Numerical and experimental investigation of the effect of geometry on combustion characteristics of solid-fuel ramjet

Science.gov (United States)

Gong, Lunkun; Chen, Xiong; Musa, Omer; Yang, Haitao; Zhou, Changsheng

2017-12-01

Numerical and experimental investigation on the solid-fuel ramjet was carried out to study the effect of geometry on combustion characteristics. The two-dimensional axisymmetric program developed in the present study adopted finite rate chemistry and second-order moment turbulence-chemistry models, together with k-ω shear stress transport (SST) turbulence model. Experimental data were obtained by burning cylindrical polyethylene using a connected pipe facility. The simulation results show that a fuel-rich zone near the solid fuel surface and an air-rich zone in the core exist in the chamber, and the chemical reactions occur mainly in the interface of this two regions; The physical reasons for the effect of geometry on regression rate is the variation of turbulent viscosity due to the geometry change. Port-to-inlet diameter ratio is the main parameter influencing the turbulent viscosity, and a linear relationship between port-to-inlet diameter and regression rate were obtained. The air mass flow rate and air-fuel ratio are the main influencing factors on ramjet performances. Based on the simulation results, the correlations between geometry and air-fuel ratio were obtained, and the effect of geometry on ramjet performances was analyzed according to the correlation. Three-dimensional regression rate contour obtained experimentally indicates that the regression rate which shows axisymmetric distribution due to the symmetry structure increases sharply, followed by slow decrease in axial direction. The radiation heat transfer in recirculation zone cannot be ignored. Compared with the experimental results, the deviations of calculated average regression rate and characteristic velocity are about 5%. Concerning the effect of geometry on air-fuel ratio, the deviations between experimental and theoretical results are less than 10%.

The physics of solid-state neutron detector materials and geometries.

Science.gov (United States)

Caruso, A N

2010-11-10

Detection of neutrons, at high total efficiency, with greater resolution in kinetic energy, time and/or real-space position, is fundamental to the advance of subfields within nuclear medicine, high-energy physics, non-proliferation of special nuclear materials, astrophysics, structural biology and chemistry, magnetism and nuclear energy. Clever indirect-conversion geometries, interaction/transport calculations and modern processing methods for silicon and gallium arsenide allow for the realization of moderate- to high-efficiency neutron detectors as a result of low defect concentrations, tuned reaction product ranges, enhanced effective omnidirectional cross sections and reduced electron-hole pair recombination from more physically abrupt and electronically engineered interfaces. Conversely, semiconductors with high neutron cross sections and unique transduction mechanisms capable of achieving very high total efficiency are gaining greater recognition despite the relative immaturity of their growth, lithographic processing and electronic structure understanding. This review focuses on advances and challenges in charged-particle-based device geometries, materials and associated mechanisms for direct and indirect transduction of thermal to fast neutrons within the context of application. Calorimetry- and radioluminescence-based intermediate processes in the solid state are not included.

Planning for Evolution in a Production Environment: Migration from a Legacy Geometry Code to an Abstract Geometry Modeling Language in STAR

Science.gov (United States)

Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor

2012-12-01

Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.

Manipulation of volumetric solids with applications to sculpting

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas

2002-01-01

that it is reasonable to classify the tools in a sculpting system according to whether the tools tend to deform the sculpted object or work according to the paradigm of Constructive Solid Geometry (CSG). Existing volume sculpting systems are surveyed, and it is found that almost all systems provide sculpting tools...... representation where the meaning of a voxel is shortest distance. The deformative tools are based on a specialization of the Level Set Method. The main advantage of using the Level Set Method is that it is a very generic technique as opposed to methods previously proposed. The main task here has been to restrict....... The most important disadvantage of the volume representation is its lack of support for features at different scales. By choosing a volume representation, we implicitly choose a scale, and features that are very small with respect to that scale are essentially un-representable. As a solution, I propose...

Representation Discovery using Harmonic Analysis

CERN Document Server

Mahadevan, Sridhar

2008-01-01

Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu

METHODS FOR THE REPRESENTATION OF THE HELICOIDAL SURFACE

Directory of Open Access Journals (Sweden)

SCURTU Liviu-Iacob

2017-05-01

Full Text Available In this paper there are presented the graphical methods to determine the parameters of an helicoidal stairs. The first part of this paper shows the used methods to generate the helicoidal curves using descriptive geometry methods. It has represented the state of the art of the generation of a helical surface studies. The second part of this study shows the helical stairs surface representation using descriptive geometry methods. For the representation of the helicoidal stairs are used two projections, the front and top view. A method of the stairs representation is solved using CAD modelling dedicated software. Following the helical surface representation in both methods, has been achieved a comparative study by using two representation methods. Conclusions about these two representation methods are presented in the end of this paper.

Virial coefficients of anisotropic hard solids of revolution: The detailed influence of the particle geometry

Science.gov (United States)

Herold, Elisabeth; Hellmann, Robert; Wagner, Joachim

2017-11-01

We provide analytical expressions for the second virial coefficients of differently shaped hard solids of revolution in dependence on their aspect ratio. The second virial coefficients of convex hard solids, which are the orientational averages of the mutual excluded volume, are derived from volume, surface, and mean radii of curvature employing the Isihara-Hadwiger theorem. Virial coefficients of both prolate and oblate hard solids of revolution are investigated in dependence on their aspect ratio. The influence of one- and two-dimensional removable singularities of the surface curvature to the mutual excluded volume is analyzed. The virial coefficients of infinitely thin oblate and infinitely long prolate particles are compared, and analytical expressions for their ratios are derived. Beyond their dependence on the aspect ratio, the second virial coefficients are influenced by the detailed geometry of the particles.

Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

CERN Document Server

Landau, Olav Arnfinn

2011-01-01

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

Solid state supramolecular structure of diketopyrrolopyrrole chromophores: correlating stacking geometry with visible light absorption

OpenAIRE

Pop, Flavia; Lewis, William; Amabilino, David B.

2016-01-01

Mono- and di-alkylated 1,4-diketo-3,6-dithiophenylpyrrolo[3-4-c]pyrrole derivatives (TDPPs) have been synthesised and their solid state packing and absorption properties have been correlated. In this library of compounds the bulkier substituents distort the geometry of the chromophores and shift the lowest energy absorption band as a consequence of reduced π–π stacking and inter-chromophore overlap. Longitudinal displacement of the conjugated core is affected by donor–acceptor intermolecular ...

Phase transitions of amorphous solid acetone in confined geometry investigated by reflection absorption infrared spectroscopy.

Science.gov (United States)

Shin, Sunghwan; Kang, Hani; Kim, Jun Soo; Kang, Heon

2014-11-26

We investigated the phase transformations of amorphous solid acetone under confined geometry by preparing acetone films trapped in amorphous solid water (ASW) or CCl4. Reflection absorption infrared spectroscopy (RAIRS) and temperature-programmed desorption (TPD) were used to monitor the phase changes of the acetone sample with increasing temperature. An acetone film trapped in ASW shows an abrupt change in the RAIRS features of the acetone vibrational bands during heating from 80 to 100 K, which indicates the transformation of amorphous solid acetone to a molecularly aligned crystalline phase. Further heating of the sample to 140 K produces an isotropic solid phase, and eventually a fluid phase near 157 K, at which the acetone sample is probably trapped in a pressurized, superheated condition inside the ASW matrix. Inside a CCl4 matrix, amorphous solid acetone crystallizes into a different, isotropic structure at ca. 90 K. We propose that the molecularly aligned crystalline phase formed in ASW is created by heterogeneous nucleation at the acetone-water interface, with resultant crystal growth, whereas the isotropic crystalline phase in CCl4 is formed by homogeneous crystal growth starting from the bulk region of the acetone sample.

Group representations

CERN Document Server

Karpilovsky, G

1994-01-01

This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory

Symplectic geometry and Fourier analysis

CERN Document Server

Wallach, Nolan R

2018-01-01

Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

Theoretical concepts of fractal geometry semkow by radon emanation in solids

International Nuclear Information System (INIS)

Cruz G, H.

1996-01-01

The objective of this work is to introduce the fractal geometry concept to the study of gaseous emanations in solids, specially with reference to radon emission in mineral grains. The basic elements of fractals theory are developed. A fractal is defined as an auto similar subassembly, which fractal dimension is greater than the topological dimension. Starting from this, and making a brief description of the physicals basis of radon emission in solids, a model between emanation power (E R ) and the ratio s/v (surface to volume), is founded. A Gaussian model is assumed for extent of recoil from alpha decay of Ra-226. Using the results of Pfeifer it is obtained that distribution of pore size is scaled like Br -D-1 , where D: fractal[dimension, B: constant and r: pore radius. After an adequate mathematics expansion, it is found that the expression for emanation power is scaled like r 0 D-3 (r 0 grain radius). We may concluded that if we have a logarithmic graph of E R vs size of grain we can deduce the fractal dimension of the emanation surface. The experimental data of different materials provides an interval into fractal dimension D , between 2.1 to 2.86. (author). 5 refs., 1 tab

Teacher spatial skills are linked to differences in geometry instruction.

Science.gov (United States)

Otumfuor, Beryl Ann; Carr, Martha

2017-12-01

Spatial skills have been linked to better performance in mathematics. The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Fifty-six middle school teachers participated in the study. The teachers were administered spatial measures of mental rotations and spatial visualization. Next, a single geometry class was videotaped. Correlational analyses revealed that spatial skills significantly correlate with teacher's use of representational gestures and content and pedagogical knowledge during instruction of geometry. Spatial skills did not independently correlate with the use of pointing gestures or the use of pictorial representations. However, an interaction term between spatial skills and content and pedagogical knowledge did correlate significantly with the use of pictorial representations. Teacher experience as measured by the number of years of teaching and highest degree did not appear to affect the relationships among the variables with the exception of the relationship between spatial skills and teacher content and pedagogical knowledge. Teachers with better spatial skills are also likely to use representational gestures and to show better content and pedagogical knowledge during instruction. Spatial skills predict pictorial representation use only as a function of content and pedagogical knowledge. © 2017 The British Psychological Society.

