On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation

We present a method for hierarchical data approximation using curved quadratic simplicial elements for domain decomposition. Scientific data defined over two- or three-dimensional domains typically contain boundaries and discontinuities that are to be preserved and approximated well for data analysis and visualization. Curved simplicial elements make possible a better representation of curved geometry, domain boundaries, and discontinuities than simplicial elements with non-curved edges and faces. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are $C^0$-continuous everywhere except where field discontinuities occur whose locations we assume to be given. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. Our method can be used for hierarchical data processing and visualization

Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory

We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that flat NC space-time realizes two copies of the Lifshitz algebra that together form a Schroedinger algebra (without the central element). We show why the Schroedinger scalar model has both copies as symmetries and the Lifshitz scalar model only one. Finally we discuss the holographic dual of this phenomenon by showing that the bulk Lifshitz space-time realizes the same two copies of the Lifshitz algebra.Comment: 5 pages, modified abstract, clarifications added, typos fixed, refs update

A Survey of Dimension Reduction Methods for High-dimensional Data Analysis and Visualization

Dimension reduction is commonly defined as the process of mapping high-dimensional data to a lower-dimensional embedding. Applications of dimension reduction include, but are not limited to, filtering, compression, regression, classification, feature analysis, and visualization. We review methods that compute a point-based visual representation of high-dimensional data sets to aid in exploratory data analysis. The aim is not to be exhaustive but to provide an overview of basic approaches, as well as to review select state-of-the-art methods. Our survey paper is an introduction to dimension reduction from a visualization point of view. Subsequently, a comparison of state-of-the-art methods outlines relations and shared research foci

Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes

Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and bio-medical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation. We present two different approaches for using subdivision solids as the only representation for modeling, simulation and visualization. This has the advantage that no data must be converted between the CAD and CAE phases. The first approach is based on an adaptive and feature-preserving tetrahedral subdivision scheme. The second approach is based on Catmull-Clark subdivision solids

Beitrag zur Erzeugung hoher Temperaturen in anorganisch-nichtmetallischen Stoffen durch kapazitive Hochfrequenzerwärmung

Gegenstand der Arbeit ist es, das Verfahren der kapazitiven Hochfrequenzerwärmung im Hochtemperaturbereich anzuwenden. Dabei besteht das Ziel darin, Rohstoffgemische (Gemenge) mit verdampfenden Bestandteilen zu schmelzen, die danach eine Weiterverarbeitung z. B. zu Substrat Scheiben von Mikrowellen-Oszillatoren oder zu Festkörperdotierquellen für die Mikroelektronik sowie zu bioaktiven Implantatwerkstoffen erfahren. Basierend auf den dargelegten physikalischen Verfahrensgrundlagen und den elektrischen Eigenschaften der Gemenge im HFBereich erfolgen Berechnungen zum gerätetechnischen Aufbau der eingesetzten HF-Schmelzanlage (Arbeitsfrequenz 27,12 MHz). Zur Bestimmung von Frequenz- und Temperaturabhängigkeit der elektrischen Eigenschaften der Gemenge ist eine speziell geschaffene HF-Meßeinrichtung dokumentiert. Aus dem Vergleich zwischen ermittelten elektrischen Gemengeeigenschaften, den sich auf Grundlage wärmetechnischer Berechnungen ergebenden Werten und den durchgeführten Schmelzversuchen kann prognostisch auf die Anwendbarkeit des Verfahrens geschlossen werden. Orientierende Versuche an geeigneten Phosphorquellscheiben- und Tricalciumphosphatgemengen weisen deren Erwärmbarkeit von Raumtemperatur bis zu hohen Temperaturen nach. Dabei wurden Temperaturen > 1250 °C erzielt, die bei einer durchschnittlichen Aufheizgeschwindigkeit von 300...350 K-min-1 erreicht werden

On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches

Given a three-dimensional (3D) array of function values Fijk on a rectilinear grid, the marching cubes(MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x,y,z)=T. We describe the construction of a Co-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational-quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices

CFD Simulation of Liquid-Liquid Extraction Columns and Visualization of Eulerian Datasets

In this joint work, a complete framework for modeling, simulating and visualizing multiphase fluid flow within an extraction column is presented. We first present a volume-of-fluid simulation, which is able to predict the surface of the droplets during coalescence. However, a fast and efficient model is needed for the simulation of a liquid-liquid extraction column due to the high number of occurring droplets. To simulate the velocity and droplet size in a DN32 extraction column, a coupled computational fluid dynamic-population balance model solver is used. The simulation is analyzed using path-line based visualization techniques. A novel semi-automatic re-seeding technique for droplet path-line integration is proposed. With our technique, path-lines of fluid droplets can be re-initialized after contact with the stirring devices. The droplet breakage is captured, allowing the engineer to improve the design of liquid-liquid columns layout

CFD Simulation of Liquid-Liquid Extraction Columns and Visualization of Eulerian Datasets

In this joint work, a complete framework for modeling, simulating and visualizing multiphase fluid flow within an extraction column is presented. We first present a volume-of-fluid simulation, which is able to predict the surface of the droplets during coalescence. However, a fast and efficient model is needed for the simulation of a liquid-liquid extraction column due to the high number of occurring droplets. To simulate the velocity and droplet size in a DN32 extraction column, a coupled computational fluid dynamic-population balance model solver is used. The simulation is analyzed using path-line based visualization techniques. A novel semi-automatic re-seeding technique for droplet path-line integration is proposed. With our technique, path-lines of fluid droplets can be re-initialized after contact with the stirring devices. The droplet breakage is captured, allowing the engineer to improve the design of liquid-liquid columns layout

A Multi-Resolution Interactive Previewer for Volumetric Data on Arbitary Meshes

In this paper we describe a rendering method suitable for interactive previewing of large-scale arbitary-mesh volume data sets. A data set to be visualized is represented by a ''point cloud,'' i. e., a set of points and associated data values without known connectivity between the points. The method uses a multi-resolution approach to achieve interactive rendering rates of several frames per second for arbitrarily large data sets. Lower-resolution approximations of an original data set are created by iteratively applying a point- decimation operation to higher-resolution levels. The goal of this method is to provide the user with an interactive navigation and exploration tool to determine good viewpoints and transfer functions to pass on to a high-quality volume renderer that uses a standard algorithm