Analytical expressions for fringe fields in multipole magnets

Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beamline. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modelled at an early stage of accelerator design in such codes as MAD8, MADX or ELEGANT. However, usually it is not until the final stages of a design project that it is possible to model fringe fields for quadrupoles or higher order multipoles. Even then, existing techniques rely on the use of a numerical field map, which will usually not be available until the magnet design is well developed. Substitutes for the full field map exist but these are typically based on expansions about the origin and rely heavily on the assumption that the beam travels more or less on axis throughout the beam line. In some types of machine (for example, a non-scaling FFAG such as EMMA) this is not a good assumption. In this paper, a method for calculating fringe fields based on analytical expressions is presented, which allows fringe field effects to be included at the start of an accelerator design project. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. Two examples of quadrupole fringe fields are presented. The first example is a magnet in the LHC inner triplet, which consists of a set of four quadrupoles providing the final focus to the beam, just before the interaction point. Quadrupoles in EMMA provide the second example. In both examples, the analytical expressions derived in this paper for quadrupole fringe fields provide a good approximation to the field maps obtained from a numerical magnet modelling code.Comment: 27 pages, 39 figures. The figures are new with respect to the previous version, Several mistakes also correcte

Perceptual model for adaptive local shading and refresh rate

When the rendering budget is limited by power or time, it is necessary to find the combination of rendering parameters, such as resolution and refresh rate, that could deliver the best quality. Variable-rate shading (VRS), introduced in the last generations of GPUs, enables fine control of the rendering quality, in which each 16×16 image tile can be rendered with a different ratio of shader executions. We take advantage of this capability and propose a new method for adaptive control of local shading and refresh rate. The method analyzes texture content, on-screen velocities, luminance, and effective resolution and suggests the refresh rate and a VRS state map that maximizes the quality of animated content under a limited budget. The method is based on the new content-adaptive metric of judder, aliasing, and blur, which is derived from the psychophysical models of contrast sensitivity. To calibrate and validate the metric, we gather data from literature and also collect new measurements of motion quality under variable shading rates, different velocities of motion, texture content, and display capabilities, such as refresh rate, persistence, and angular resolution. The proposed metric and adaptive shading method is implemented as a game engine plugin. Our experimental validation shows a substantial increase in preference of our method over rendering with a fixed resolution and refresh rate, and an existing motion-adaptive techniqu

Elastic properties of cubic crystals: Every's versus Blackman's diagram

Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams of various groups of materials are greater than for Blackaman's diagrams, revealing the existence of a linear relationship between two dimensionless Every's variables. Alignment of elements and compounds along lines of constant Poisson's ratio $\nu(,\textbf{m})$, ($\textbf{m}$ arbitrary perpendicular to ) is observed. Division of the stability region in Blackman's diagram into region of complete auxetics, auxetics and non-auxetics is introduced. Correlations of a scaling and an acoustic anisotropy parameter are considered.Comment: 8 pages, 9 figures, presented on The Ninth International School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter", 5 - 12 September 2007, Myczkowce, Polan

Selecting texture resolution using a task-specific visibility metric

In real-time rendering, the appearance of scenes is greatly affected by the quality and resolution of the textures used for image synthesis. At the same time, the size of textures determines the performance and the memory requirements of rendering. As a result, finding the optimal texture resolution is critical, but also a non-trivial task since the visibility of texture imperfections depends on underlying geometry, illumination, interactions between several texture maps, and viewing positions. Ideally, we would like to automate the task with a visibility metric, which could predict the optimal texture resolution. To maximize the performance of such a metric, it should be trained on a given task. This, however, requires sufficient user data which is often difficult to obtain. To address this problem, we develop a procedure for training an image visibility metric for a specific task while reducing the effort required to collect new data. The procedure involves generating a large dataset using an existing visibility metric followed by refining that dataset with the help of an efficient perceptual experiment. Then, such a refined dataset is used to retune the metric. This way, we augment sparse perceptual data to a large number of per-pixel annotated visibility maps which serve as the training data for application-specific visibility metrics. While our approach is general and can be potentially applied for different image distortions, we demonstrate an application in a game-engine where we optimize the resolution of various textures, such as albedo and normal maps

Charge and spin transport in a metal-semiconductor heterostructure with double Schottky barriers

Taking into account the available experimental results, we model the electronic properties and current-voltage characteristics of a ferromagnet-semiconductor junction. The Fe/GaAs interface is considered as a Fe/(i-GaAs)/n+-GaAs/n-GaAs multilayer structure with the Schottky barrier. We also calculate numerically the current-voltage characteristics of a double-Schottky-barrier structure Fe/GaAs/Fe, which are in agreement with available experimental data. For this structure, we have estimated the spin current in the GaAs layer, which characterizes spin injection from the ferromagnet to the semiconductor.Comment: 3 pages, 5 figures, presented on The European Conference Physics of Magnetism 2014 (PM'14), June 23-27, 2014 Pozna\'n, POLAN

Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices

This contribution compiles the benefits of lattice symmetry in the context of closed orbit correction. A symmetric arrangement of BPMs and correctors results in structured orbit response matrices of Circulant or block Circulant type. These forms of matrices provide favorable properties in terms of computational complexity, information compression and interpretation of mathematical vector spaces of BPMs and correctors. For broken symmetries, a nearest-Circulant approximation is introduced and the practical advantages of symmetry exploitation are demonstrated with the help of simulations and experiments in the context of FAIR synchrotrons

Dataset and metrics for predicting local visible differences

A large number of imaging and computer graphics applications require localized information on the visibility of image distortions. Existing image quality metrics are not suitable for this task as they provide a single quality value per image. Existing visibility metrics produce visual difference maps, and are specifically designed for detecting just noticeable distortions but their predictions are often inaccurate. In this work, we argue that the key reason for this problem is the lack of large image collections with a good coverage of possible distortions that occur in different applications. To address the problem, we collect an extensive dataset of reference and distorted image pairs together with user markings indicating whether distortions are visible or not. We propose a statistical model that is designed for the meaningful interpretation of such data, which is affected by visual search and imprecision of manual marking. We use our dataset for training existing metrics and we demonstrate that their performance significantly improves. We show that our dataset with the proposed statistical model can be used to train a new CNN-based metric, which outperforms the existing solutions. We demonstrate the utility of such a metric in visually lossless JPEG compression, super-resolution and watermarking.</jats:p