Memetics of representation

Directory of Open Access Journals (Sweden)

Roberto De Rubertis

2012-06-01

Full Text Available This article will discuss about the physiological genesis of representation and then it will illustrate the developments, especially in evolutionary perspective, and it will show how these are mainly a result of accidental circumstances, rather than of deliberate intention of improvement. In particular, it will be argue that the representation has behaved like a meme that has arrived to its own progressive evolution coming into symbiosis with the different cultures in which it has spread, and using in this activity human work “unconsciously”. Finally it will be shown how in this action the geometry is an element key, linked to representation both to construct images using graphics operations and to erect buildings using concrete operations.

U.S. Army Armament Research, Development and Engineering Center Grain Evaluation Software to Numerically Predict Linear Burn Regression for Solid Propellant Grain Geometries

Science.gov (United States)

2017-10-01

ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...distribution is unlimited. AD U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER Munitions Engineering Technology Center Picatinny...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID

Representation Theory of Algebraic Groups and Quantum Groups

CERN Document Server

Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki

2010-01-01

Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Learners engaging with transformation geometry

African Journals Online (AJOL)

participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...

Perception of global facial geometry is modulated through experience

Directory of Open Access Journals (Sweden)

Meike Ramon

2015-03-01

Full Text Available Identification of personally familiar faces is highly efficient across various viewing conditions. While the presence of robust facial representations stored in memory is considered to aid this process, the mechanisms underlying invariant identification remain unclear. Two experiments tested the hypothesis that facial representations stored in memory are associated with differential perceptual processing of the overall facial geometry. Subjects who were personally familiar or unfamiliar with the identities presented discriminated between stimuli whose overall facial geometry had been manipulated to maintain or alter the original facial configuration (see Barton, Zhao & Keenan, 2003. The results demonstrate that familiarity gives rise to more efficient processing of global facial geometry, and are interpreted in terms of increased holistic processing of facial information that is maintained across viewing distances.

Geometry, structure and randomness in combinatorics

CERN Document Server

Nešetřil, Jaroslav; Pellegrini, Marco

2014-01-01

This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include:  graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Basic algebraic geometry, v.2

CERN Document Server

Shafarevich, Igor Rostislavovich

1994-01-01

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

Introduction to representation theory

CERN Document Server

Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex

2011-01-01

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...

Guide to Computational Geometry Processing

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

A first course in geometry

CERN Document Server

Walsh, Edward T

2014-01-01

This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

An introduction to algebraic geometry and algebraic groups

CERN Document Server

Geck, Meinolf

2003-01-01

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups

A study in derived algebraic geometry volume I : correspondences and duality

CERN Document Server

Gaitsgory, Dennis

2017-01-01

Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a "renormalization" of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of \\infty-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the \\mathrm{(}\\infty, 2\\mathrm{)}-category of correspondences needed for the sec...

Fast rendering of scanned room geometries

DEFF Research Database (Denmark)

Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte

2014-01-01

Room acoustics are rendered in Virtual Realities based on models of the real world. These are typically rather coarse representations of the true geometry resulting in room impulse responses with a lack of natural detail. This problem can be overcome by using data scanned by sensors, such as e...

Room acoustics modeling using a point-cloud representation of the room geometry

DEFF Research Database (Denmark)

Markovic, Milos; Olesen, Søren Krarup; Hammershøi, Dorte

2013-01-01

Room acoustics modeling is usually based on the room geometry that is parametrically described prior to a sound transmission calculation. This is a highly room-specific task and rather time consuming if a complex geometry is to be described. Here, a run time generic method for an arbitrary room...... geometry acquisition is presented. The method exploits a depth sensor of the Kinect device that provides a point based information of a scanned room interior. After post-processing of the Kinect output data, a 3D point-cloud model of the room is obtained. Sound transmission between two selected points...... level of user immersion by a real time acoustical simulation of a dynamic scenes....

The Kerr geometry, complex world lines and hyperbolic strings

International Nuclear Information System (INIS)

Burinskii, A.Ya.

1994-01-01

In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)

Geometry The Language of Space and Form (Revised Edition)

CERN Document Server

Tabak, John

2011-01-01

Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernha

SACALCCYL, Calculates the average solid angle subtended by a volume; SACALC2B, Calculates the average solid angle for source-detector geometries

International Nuclear Information System (INIS)

Whitcher, Ralph

2007-01-01

1 - Description of program or function: SACALC2B calculates the average solid angle subtended by a rectangular or circular detector window to a coaxial or non-coaxial rectangular, circular or point source, including where the source and detector planes are not parallel. SACALC C YL calculates the average solid angle subtended by a cylinder to a rectangular or circular source, plane or thick, at any location and orientation. This is needed, for example, in calculating the intrinsic gamma efficiency of a detector such as a GM tube. The program also calculates the number of hits on the cylinder side and on each end, and the average path length through the detector volume (assuming no scattering or absorption). Point sources can be modelled by using a circular source of zero radius. NEA-1688/03: Documentation has been updated (January 2006). 2 - Methods: The program uses a Monte Carlo method to calculate average solid angle for source-detector geometries that are difficult to analyse by analytical methods. The values of solid angle are calculated to accuracies of typically better than 0.1%. The calculated values from the Monte Carlo method agree closely with those produced by polygon approximation and numerical integration by Gardner and Verghese, and others. 3 - Restrictions on the complexity of the problem: The program models a circular or rectangular detector in planes that are not necessarily coaxial, nor parallel. Point sources can be modelled by using a circular source of zero radius. The sources are assumed to be uniformly distributed. NEA-1688/04: In SACALC C YL, to avoid rounding errors, differences less than 1 E-12 are assumed to be zero

The Koslowski-Sahlmann representation: quantum configuration space

Science.gov (United States)

Campiglia, Miguel; Varadarajan, Madhavan

2014-09-01

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.

Categorification in geometry, topology, and physics

CERN Document Server

Beliakova, Anna

2017-01-01

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Geometry of the Borel - de Siebenthal discrete series

DEFF Research Database (Denmark)

Ørsted, Bent; Wolf, Joseph A

Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguished positive root system + for which there is a unique noncompact simple root , the “Borel – de Siebenthal...... system”. There is a lot of fascinating geometry associated to the corresponding “Borel – de Siebenthal discrete series” representations of G0. In this paper we explore some of those geometric aspects and we work out the K0–spectra of the Borel – de Siebenthal discrete series representations. This has...

Boundary representation modelling techniques

CERN Document Server

2006-01-01

Provides the most complete presentation of boundary representation solid modelling yet publishedOffers basic reference information for software developers, application developers and users Includes a historical perspective as well as giving a background for modern research.

Generalizing optical geometry

International Nuclear Information System (INIS)

Jonsson, Rickard; Westman, Hans

2006-01-01

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

A CAD based geometry model for simulation and analysis of particle detector data

Energy Technology Data Exchange (ETDEWEB)

Milde, Michael; Losekamm, Martin; Poeschl, Thomas; Greenwald, Daniel; Paul, Stephan [Technische Universitaet Muenchen, 85748 Garching (Germany)

2016-07-01

The development of a new particle detector requires a good understanding of its setup. A detailed model of the detector's geometry is not only needed during construction, but also for simulation and data analysis. To arrive at a consistent description of the detector geometry a representation is needed that can be easily implemented in different software tools used during data analysis. We developed a geometry representation based on CAD files that can be easily used within the Geant4 simulation framework and analysis tools based on the ROOT framework. This talk presents the structure of the geometry model and show its implementation using the example of the event reconstruction developed for the Multi-purpose Active-target Particle Telescope (MAPT). The detector consists of scintillating plastic fibers and can be used as a tracking detector and calorimeter with omnidirectional acceptance. To optimize the angular resolution and the energy reconstruction of measured particles, a detailed detector model is needed at all stages of the reconstruction.

Conformal-Based Surface Morphing and Multi-Scale Representation

Directory of Open Access Journals (Sweden)

Ka Chun Lam

2014-05-01

Full Text Available This paper presents two algorithms, based on conformal geometry, for the multi-scale representations of geometric shapes and surface morphing. A multi-scale surface representation aims to describe a 3D shape at different levels of geometric detail, which allows analyzing or editing surfaces at the global or local scales effectively. Surface morphing refers to the process of interpolating between two geometric shapes, which has been widely applied to estimate or analyze deformations in computer graphics, computer vision and medical imaging. In this work, we propose two geometric models for surface morphing and multi-scale representation for 3D surfaces. The basic idea is to represent a 3D surface by its mean curvature function, H, and conformal factor function λ, which uniquely determine the geometry of the surface according to Riemann surface theory. Once we have the (λ, H parameterization of the surface, post-processing of the surface can be done directly on the conformal parameter domain. In particular, the problem of multi-scale representations of shapes can be reduced to the signal filtering on the λ and H parameters. On the other hand, the surface morphing problem can be transformed to an interpolation process of two sets of (λ, H parameters. We test the proposed algorithms on 3D human face data and MRI-derived brain surfaces. Experimental results show that our proposed methods can effectively obtain multi-scale surface representations and give natural surface morphing results.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects

Exploring the Structure of Spatial Representations

Science.gov (United States)

Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela

2016-01-01

It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these ‘cognitive maps’ are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics) characterizing participants’ psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants’ cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants’ spatial representations, providing further support for clustering in spatial memory. PMID:27347681

Some Remarks on Navajo Geometry and Piagetian Genetic Theory.

Science.gov (United States)

Pinxten, Rik

1991-01-01

Examines aspects of Navajo cosmology relevant to understanding Navajo spatial representations. Compares Navajo children's spatial knowledge with Piaget's findings about the development of geometric concepts in Swiss children. Describes classroom activities whereby Navajo children explore the geometry inherent in their cultural and physical…

Poincaré Embeddings for Learning Hierarchical Representations

CERN Multimedia

CERN. Geneva

2018-01-01

Abstracts: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically do not account for this property. In this talk, I will discuss a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.      &...

