession of bird communities, particularly to conserve rare species found in unsalvaged disturbed forests.Ministry of Science and Technology; Gregor Louisoder Environmental Foundatio