Spectral properties of a limit-periodic Schr\"odinger operator in dimension two

We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i\langle \vec k,\vec x\rangle }$ at the high energy region. Second, the isoenergetic curves in the space of momenta $\vec k$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.Comment: 89 pages, 6 figure

Transition behavior of k-surface from hyperbola to ellipse

The transition behavior of the k-surface of a lossy anisotropic indefinite slab is investigated. It is found that, if the material loss is taken into account, the k-surface does not show a sudden change from hyperbola to the ellipse when one principle element of the permittivity tensor changes from negative to positive. In fact, after introducing a small material loss, the shape of the k-surface can be a combination of a hyperbola and an ellipse, and a selective high directional transmission can be obtained in such a slab

Comparative approaches for assessing access to alcohol outlets: exploring the utility of a gravity potential approach.

BackgroundA growing body of research recommends controlling alcohol availability to reduce harm. Various common approaches, however, provide dramatically different pictures of the physical availability of alcohol. This limits our understanding of the distribution of alcohol access, the causes and consequences of this distribution, and how best to reduce harm. The aim of this study is to introduce both a gravity potential measure of access to alcohol outlets, comparing its strengths and weaknesses to other popular approaches, and an empirically-derived taxonomy of neighborhoods based on the type of alcohol access they exhibit.MethodsWe obtained geospatial data on Seattle, including the location of 2402 alcohol outlets, United States Census Bureau estimates on 567 block groups, and a comprehensive street network. We used exploratory spatial data analysis and employed a measure of inter-rater agreement to capture differences in our taxonomy of alcohol availability measures.ResultsSignificant statistical and spatial variability exists between measures of alcohol access, and these differences have meaningful practical implications. In particular, standard measures of outlet density (e.g., spatial, per capita, roadway miles) can lead to biased estimates of physical availability that over-emphasize the influence of the control variables. Employing a gravity potential approach provides a more balanced, geographically-sensitive measure of access to alcohol outlets.ConclusionsAccurately measuring the physical availability of alcohol is critical for understanding the causes and consequences of its distribution and for developing effective evidence-based policy to manage the alcohol outlet licensing process. A gravity potential model provides a superior measure of alcohol access, and the alcohol access-based taxonomy a helpful evidence-based heuristic for scholars and local policymakers

Design and finite element mode analysis of noncircular gear

The noncircular gear transmission is an important branch of the gear transmission, it is characterized by its compact structure, good dynamic equilibration and other advantages, and can be used in the automobile, engineering machine, ship, machine tool, aviation and spaceflight field etc. Studying on the dynamics feature of noncircular gear transmission can improve the ability to carry loads of, reduce the vibration and noise of, increase the life of the noncircular gear transmission machine, provides guidance for the design of the noncircular gear, and has significant theories and practical meanings. In this paper, the gear transmission technique is used to studied the design method of the noncircular gear, which contains distribution of teeth on the pitch curve, designs of the tooth tip curve and the tooth root curve, design of the tooth profile curve, the gear system dynamics principle is introduced to establish dynamics model for the noncircular gear; basic theory of finite element and mode analysis method are applied, finite element model for the noncircular gear is established, natural vibration characteristic of the noncircular gear is studied. And the oval gear is taken as an example, the mathematics software MathCAD, the 3D modeling software UG and the finite element software ABAQUS are used to realize precise 3D model of the oval gear. The finite element method is used, the natural vibration characteristic of the oval gear is studied, the main vibration types and natural frequencies of the oval gear and that of the equivalent cylindrical gears are analyzed and compared, the conclusions received reflect the dynamics performance of the oval gear, and solid foundation is laid for dynamics research and engineering application of the oval gear transmission

Fermionic Hopf solitons and Berry's phase in topological surface superconductors

A central theme in many body physics is emergence - new properties arise when several particles are brought together. Particularly fascinating is the idea that the quantum statistics may be an emergent property. This was first noted in the Skyrme model of nuclear matter, where a theory formulated entirely in terms of a bosonic order parameter field contains fermionic excitations. These excitations are smooth field textures, and believed to describe neutrons and protons. We argue that a similar phenomenon occurs in topological insulators when superconductivity gaps out their surface states. Here, a smooth texture is naturally described by a three component real vector. Two components describe superconductivity, while the third captures the band topology. Such a vector field can assume a 'knotted' configuration in three dimensional space - the Hopf texture - that cannot smoothly be unwound. Here we show that the Hopf texture is a fermion. To describe the resulting state, the regular Landau-Ginzburg theory of superconductivity must be augmented by a topological Berry phase term. When the Hopf texture is the cheapest fermionic excitation, striking consequences for tunneling experiments are predicted

Synaptic Partner Assignment Using Attentional Voxel Association Networks

Connectomics aims to recover a complete set of synaptic connections within a dataset imaged by volume electron microscopy. Many systems have been proposed for locating synapses, and recent research has included a way to identify the synaptic partners that communicate at a synaptic cleft. We re-frame the problem of identifying synaptic partners as directly generating the mask of the synaptic partners from a given cleft. We train a convolutional network to perform this task. The network takes the local image context and a binary mask representing a single cleft as input. It is trained to produce two binary output masks: one which labels the voxels of the presynaptic partner within the input image, and another similar labeling for the postsynaptic partner. The cleft mask acts as an attentional gating signal for the network. We find that an implementation of this approach performs well on a dataset of mouse somatosensory cortex, and evaluate it as part of a combined system to predict both clefts and connections