Development of CAD-Based Geometry Processing Module for a Monte Carlo Particle Transport Analysis Code

International Nuclear Information System (INIS)

Choi, Sung Hoon; Kwark, Min Su; Shim, Hyung Jin

2012-01-01

As The Monte Carlo (MC) particle transport analysis for a complex system such as research reactor, accelerator, and fusion facility may require accurate modeling of the complicated geometry. Its manual modeling by using the text interface of a MC code to define the geometrical objects is tedious, lengthy and error-prone. This problem can be overcome by taking advantage of modeling capability of the computer aided design (CAD) system. There have been two kinds of approaches to develop MC code systems utilizing the CAD data: the external format conversion and the CAD kernel imbedded MC simulation. The first approach includes several interfacing programs such as McCAD, MCAM, GEOMIT etc. which were developed to automatically convert the CAD data into the MCNP geometry input data. This approach makes the most of the existing MC codes without any modifications, but implies latent data inconsistency due to the difference of the geometry modeling system. In the second approach, a MC code utilizes the CAD data for the direct particle tracking or the conversion to an internal data structure of the constructive solid geometry (CSG) and/or boundary representation (B-rep) modeling with help of a CAD kernel. MCNP-BRL and OiNC have demonstrated their capabilities of the CAD-based MC simulations. Recently we have developed a CAD-based geometry processing module for the MC particle simulation by using the OpenCASCADE (OCC) library. In the developed module, CAD data can be used for the particle tracking through primitive CAD surfaces (hereafter the CAD-based tracking) or the internal conversion to the CSG data structure. In this paper, the performances of the text-based model, the CAD-based tracking, and the internal CSG conversion are compared by using an in-house MC code, McSIM, equipped with the developed CAD-based geometry processing module

On an analytical representation of the solution of the one-dimensional transport equation for a multi-group model in planar geometry

Energy Technology Data Exchange (ETDEWEB)

Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)

2015-07-01

In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)

Computational geometry for reactor applications

International Nuclear Information System (INIS)

Brown, F.B.; Bischoff, F.G.

1988-01-01

Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications

Differential geometry based solvation model II: Lagrangian formulation.

Science.gov (United States)

Chen, Zhan; Baker, Nathan A; Wei, G W

2011-12-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of

GPU-accelerated depth map generation for X-ray simulations of complex CAD geometries

Science.gov (United States)

Grandin, Robert J.; Young, Gavin; Holland, Stephen D.; Krishnamurthy, Adarsh

2018-04-01

Interactive x-ray simulations of complex computer-aided design (CAD) models can provide valuable insights for better interpretation of the defect signatures such as porosity from x-ray CT images. Generating the depth map along a particular direction for the given CAD geometry is the most compute-intensive step in x-ray simulations. We have developed a GPU-accelerated method for real-time generation of depth maps of complex CAD geometries. We preprocess complex components designed using commercial CAD systems using a custom CAD module and convert them into a fine user-defined surface tessellation. Our CAD module can be used by different simulators as well as handle complex geometries, including those that arise from complex castings and composite structures. We then make use of a parallel algorithm that runs on a graphics processing unit (GPU) to convert the finely-tessellated CAD model to a voxelized representation. The voxelized representation can enable heterogeneous modeling of the volume enclosed by the CAD model by assigning heterogeneous material properties in specific regions. The depth maps are generated from this voxelized representation with the help of a GPU-accelerated ray-casting algorithm. The GPU-accelerated ray-casting method enables interactive (> 60 frames-per-second) generation of the depth maps of complex CAD geometries. This enables arbitrarily rotation and slicing of the CAD model, leading to better interpretation of the x-ray images by the user. In addition, the depth maps can be used to aid directly in CT reconstruction algorithms.

Preliminary investigation of solid target geometry

Energy Technology Data Exchange (ETDEWEB)

Haga, Katsuhiro; Kaminaga, Masanori; Hino, Ryutaro; Takada, Hiroshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Shafiqul, I.M.; Tsuji, Nobumasa; Okamoto, Hutoshi; Kumasaka, Katsuyuki; Hayashi, Katsumi

1997-11-01

In this report, we introduce the developing plan for a solid metal target structure. Supposing tantalum as the target material, the temperature distribution and the maximum thermal stress in a tantalum plate of a solid metal target was evaluated under a water cooling condition, using the heat generation rate calculated with the JAERI`s neutron transport code. The calculation results showed that the water velocity was higher than 10 m/s in order to cool the 3mm-thick target plate down to 200degC when the target surface was smooth and heat transfer rate was calculated with the Dittus-Boelter equation. In this case, the maximum thermal stress is 50 MPa at the target plate surface. The coolant water flow distribution in a target vessel was also evaluated for ISIS-type flow channels and the parallel flow channels. In the ISIS-type flow channels, at least 25mm height of the coolant plenum is needed for a uniform flow distribution. The maximum flow velocity difference between the flow gaps in the parallel flow channels was 30%. A heat transfer augmentation experiment was conducted using ribbed-surface flow channel. The heat transfer rate was confirmed to increase up to twice the value of that for a smooth surface. (author)

Deep supervised, but not unsupervised, models may explain IT cortical representation.

Directory of Open Access Journals (Sweden)

Seyed-Mahdi Khaligh-Razavi

2014-11-01

Full Text Available Inferior temporal (IT cortex in human and nonhuman primates serves visual object recognition. Computational object-vision models, although continually improving, do not yet reach human performance. It is unclear to what extent the internal representations of computational models can explain the IT representation. Here we investigate a wide range of computational model representations (37 in total, testing their categorization performance and their ability to account for the IT representational geometry. The models include well-known neuroscientific object-recognition models (e.g. HMAX, VisNet along with several models from computer vision (e.g. SIFT, GIST, self-similarity features, and a deep convolutional neural network. We compared the representational dissimilarity matrices (RDMs of the model representations with the RDMs obtained from human IT (measured with fMRI and monkey IT (measured with cell recording for the same set of stimuli (not used in training the models. Better performing models were more similar to IT in that they showed greater clustering of representational patterns by category. In addition, better performing models also more strongly resembled IT in terms of their within-category representational dissimilarities. Representational geometries were significantly correlated between IT and many of the models. However, the categorical clustering observed in IT was largely unexplained by the unsupervised models. The deep convolutional network, which was trained by supervision with over a million category-labeled images, reached the highest categorization performance and also best explained IT, although it did not fully explain the IT data. Combining the features of this model with appropriate weights and adding linear combinations that maximize the margin between animate and inanimate objects and between faces and other objects yielded a representation that fully explained our IT data. Overall, our results suggest that explaining

Parameterized combinatorial geometry modeling in Moritz

International Nuclear Information System (INIS)

Van Riper, K.A.

2005-01-01

We describe the use of named variables as surface and solid body coefficients in the Moritz geometry editing program. Variables can also be used as material numbers, cell densities, and transformation values. A variable is defined as a constant or an arithmetic combination of constants and other variables. A variable reference, such as in a surface coefficient, can be a single variable or an expression containing variables and constants. Moritz can read and write geometry models in MCNP and ITS ACCEPT format; support for other codes will be added. The geometry can be saved with either the variables in place, for modifying the models in Moritz, or with the variables evaluated for use in the transport codes. A program window shows a list of variables and provides fields for editing them. Surface coefficients and other values that use a variable reference are shown in a distinctive style on object property dialogs; associated buttons show fields for editing the reference. We discuss our use of variables in defining geometry models for shielding studies in PET clinics. When a model is parameterized through the use of variables, changes such as room dimensions, shielding layer widths, and cell compositions can be quickly achieved by changing a few numbers without requiring knowledge of the input syntax for the transport code or the tedious and error prone work of recalculating many surface or solid body coefficients. (author)

Geometry and project: the example of Piazza della Vittoria in Genoa

Directory of Open Access Journals (Sweden)

Luisa Cogorno

2012-06-01

Full Text Available The study on the Genoese architectures in the thirties of Piazza della Vittoria  highlights the paramount  role of geometry for the project. The square, created by architect Marcello Piacentini between 1927 and 1930, stands opposite the railway station Genoa Brignole, pursuing a very logical representation: a new, very wide square surrounded by arcades ... the new civic-wordly heart of the  city (M. Piacentini. The methodological tool applied for the critical reading  was the  integrated relief: perceptual and historical analysis, relief and graphic representation of the whole and of the details, reconstruction of the compositional logic, study of materials used; the different phases showed the trasversality of the role of geometry –verified by the metric survey and by the compositive reading of the proportions- and the presence of dimensional canons unusual for the city.

Children's schemes for anticipating the validity of nets for solids

Science.gov (United States)

Wright, Vince; Smith, Ken

2017-09-01

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were interviewed on two occasions about their anticipation of whether or not given nets for the cube- and square-based pyramid would fold to form the target solid. Vergnaud's ( Journal of Mathematical Behavior, 17(2), 167-181, 1998, Human Development, 52, 83-94, 2009) four characteristics of schemes were used as a theoretical lens to analyse the data. Successful schemes depended on the interaction of operational invariants, such as strategic choice of the base, rules for action, particularly rotation of shapes, and anticipations of composites of polygons in the net forming arrangements of faces in the solid. Inferences were rare. These data suggest that students need teacher support to make inferences, in order to create transferable schemes.

CAD-based Monte Carlo automatic modeling method based on primitive solid

International Nuclear Information System (INIS)

Wang, Dong; Song, Jing; Yu, Shengpeng; Long, Pengcheng; Wang, Yongliang

2016-01-01

Highlights: • We develop a method which bi-convert between CAD model and primitive solid. • This method was improved from convert method between CAD model and half space. • This method was test by ITER model and validated the correctness and efficiency. • This method was integrated in SuperMC which could model for SuperMC and Geant4. - Abstract: Monte Carlo method has been widely used in nuclear design and analysis, where geometries are described with primitive solids. However, it is time consuming and error prone to describe a primitive solid geometry, especially for a complicated model. To reuse the abundant existed CAD models and conveniently model with CAD modeling tools, an automatic modeling method for accurate prompt modeling between CAD model and primitive solid is needed. An automatic modeling method for Monte Carlo geometry described by primitive solid was developed which could bi-convert between CAD model and Monte Carlo geometry represented by primitive solids. While converting from CAD model to primitive solid model, the CAD model was decomposed into several convex solid sets, and then corresponding primitive solids were generated and exported. While converting from primitive solid model to the CAD model, the basic primitive solids were created and related operation was done. This method was integrated in the SuperMC and was benchmarked with ITER benchmark model. The correctness and efficiency of this method were demonstrated.

Granular flows in constrained geometries

Science.gov (United States)

Murthy, Tejas; Viswanathan, Koushik

Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

On a microscopic representation of space-time

International Nuclear Information System (INIS)

Dahm, R.

2012-01-01

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and “reduce” the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) → usp(4) → su(2) × u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H 5 with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H 2 ⊕ H 3 with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.

A Framework for Parallel Numerical Simulations on Multi-Scale Geometries

KAUST Repository

Varduhn, Vasco

2012-06-01

In this paper, an approach on performing numerical multi-scale simulations on fine detailed geometries is presented. In particular, the focus lies on the generation of sufficient fine mesh representations, whereas a resolution of dozens of millions of voxels is inevitable in order to sufficiently represent the geometry. Furthermore, the propagation of boundary conditions is investigated by using simulation results on the coarser simulation scale as input boundary conditions on the next finer scale. Finally, the applicability of our approach is shown on a two-phase simulation for flooding scenarios in urban structures running from a city wide scale to a fine detailed in-door scale on feature rich building geometries. © 2012 IEEE.

Simulation technique for slurries interacting with moving parts and deformable solids with applications

Science.gov (United States)

Mutabaruka, Patrick; Kamrin, Ken

2018-04-01

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

Evaluation of tomographic-image based geometries with PENELOPE Monte Carlo

International Nuclear Information System (INIS)

Kakoi, A.A.Y.; Galina, A.C.; Nicolucci, P.

2009-01-01

The Monte Carlo method can be used to evaluate treatment planning systems or for the determination of dose distributions in radiotherapy planning due to its accuracy and precision. In Monte Carlo simulation packages typically used in radiotherapy, however, a realistic representation of the geometry of the patient can not be used, which compromises the accuracy of the results. In this work, an algorithm for the description of geometries based on CT images of patients, developed to be used with Monte Carlo simulation package PENELOPE, is tested by simulating the dose distribution produced by a photon beam of 10 MV. The geometry simulated was based on CT images of a planning of prostate cancer. The volumes of interest in the treatment were adequately represented in the simulation geometry, allowing the algorithm to be used in verification of doses in radiotherapy treatments. (author)

Finsler geometry, relativity and gauge theories

International Nuclear Information System (INIS)

Asanov, G.S.

1985-01-01

This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)

Effective elastic properties of damaged isotropic solids

International Nuclear Information System (INIS)

Lee, U Sik

1998-01-01

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two-and three-dimensional isotropic solids

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Perbandingan antara Keefektifan Model Guided Discovery Learning dan Project-Based Learning pada Matakuliah Geometri

Directory of Open Access Journals (Sweden)

Okky Riswandha Imawan

2015-12-01

Abstract This research aims to describe the effectiveness and effectiveness differences of the Guided Discovery Learning (GDL Model and the Project Based Learning (PjBL Model in terms of achievement, self-confidence, and critical thinking skills of students on the Solid Geometry subjects. This research was quasi experimental. The research subjects were two undergraduate classes of Mathematics Education Program, Ahmad Dahlan University, in their second semester, established at random. The data analysis to test the effectiveness of the GDL and PjBL Models in terms of each of the dependent variables used the t-test. The data analysis to test differences between effectiveness of the GDL and that of the PjBL Model used the MANOVA test. The results of this research show that viewed from achievement, self confidence, and critical thinking skills of the students are the application of the GDL Model on Solid Geometry subject is effective, the application of the PjBL Model on Solid Geometry subject is effective, and there is no difference in the effectiveness of GDL and PjBL Models on Solid Geometry subject in terms of achievement, self confidence, and critical thinking skills of the students. Keywords: guided discovery learning model, project-based learning model, achievement, self-confidence, critical thinking skills

An integral equation-based numerical solver for Taylor states in toroidal geometries

Science.gov (United States)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Comparison of Microinstability Properties for Stellarator Magnetic Geometries

International Nuclear Information System (INIS)

Rewoldt, G.; Ku, L.-P.; Tang, W.M.

2005-01-01

The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

PENILAIAN PEMAHAMAN REPRESENTASI GRAFIK MATERI OPTIKA GEOMETRI MENGGUNAKAN TES DIAGNOSTIK

Directory of Open Access Journals (Sweden)

Wawan Bunawan

2015-06-01

Full Text Available Abstrak: Tujuan penelitian adalah mengembangkan dan menerapkan tes diagnostik pilihan ganda tiga tingkat untuk mengukur pemahaman representasi grafik mahasiswa terkait esensi inkuiri sains dan materi optika geometri. Penelitian menggunakan metode campuran melibatkan 83 mahasiswa calon guru fisika di satu LPTK Sumatera Utara. Instrumen tes diagnostik terlebih dahulu didesain kemudian disempurnakan selama proses, direvisi, dan digunakan untuk mendeteksi dan menilai pemahaman representasi grafik mahasiswa calon guru fisika. Instrumen tes telah dikembangkan untuk dapat mendiagnosis dan memperbaiki kesalahan-kesalahan yang dilakukan calon guru fisika terkait dengan keterampilan mengonstruk grafik, menemukan kesulitan-kesulitan dalam membaca dan menginterpretasi grafik. Analisis data dilakukan secara kualitatif dan kuantitatif. Hasil studi menunjukkan pembacaan grafik dan keterampilan menginterpretasi grafik calon guru fisika masih belum memadai dan juga kemahiran dalam menganalisis grafik bergantung pada jenis grafik dan level atau tipe pertanyaan yang dikembangkan. Kata Kunci: representasi grafik, optik geometri, diagnostik tes ASSESSING OF UNDERSTANDING GRAPHICAL REPRESENTATION CONTENT GEOMETRICAL OPTIC USING DIAGNOSTIC TEST Abstract: The purpose of this study is to develop and apply three tier multiple choice diagnostic test to measure student’s understanding of graphical representation about essential features of inquiry and content geometrical optic. The study was conducted using mixed methods and carried out with 83 prephysics teachers at a University of Teachers Education in North Sumatera. The diagnostic instrument was designed and then progressively refined, revised, and implemented to detect and assess student’s understanding of graphical representation. Test instrument was developed to diagnose and correct the mistakes made by pre-service physics teachers about construction graphic skills, difficulties in the reading and interpretation

Multiple-view, Multiple-selection Visualization of Simulation Geometry in CMS

International Nuclear Information System (INIS)

Bauerdick, L A T; Eulisse, G; Jones, C; McCauley, T; Osborne, I; Kovalskyi, D; Mrak Tadel, A; Tadel, M; Yagil, A

2012-01-01

Fireworks, the event-display program of CMS, was extended with an advanced geometry visualization package. ROOT's TGeo geometry is used as internal representation, shared among several geometry views. Each view is represented by a GUI list-tree widget, implemented as a flat vector to allow for fast searching, selection, and filtering by material type, node name, and shape type. Display of logical and physical volumes is supported. Color, transparency, and visibility flags can be modified for each node or for a selection of nodes. Further operations, like opening of a new view or changing of the root node, can be performed via a context menu. Node selection and graphical properties determined by the list-tree view can be visualized in any 3D graphics view of Fireworks. As each 3D view can display any number of geometry views, a user is free to combine different geometry-view selections within the same 3D view. Node-selection by proximity to a given point is possible. A visual clipping box can be set for each geometry view to limit geometry drawing into a specified region. Visualization of geometric overlaps, as detected by TGeo, is also supported. The geometry visualization package is used for detailed inspection and display of simulation geometry with or without the event data. It also serves as a tool for geometry debugging and inspection, facilitating development of geometries for CMS detector upgrades and for SLHC.

Geometry and trigonometry

CERN Document Server

2015-01-01

This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent

Interactive three-dimensional visualization and creation of geometries for Monte Carlo calculations

International Nuclear Information System (INIS)

Theis, C.; Buchegger, K.H.; Brugger, M.; Forkel-Wirth, D.; Roesler, S.; Vincke, H.

2006-01-01

The implementation of three-dimensional geometries for the simulation of radiation transport problems is a very time-consuming task. Each particle transport code supplies its own scripting language and syntax for creating the geometries. All of them are based on the Constructive Solid Geometry scheme requiring textual description. This makes the creation a tedious and error-prone task, which is especially hard to master for novice users. The Monte Carlo code FLUKA comes with built-in support for creating two-dimensional cross-sections through the geometry and FLUKACAD, a custom-built converter to the commercial Computer Aided Design package AutoCAD, exists for 3D visualization. For other codes, like MCNPX, a couple of different tools are available, but they are often specifically tailored to the particle transport code and its approach used for implementing geometries. Complex constructive solid modeling usually requires very fast and expensive special purpose hardware, which is not widely available. In this paper SimpleGeo is presented, which is an implementation of a generic versatile interactive geometry modeler using off-the-shelf hardware. It is running on Windows, with a Linux version currently under preparation. This paper describes its functionality, which allows for rapid interactive visualization as well as generation of three-dimensional geometries, and also discusses critical issues regarding common CAD systems

Differential geometry the mathematical works of J. H. C. Whitehead

CERN Document Server

James, I M

1962-01-01

The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations

Dependence of displacement fields on the damage cluster nucleus geometry

International Nuclear Information System (INIS)

Grigor'ev, A.N.; Zabela, A.G.; Nikolajchuk, L.I.; Prokhorenko, E.M.; Khizhnyak, N.A.

1988-01-01

Displacement fields in doped crystals of cubic and hexagonal structures containing extended defects are studied. The numerical results are presented depending on the damage cluster nucleus geometry. All calculations are based on analytical representations of displacement fields in an integral form using elasticity theory equations. The investigation results are vital for radiation physics as they permit to predict and calculate both the character and geometry of distortions near damaged region cluster and determine cluster parameters on the basis of the known structure of distortions. Dependences are obtained for the following monocrystals: Mg, ZnO, CdS, W, Au. 6 refs.; 3 figs

Multiple-view, multiple-selection visualization of simulation geometry in CMS

CERN Document Server

Mrak Tadel, Alja

2012-01-01

Fireworks, the event-display program of CMS, was extended with an advanced geometry visualization package. ROOT's TGeo geometry is used as internal representation, shared among several geometry views. Each view is represented by a GUI list-tree widget, implemented as a flat vector to allow for fast searching, selection, and filtering by material type, node name, and shape type. Display of logical and physical volumes is supported. Color, transparency, and visibility flags can be modified for each node or for a selection of nodes. Further operations, like opening of a new view or changing of the root node, can be performed via a context menu. Node selection and graphical properties determined by the list-tree view can be visualized in any 3D graphics view of Fireworks. As each 3D view can display any number of geometry views, a user is free to combine different geometry-view selections within the same 3D view. Node-selection by proximity to a given point is possible. A visual clipping box can be set for each g...

Stages as models of scene geometry.

Science.gov (United States)

Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark

2010-09-01

Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.

Nonperturbative quantum geometries

International Nuclear Information System (INIS)

Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara

1988-01-01

Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)

The Search for Fidelity in Geometry Apps: An Exercise in Futility?

Science.gov (United States)

Larkin, Kevin

2015-01-01

As the use of mathematics apps in classrooms becomes more prevalent, robust research into their effectiveness is required to inform best practice regarding their use. This is particularly the case for Geometry apps where accurate and dynamic representations are critical in enhancing mathematical learning. This paper provides findings from an…

Representations of the algebra Uq'(son) related to quantum gravity

International Nuclear Information System (INIS)

Klimyk, A.U.

2002-01-01

The aim of this paper is to review our results on finite dimensional irreducible representations of the nonstandard q-deformation U q ' (so n ) of the universal enveloping algebra U(so(n)) of the Lie algebra so(n) which does not coincide with the Drinfeld-Jimbo quantum algebra U q (so n ).This algebra is related to algebras of observables in quantum gravity and to algebraic geometry.Irreducible finite dimensional representations of the algebra U q ' (so n ) for q not a root of unity and for q a root of unity are given

A Geometry Based Infra-Structure for Computational Analysis and Design

Science.gov (United States)

Haimes, Robert

1998-01-01

). This is particularly onerous for modern CAD systems based on solid modeling. The part was a proper solid and in the translation to IGES has lost this important characteristic. STEP is another standard for CAD data that exists and supports the concept of a solid. The problem with STEP is that a solid modeling geometry kernel is required to query and manipulate the data within this type of file. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. Adroit multi-block methods are not far behind. This means that a million node steady-state solution can be computed on the order of hours (using current high performance computers) starting from this 'good' geometry. Unfortunately, the geometry usually transmitted from the CAD system is not 'good' in the grid generator sense. The grid generator needs smooth closed solid geometry. It can take a week (or more) of interaction with the CAD output (sometimes by hand) before the process can begin. One way Communication. (3) One-way Communication -- All information travels on from one phase to the next. This makes procedures like node adaptation difficult when attempting to add or move nodes that sit on bounding surfaces (when the actual surface data has been lost after the grid generation phase). Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive. There is also no way to easily deal with this system in a modular manner. One can only replace the grid generator, for example, if the software reads and writes the same files. Instead of the serial approach to analysis as described above, CAPRI takes a geometry centric approach. This makes the actual geometry (not a discretized version) accessible to all phases of the

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Directory of Open Access Journals (Sweden)

Frédéric Barbaresco

2016-11-01

Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

On Finsler Geometry and Applications in Mechanics: Review and New Perspectives

Directory of Open Access Journals (Sweden)

J. D. Clayton

2015-01-01

direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.

Galileo symmetries in polymer particle representation

International Nuclear Information System (INIS)

Chiou, D-W

2007-01-01

To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description

The geometry of celestial mechanics

CERN Document Server

Geiges, Hansjörg

2016-01-01

Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

Power Block Geometry Applied to the Building of Power Electronics Converters

Science.gov (United States)

dos Santos, E. C., Jr.; da Silva, E. R. C.

2013-01-01

This paper proposes a new methodology, Power Block Geometry (PBG), for the presentation of power electronics topologies that process ac voltage. PBG's strategy uses formal methods based on a geometrical representation with particular rules and defines a universe with axioms and conjectures to establish a formation law. It allows power…

3rd International Conference on Computational Mathematics and Computational Geometry

CERN Document Server

Ravindran, Anton

2016-01-01

This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computati...

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

Electronic Properties of Corrugated Graphene, the Heisenberg Principle and Wormhole Geometry in Solid State

International Nuclear Information System (INIS)

Atanasov, Victor; Saxena, Avadh

2010-12-01

Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and in the process the embedding of this surface into the three dimensional world is accounted for. As a result an invariant geometric potential arises which scales linearly with the Mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or 'straintronics' is clearly an important field of study in graphene. This opens a venue to producing electronic devices, MEMS and NEMS where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks like in the curved space-time of general relativity. In this context, we explore a two-dimensional cross-section of the wormhole geometry realized with graphene as a solid state thought experiment. (author)

Geometry of supersymmetric gauge theories

International Nuclear Information System (INIS)

Gieres, F.

1988-01-01

This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism

Geometry Effect Investigation on a Conical Chamber with Porous Media Boundary Condition Using Computational Fluid Dynamic (CFD Technique

Directory of Open Access Journals (Sweden)

Yazid Bindar

2009-11-01

Full Text Available The present study is an attempt to introduce the method for optimizing the geometry of the unit process. The comprehensive unit process performances are generated by a CFD engine. The CFD engine can simulate the unit process performances at what ever conditions. Both design geometry and operating variables weree used on the CFD simulation. The burden on a simplified process was taken out from CFD simulation. A complex geometry of a unit process is represented by a secondary reformer. A secondary reformer has a conical volume as a space to undergo the combustion reaction before entering the catalyst bed. This complexity is added by the boundary of the porous solid surface as the top surface of catalyst bed. The spread angle affect the flow pattern in side the conical volume having a porous solid surface as a base. The spread angle above 65o results the disappearing of the recirculation flow. The inlet distance from the porous solid surface also can exhibit different characteristics of recirculation flow. The closer the distance to the porous solid surface, the stronger the recirculation is. The inlet velocity values have no significant effect on the flow pattern. The introduction of a solid volume inside the geometry creates the distortion of the flow pattern. In the application, the inserted solid volume is equivalent to a burner. It means that the use of the burner inherently produces some problems of the flow distribution

Representations and Techniques for 3D Object Recognition and Scene Interpretation

CERN Document Server

Hoiem, Derek

2011-01-01

One of the grand challenges of artificial intelligence is to enable computers to interpret 3D scenes and objects from imagery. This book organizes and introduces major concepts in 3D scene and object representation and inference from still images, with a focus on recent efforts to fuse models of geometry and perspective with statistical machine learning. The book is organized into three sections: (1) Interpretation of Physical Space; (2) Recognition of 3D Objects; and (3) Integrated 3D Scene Interpretation. The first discusses representations of spatial layout and techniques to interpret physi

The use of tetrahedral mesh geometries in Monte Carlo simulation of applicator based brachytherapy dose distributions

International Nuclear Information System (INIS)

Fonseca, Gabriel Paiva; Yoriyaz, Hélio; Landry, Guillaume; White, Shane; Reniers, Brigitte; Verhaegen, Frank; D’Amours, Michel; Beaulieu, Luc

2014-01-01

Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192 Ir sources and 50 kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator. All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios. In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases. In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator. (paper)

Space Charge Effect in the Sheet and Solid Electron Beam

Science.gov (United States)

Song, Ho Young; Kim, Hyoung Suk; Ahn, Saeyoung

1998-11-01

We analyze the space charge effect of two different types of electron beam ; sheet and solid electron beam. Electron gun simulations are carried out using shadow and control grids for high and low perveance. Rectangular and cylindrical geometries are used for sheet and solid electron beam in planar and disk type cathode. The E-gun code is used to study the limiting current and space charge loading in each geometries.

Poincare ball embeddings of the optical geometry

International Nuclear Information System (INIS)

Abramowicz, M A; Bengtsson, I; Karas, V; Rosquist, K

2002-01-01

It is shown that the optical geometry of the Reissner-Nordstroem exterior metric can be embedded in a hyperbolic space all the way down to its outer horizon. The adopted embedding procedure removes a breakdown of flat-space embeddings which occurs outside the horizon, at and below the Buchdahl-Bondi limit (R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured in the optical geometry embedding diagram. Moreover, by using the compact Poincare ball representation of the hyperbolic space, the embedding diagram can cover the whole extent of radius from spatial infinity down to the horizon. Attention is drawn to the advantages of such embeddings in an appropriately curved space: this approach gives compact embeddings and it clearly distinguishes the case of an extremal black hole from a non-extremal one in terms of the topology of the embedded horizon

Thermal analysis on motorcycle disc brake geometry

Science.gov (United States)

W. M. Zurin W., S.; Talib, R. J.; Ismail, N. I.

2017-08-01

Braking is a phase of slowing and stop the movement of motorcycle. During braking, the frictional heat was generated and the energy was ideally should be faster dissipated to surrounding to prevent the built up of the excessive temperature which may lead to brake fluid vaporization, thermoelastic deformation at the contact surface, material degradation and failure. In this paper, solid and ventilated type of motorcycle disc brake are being analyse using Computational Fluid Dynamic (CFD) software. The main focus of the analysis is the thermal behaviour during braking for solid and ventilated disc brake. A comparison between both geometries is being discussed to determine the better braking performance in term of temperature distribution. It is found that ventilated disc brake is having better braking performance in terms of heat transfer compare to solid disc.

Prediction of the weld pool geometry of TIG arc welding by using ...

African Journals Online (AJOL)

Prediction of the weld pool geometry of TIG arc welding by using fuzzy logic controller. ... The experimental data were then used for building a fuzzy logic model to predict the effects of control factors on the responses. A graphical mapping scheme was employed for the graphical representation of the macrostructure zones' ...

Investigation of Surface Phenomena in Shocked Tin in Converging Geometry

Energy Technology Data Exchange (ETDEWEB)

Rousculp, Christopher L. [Los Alamos National Laboratory; Oro, David Michael [Los Alamos National Laboratory; Griego, Jeffrey Randall [Los Alamos National Laboratory; Turchi, Peter John [Los Alamos National Laboratory; Reinovsky, Robert Emil [Los Alamos National Laboratory; Bradley, Joseph Thomas [Los Alamos National Laboratory; Cheng, Baolian [Los Alamos National Laboratory; Freeman, Matthew Stouten [Los Alamos National Laboratory; Patten, Austin Randall [Los Alamos National Laboratory

2016-03-21

There is great interest in the behavior of the free surface of tin under shock loading. While it is known that meso-scale surface imperfections can seed the Richtmyer- Meshkov Instability (RMI) for a surface that is melted on release, much less is known about a tin surface that is solid, but plastically deforming. Here material properties such as shear and yield strength come into play especially in converging geometry. Previous experiments have been driven by direct contact HE. Usually a thin, flat target coupon is fielded with various single-mode, sinusoidal, machined, profiles on the free surface. The free surface is adjacent to either vacuum or an inert receiver gas. Most of these previous driver/target configurations have been nominal planer geometry. With modern HE it has been straightforward to shock tin into melt on release. However it has been challenging to achieve a low enough pressure for solid state on release. Here we propose to extend the existing base of knowledge to include the behavior of the free surface of tin in cylindrical converging geometry. By shock loading a cylindrical tin shell with a magnetically driven cylindrical liner impactor, the free surface evolution can be diagnosed with proton radiography. With the PHELIX capacitor bank, the drive can easily be varied to span the pressure range to achieve solid, mixed, and liquid states on release. A conceptual cylindrical liner and target is shown in Figure 1.

Solid-state nanopores of controlled geometry fabricated in a transmission electron microscope

Science.gov (United States)

Qian, Hui; Egerton, Ray F.

2017-11-01

Energy-filtered transmission electron microscopy and electron tomography were applied to in situ studies of the formation, shape, and diameter of nanopores formed in a silicon nitride membrane in a transmission electron microscope. The nanopore geometry was observed in three dimensions by electron tomography. Drilling conditions, such as probe current, beam convergence angle, and probe position, affect the formation rate and the geometry of the pores. With a beam convergence semi-angle of α = 22 mrad, a conical shaped nanopore is formed but at α = 45 mrad, double-cone (hourglass-shaped) nanopores were produced. Nanopores with an effective diameter between 10 nm and 1.8 nm were fabricated by controlling the drilling time.

Contribution to study of interfaces instabilities in plane, cylindrical and spherical geometry

Science.gov (United States)

Toque, Nathalie

1996-12-01

This thesis proposes several experiments of hydrodynamical instabilities which are studied, numerically and theoretically. The experiments are in plane and cylindrical geometry. Their X-ray radiographies show the evolution of an interface between two solid media crossed by a detonation wave. These materials are initially solid. They become liquide under shock wave or stay between two phases, solid and liquid. The numerical study aims at simulating with the codes EAD and Ouranos, the interfaces instabilities which appear in the experiments. The experimental radiographies and the numerical pictures are in quite good agreement. The theoretical study suggests to modelise a spatio-temporal part of the experiments to obtain the quantitative development of perturbations at the interfaces and in the flows. The models are linear and in plane, cylindrical and spherical geometry. They preceed the inoming study of transition between linear and non linear development of instabilities in multifluids flows crossed by shock waves.

Solid Rocket Motor Design Using Hybrid Optimization

Directory of Open Access Journals (Sweden)

Kevin Albarado

2012-01-01

Full Text Available A particle swarm/pattern search hybrid optimizer was used to drive a solid rocket motor modeling code to an optimal solution. The solid motor code models tapered motor geometries using analytical burn back methods by slicing the grain into thin sections along the axial direction. Grains with circular perforated stars, wagon wheels, and dog bones can be considered and multiple tapered sections can be constructed. The hybrid approach to optimization is capable of exploring large areas of the solution space through particle swarming, but is also able to climb “hills” of optimality through gradient based pattern searching. A preliminary method for designing tapered internal geometry as well as tapered outer mold-line geometry is presented. A total of four optimization cases were performed. The first two case studies examines designing motors to match a given regressive-progressive-regressive burn profile. The third case study studies designing a neutrally burning right circular perforated grain (utilizing inner and external geometry tapering. The final case study studies designing a linearly regressive burning profile for right circular perforated (tapered grains.

Difference sets connecting algebra, combinatorics, and geometry

CERN Document Server

Moore, Emily H

2013-01-01

Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of finite groups. It makes the research literature on difference sets accessible to students who have studied linear algebra and abstract algebra, and it prepares them to do their own research. This text is suitable for an undergraduate capstone course, since it illuminates the many links among topics that the students have already studied. To this end, almost every chapter ends with a coda highlighting the main ideas and emphasizing mathematical connections. This book can also be used for self-study by anyone interested in these connections and concrete examples. An abundance of exercises, varying from straightforward to challenging, invites the reader to solve puzzles, construct proofs, and investigate problems--by hand or on a computer. Hints and solutions are...

Conference on Number Theory and Arithmetic Geometry

CERN Document Server

Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem

1997-01-01

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...

Symmetry representation theory and its applications in honor of Nolan R. Wallach

CERN Document Server

Hunziker, Markus; Willenbring, Jeb

2014-01-01

Symmetry has served as an organizing principle in Nolan R. Wallach's fundamental contributions to representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. This volume is a collection of 19 invited articles that pay tribute to the breadth and depth of Wallach's work. The mostly expository articles are written by distinguished mathematicians and contain sufficient preliminary material so as to reach the widest possible audience. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors:   D. Barbasch K. Baur M. Bhargava B. Casselman D. Ciubotaru M. Colarusso T. J. Enright S. Evens W. T. Gan A. M. Garsia R. Gomez G. Gour B. H. Gross G. Han P. E. Harris J. Hong R. E. Howe     M. Hunziker B. Kostant H. Kraft R. J. Miatello L. Ni W. A. Pruett G. W. Sch...

The Koslowski–Sahlmann representation: gauge and diffeomorphism invariance

International Nuclear Information System (INIS)

Campiglia, Miguel; Varadarajan, Madhavan

2014-01-01

The discrete spatial geometry underlying loop quantum gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalized the LQG representation so as to describe states labeled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalization of Sahlmann’s considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification. (paper)

Analysis of students’ spatial thinking in geometry: 3D object into 2D representation

Science.gov (United States)

Fiantika, F. R.; Maknun, C. L.; Budayasa, I. K.; Lukito, A.

2018-05-01

The aim of this study is to find out the spatial thinking process of students in transforming 3-dimensional (3D) object to 2-dimensional (2D) representation. Spatial thinking is helpful in using maps, planning routes, designing floor plans, and creating art. The student can engage geometric ideas by using concrete models and drawing. Spatial thinking in this study is identified through geometrical problems of transforming a 3-dimensional object into a 2-dimensional object image. The problem was resolved by the subject and analyzed by reference to predetermined spatial thinking indicators. Two representative subjects of elementary school were chosen based on mathematical ability and visual learning style. Explorative description through qualitative approach was used in this study. The result of this study are: 1) there are different representations of spatial thinking between a boy and a girl object, 2) the subjects has their own way to invent the fastest way to draw cube net.

Computer aided surface representation

Energy Technology Data Exchange (ETDEWEB)

Barnhill, R.E.

1990-02-19

The central research problem of this project is the effective representation, computation, and display of surfaces interpolating to information in three or more dimensions. If the given information is located on another surface, then the problem is to construct a surface defined on a surface''. Sometimes properties of an already defined surface are desired, which is geometry processing''. Visualization of multivariate surfaces is possible by means of contouring higher dimensional surfaces. These problems and more are discussed below. The broad sweep from constructive mathematics through computational algorithms to computer graphics illustrations is utilized in this research. The breadth and depth of this research activity makes this research project unique.

Analysis of Paralleling Limited Capacity Voltage Sources by Projective Geometry Method

Directory of Open Access Journals (Sweden)

Alexandr Penin

2014-01-01

Full Text Available The droop current-sharing method for voltage sources of a limited capacity is considered. Influence of equalizing resistors and load resistor is investigated on uniform distribution of relative values of currents when the actual loading corresponds to the capacity of a concrete source. Novel concepts for quantitative representation of operating regimes of sources are entered with use of projective geometry method.

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

FURNACE; a toroidal geometry neutronic program system method description and users manual

International Nuclear Information System (INIS)

Verschuur, K.A.

1984-12-01

The FURNACE program system performs neutronic and photonic calculations in 3D toroidal geometry for application to fusion reactors. The geometry description is quite general, allowing any torus cross section and any neutron source density distribution for the plasma, as well as simple parametric representations of circular, elliptic and D-shaped tori and plasmas. The numerical method is based on an approximate transport model that produces results with sufficient accuracy for reactor-design purposes, at acceptable calculational costs. A short description is given of the numerical method, and a user manual for the programs of the system: FURNACE, ANISN-PT, LIBRA, TAPEMA and DRAWER is presented

Valued Graphs and the Representation Theory of Lie Algebras

Directory of Open Access Journals (Sweden)

Joel Lemay

2012-07-01

Full Text Available Quivers (directed graphs, species (a generalization of quivers and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field. Namely, we show that the category of K -species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K -species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

A Model of Representational Spaces in Human Cortex.

Science.gov (United States)

Guntupalli, J Swaroop; Hanke, Michael; Halchenko, Yaroslav O; Connolly, Andrew C; Ramadge, Peter J; Haxby, James V

2016-06-01

Current models of the functional architecture of human cortex emphasize areas that capture coarse-scale features of cortical topography but provide no account for population responses that encode information in fine-scale patterns of activity. Here, we present a linear model of shared representational spaces in human cortex that captures fine-scale distinctions among population responses with response-tuning basis functions that are common across brains and models cortical patterns of neural responses with individual-specific topographic basis functions. We derive a common model space for the whole cortex using a new algorithm, searchlight hyperalignment, and complex, dynamic stimuli that provide a broad sampling of visual, auditory, and social percepts. The model aligns representations across brains in occipital, temporal, parietal, and prefrontal cortices, as shown by between-subject multivariate pattern classification and intersubject correlation of representational geometry, indicating that structural principles for shared neural representations apply across widely divergent domains of information. The model provides a rigorous account for individual variability of well-known coarse-scale topographies, such as retinotopy and category selectivity, and goes further to account for fine-scale patterns that are multiplexed with coarse-scale topographies and carry finer distinctions. © The Author 2016. Published by Oxford University Press.

Solid-state disk amplifiers for fusion-laser systems

Energy Technology Data Exchange (ETDEWEB)

Martin, W.E.; Trenholme, J.B.; Linford, G.J.; Yarema, S.M.; Hurley, C.A.

1981-09-01

We review the design, performance, and operation of large-aperture (10 to 46 cm) solid-state disk amplifiers for use in laser systems. We present design data, prototype tests, simulations, and projections for conventional cylindrical pump-geometry amplifiers and rectangular pump-geometry disk amplifiers. The design of amplifiers for the Nova laser system is discussed.

Simulation of biological flow and transport in complex geometries using embedded boundary/volume-of-fluid methods

International Nuclear Information System (INIS)

Trebotich, David

2007-01-01

We have developed a simulation capability to model multiscale flow and transport in complex biological systems based on algorithms and software infrastructure developed under the SciDAC APDEC CET. The foundation of this work is a new hybrid fluid-particle method for modeling polymer fluids in irregular microscale geometries that enables long-time simulation of validation experiments. Both continuum viscoelastic and discrete particle representations have been used to model the constitutive behavior of polymer fluids. Complex flow environment geometries are represented on Cartesian grids using an implicit function. Direct simulation of flow in the irregular geometry is then possible using embedded boundary/volume-of-fluid methods without loss of geometric detail. This capability has been used to simulate biological flows in a variety of application geometries including biomedical microdevices, anatomical structures and porous media

Rapid Geometry Creation for Computer-Aided Engineering Parametric Analyses: A Case Study Using ComGeom2 for Launch Abort System Design

Science.gov (United States)

Hawke, Veronica; Gage, Peter; Manning, Ted

2007-01-01

ComGeom2, a tool developed to generate Common Geometry representation for multidisciplinary analysis, has been used to create a large set of geometries for use in a design study requiring analysis by two computational codes. This paper describes the process used to generate the large number of configurations and suggests ways to further automate the process and make it more efficient for future studies. The design geometry for this study is the launch abort system of the NASA Crew Launch Vehicle.

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Multiphase CFD simulation of a solid bowl centrifuge

Energy Technology Data Exchange (ETDEWEB)

Romani Fernandez, X.; Nirschl, H. [Universitaet Karlsruhe, Institut fuer MVM, Karlsruhe (Germany)

2009-05-15

This study presents some results from the numerical simulation of the flow in an industrial solid bowl centrifuge used for particle separation in industrial fluid processing. The computational fluid dynamics (CFD) software Fluent was used to simulate this multiphase flow. Simplified two-dimensional and three-dimensional geometries were built and meshed from the real centrifuge geometry. The CFD results show a boundary layer of axially fast moving fluid at the gas-liquid interface. Below this layer there is a thin recirculation. The obtained tangential velocity values are lower than the ones for the rigid-body motion. Also, the trajectories of the solid particles are evaluated. (Abstract Copyright [2009], Wiley Periodicals, Inc.)

Creating New VLS Silicon Nanowire Contact Geometries by Controlling Catalyst Migration

DEFF Research Database (Denmark)

Alam, Sardar Bilal; Panciera, Federico; Hansen, Ole

2015-01-01

The formation of self-assembled contacts between vapor-liquid-solid grown silicon nanowires and flat silicon surfaces was imaged in situ using electron microscopy. By measuring the structural evolution of the contact formation process, we demonstrate how different contact geometries are created b...

Region-oriented CT image representation for reducing computing time of Monte Carlo simulations

International Nuclear Information System (INIS)

Sarrut, David; Guigues, Laurent

2008-01-01

Purpose. We propose a new method for efficient particle transportation in voxelized geometry for Monte Carlo simulations. We describe its use for calculating dose distribution in CT images for radiation therapy. Material and methods. The proposed approach, based on an implicit volume representation named segmented volume, coupled with an adapted segmentation procedure and a distance map, allows us to minimize the number of boundary crossings, which slows down simulation. The method was implemented with the GEANT4 toolkit and compared to four other methods: One box per voxel, parameterized volumes, octree-based volumes, and nested parameterized volumes. For each representation, we compared dose distribution, time, and memory consumption. Results. The proposed method allows us to decrease computational time by up to a factor of 15, while keeping memory consumption low, and without any modification of the transportation engine. Speeding up is related to the geometry complexity and the number of different materials used. We obtained an optimal number of steps with removal of all unnecessary steps between adjacent voxels sharing a similar material. However, the cost of each step is increased. When the number of steps cannot be decreased enough, due for example, to the large number of material boundaries, such a method is not considered suitable. Conclusion. This feasibility study shows that optimizing the representation of an image in memory potentially increases computing efficiency. We used the GEANT4 toolkit, but we could potentially use other Monte Carlo simulation codes. The method introduces a tradeoff between speed and geometry accuracy, allowing computational time gain. However, simulations with GEANT4 remain slow and further work is needed to speed up the procedure while preserving the desired accuracy

Advanced DPSM approach for modeling ultrasonic wave scattering in an arbitrary geometry

Science.gov (United States)

Yadav, Susheel K.; Banerjee, Sourav; Kundu, Tribikram

2011-04-01

Several techniques are used to diagnose structural damages. In the ultrasonic technique structures are tested by analyzing ultrasonic signals scattered by damages. The interpretation of these signals requires a good understanding of the interaction between ultrasonic waves and structures. Therefore, researchers need analytical or numerical techniques to have a clear understanding of the interaction between ultrasonic waves and structural damage. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite element method requires very fine mesh at high frequencies necessitating heavy computational power. Distributed point source method (DPSM) is a newly developed robust mesh free technique to simulate ultrasonic, electrostatic and electromagnetic fields. In most of the previous studies the DPSM technique has been applied to model two dimensional surface geometries and simple three dimensional scatterer geometries. It was difficult to perform the analysis for complex three dimensional geometries. This technique has been extended to model wave scattering in an arbitrary geometry. In this paper a channel section idealized as a thin solid plate with several rivet holes is formulated. The simulation has been carried out with and without cracks near the rivet holes. Further, a comparison study has been also carried out to characterize the crack. A computer code has been developed in C for modeling the ultrasonic field in a solid plate with and without cracks near the rivet holes.

The Prints: A Picture Book for Pre-Formal Geometry

Science.gov (United States)

Skoumpourdi, Chrysanthi; Mpakopoulou, Ifigenia

2011-01-01

A pre-test questionnaire was conducted in a kindergarten and it showed that, although the children were able to give various examples of objects, from their everyday lives, that are similar to solid shapes, the examples they gave for plane figures were also tangible objects. Since it is suggested that geometry instruction has to begin early,…

GRAFFITI: a 'menu-driven' graphics package for the manipulation of three-dimensional solids

International Nuclear Information System (INIS)

Lander, P.A.

1985-01-01

GRAFFITI was originally developed as an alternative method of geometry input for the discrete Monte Carlo code MONTY (1). The package enables users to create and manipulate three-dimensional objects, either as individual solids or as groups of solids. By filling in menus, users can quickly and easily build complex geometries, which in turn can be used as the geometry input for the MONTY program. GRAFFITI is written in the high-level 'structured' language C and is designed to run under the INIX operating system. The package was developed on a WICAT 150-3WS desk top microprocessor computer system. (author)

SAGA advances in ShApes, Geometry, and Algebra : results from the Marie Curie initial training network

CERN Document Server

Muntingh, Georg

2014-01-01

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis, and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

The sensitivity of biological finite element models to the resolution of surface geometry: a case study of crocodilian crania

Directory of Open Access Journals (Sweden)

Matthew R. McCurry

2015-06-01

Full Text Available The reliability of finite element analysis (FEA in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.

Stochastic Geometry and Quantum Gravity: Some Rigorous Results

Science.gov (United States)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.

Complex Structure of the Four-Dimensional Kerr Geometry: Stringy System, Kerr Theorem, and Calabi-Yau Twofold

Directory of Open Access Journals (Sweden)

Alexander Burinskii

2013-01-01

Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.

3D representations of amino acids—applications to protein sequence comparison and classification

Directory of Open Access Journals (Sweden)

Jie Li

2014-08-01

Full Text Available The amino acid sequence of a protein is the key to understanding its structure and ultimately its function in the cell. This paper addresses the fundamental issue of encoding amino acids in ways that the representation of such a protein sequence facilitates the decoding of its information content. We show that a feature-based representation in a three-dimensional (3D space derived from amino acid substitution matrices provides an adequate representation that can be used for direct comparison of protein sequences based on geometry. We measure the performance of such a representation in the context of the protein structural fold prediction problem. We compare the results of classifying different sets of proteins belonging to distinct structural folds against classifications of the same proteins obtained from sequence alone or directly from structural information. We find that sequence alone performs poorly as a structure classifier. We show in contrast that the use of the three dimensional representation of the sequences significantly improves the classification accuracy. We conclude with a discussion of the current limitations of such a representation and with a description of potential improvements.

Biofilm formation in geometries with different surface curvature and oxygen availability

International Nuclear Information System (INIS)

Chang, Ya-Wen; Fragkopoulos, Alexandros A; Kim, Harold D; Fernández-Nieves, Alberto; Marquez, Samantha M; Angelini, Thomas E

2015-01-01

Bacteria in the natural environment exist as interface-associated colonies known as biofilms . Complex mechanisms are often involved in biofilm formation and development. Despite the understanding of the molecular mechanisms involved in biofilm formation, it remains unclear how physical effects in standing cultures influence biofilm development. The topology of the solid interface has been suggested as one of the physical cues influencing bacteria-surface interactions and biofilm development. Using the model organism Bacillus subtilis, we study the transformation of swimming bacteria in liquid culture into robust biofilms in a range of confinement geometries (planar, spherical and toroidal) and interfaces (air/water, silicone/water, and silicone elastomer/water). We find that B. subtilis form submerged biofilms at both solid and liquid interfaces in addition to air-water pellicles. When confined, bacteria grow on curved surfaces of both positive and negative Gaussian curvature. However, the confinement geometry does affect the resulting biofilm roughness and relative coverage. We also find that the biofilm location is governed by oxygen availability as well as by gravitational effects; these compete with each other in some situations. Overall, our results demonstrate that confinement geometry is an effective way to control oxygen availability and subsequently biofilm growth. (paper)

Age-related changes in thoracic skeletal geometry of elderly females.

Science.gov (United States)

Holcombe, Sven A; Wang, Stewart C; Grotberg, James B

2017-05-29

-mm difference in anterior placement of the sternum between young and old subjects. This study provides new geometric data regarding the variability in anthropometry of adult females with age and has utility in advancing the veracity of current human body models. A simplified scaffold representation of underlying 3-dimensional bones within the thorax is presented, and the reported young and old female parameter sets can be used to characterize the anatomic differences expected with age and to both validate and drive morphing algorithms for aged human body models. The modular approach taken allows model parameters to hold inherent and intuitive meaning, offering advantages over more generalized methods such as principal component analysis. Geometry can be assessed on a component level or a whole thorax level, and the parametric representation of thorax shape allows direct comparisons between the current study and other individuals or human body models.

Physical modeling and numerical simulation of subcooled boiling in one- and three-dimensional representation of bundle geometry

International Nuclear Information System (INIS)

Bottoni, M.; Lyczkowski, R.; Ahuja, S.

1995-01-01

Numerical simulation of subcooled boiling in one-dimensional geometry with the Homogeneous Equilibrium Model (HEM) may yield difficulties related to the very low sonic velocity associated with the HEM. These difficulties do not arise with subcritical flow. Possible solutions of the problem include introducing a relaxation of the vapor production rate. Three-dimensional simulations of subcooled boiling in bundle geometry typical of fast reactors can be performed by using two systems of conservation equations, one for the HEM and the other for a Separated Phases Model (SPM), with a smooth transition between the two models

Computer Aided Design of Kaplan Turbine Piston with SolidWorks

OpenAIRE

Camelia Jianu

2010-01-01

The paper presents the steps for 3D computer aided design (CAD) of Kaplan turbine piston made in SolidWorks.The present paper is a tutorial for a Kaplan turbine piston 3D geometry, which is dedicaded to the Parts Sketch and Parts Features design and Drawing Geometry and Drawing Annotation.

The Effect of Visual-Chunking-Representation Accommodation on Geometry Testing for Students with Math Disabilities

Science.gov (United States)

Zhang, Dake; Ding, Yi; Stegall, Joanna; Mo, Lei

2012-01-01

Students who struggle with learning mathematics often have difficulties with geometry problem solving, which requires strong visual imagery skills. These difficulties have been correlated with deficiencies in visual working memory. Cognitive psychology has shown that chunking of visual items accommodates students' working memory deficits. This…

Preparation of water-equivalent radioactive solid sources

International Nuclear Information System (INIS)

Yamazaki, Ione M.; Koskinas, Marina F.; Dias, Mauro S.

2011-01-01

The development of water-equivalent solid sources in two geometries, cylindrical and flat without the need of irradiation in a strong gamma radiation source to obtain polymerization is described. These sources should have density similar to water and good uniformity. Therefore, the density and uniformity of the distribution of radioactive material in the resins were measured. The variation of these parameters in the cylindrical geometry was better than 2.0% for the density and 2.3% for the uniformity and for the flat geometry the values obtained were better than 2.0 % and better than 1.3%, respectively. These values are in good agreement with the literature. (author)

Spin, statistics, and geometry of random walks

International Nuclear Information System (INIS)

Jaroszewicz, T.; Kurzepa, P.S.

1991-01-01

The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories

Solid state nuclear track detection principles, methods and applications

CERN Document Server

Durrani, S A; ter Haar, D

1987-01-01

Solid State Nuclear Track Detection: Principles, Methods and Applications is the second book written by the authors after Nuclear Tracks in Solids: Principles and Applications. The book is meant as an introduction to the subject solid state of nuclear track detection. The text covers the interactions of charged particles with matter; the nature of the charged-particle track; the methodology and geometry of track etching; thermal fading of latent damage trails on tracks; the use of dielectric track recorders in particle identification; radiation dossimetry; and solid state nuclear track detecti

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

A Monte Carlo modeling on charging effect for structures with arbitrary geometries

Science.gov (United States)

Li, C.; Mao, S. F.; Zou, Y. B.; Li, Yong Gang; Zhang, P.; Li, H. M.; Ding, Z. J.

2018-04-01

Insulating materials usually suffer charging effects when irradiated by charged particles. In this paper, we present a Monte Carlo study on the charging effect caused by electron beam irradiation for sample structures with any complex geometry. When transporting in an insulating solid, electrons encounter elastic and inelastic scattering events; the Mott cross section and a Lorentz-type dielectric function are respectively employed to describe such scatterings. In addition, the band gap and the electron–long optical phonon interaction are taken into account. The electronic excitation in inelastic scattering causes generation of electron–hole pairs; these negative and positive charges establish an inner electric field, which in turn induces the drift of charges to be trapped by impurities, defects, vacancies etc in the solid, where the distributions of trapping sites are assumed to have uniform density. Under charging conditions, the inner electric field distorts electron trajectories, and the surface electric potential dynamically alters secondary electron emission. We present, in this work, an iterative modeling method for a self-consistent calculation of electric potential; the method has advantages in treating any structure with arbitrary complex geometry, in comparison with the image charge method—which is limited to a quite simple boundary geometry. Our modeling is based on: the combination of the finite triangle mesh method for an arbitrary geometry construction; a self-consistent method for the spatial potential calculation; and a full dynamic description for the motion of deposited charges. Example calculations have been done to simulate secondary electron yield of SiO2 for a semi-infinite solid, the charging for a heterostructure of SiO2 film grown on an Au substrate, and SEM imaging of a SiO2 line structure with rough surfaces and SiO2 nanoparticles with irregular shapes. The simulations have explored interesting interlaced charge layer distribution

Lie groups, differential equations, and geometry advances and surveys

CERN Document Server

2017-01-01

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

Crystal structure representations for machine learning models of formation energies

Energy Technology Data Exchange (ETDEWEB)

Faber, Felix [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Lindmaa, Alexander [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden; von Lilienfeld, O. Anatole [Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel Switzerland; Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue Lemont Illinois 60439; Armiento, Rickard [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping Sweden

2015-04-20

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Computer Aided Design of Kaplan Turbine Piston with\tSolidWorks

Directory of Open Access Journals (Sweden)

Camelia Jianu

2010-10-01

Full Text Available The paper presents the steps for 3D computer aided design (CAD of Kaplan turbine piston made in SolidWorks.The present paper is a tutorial for a Kaplan turbine piston 3D geometry, which is dedicaded to the Parts Sketch and Parts Features design and Drawing Geometry and Drawing Annotation.

Geometrical setting of solid mechanics

International Nuclear Information System (INIS)

Fiala, Zdenek

2011-01-01

Highlights: → Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). → Generalized logarithmic strain. → Consistent linearization. → Incremental principle of virtual power. → Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.

Mathematical model of geometry and fibrous structure of the heart.

Science.gov (United States)

Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J

1991-04-01

We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

Solid Mesh Registration for Radiotherapy Treatment Planning

DEFF Research Database (Denmark)

Noe, Karsten Østergaard; Sørensen, Thomas Sangild

2010-01-01

We present an algorithm for solid organ registration of pre-segmented data represented as tetrahedral meshes. Registration of the organ surface is driven by force terms based on a distance field representation of the source and reference shapes. Registration of internal morphology is achieved usi...

Theory of corticothalamic brain activity in a spherical geometry: Spectra, coherence, and correlation

Science.gov (United States)

Mukta, K. N.; MacLaurin, J. N.; Robinson, P. A.

2017-11-01

Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1 /f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1 /f2 . Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks

Solution of the neutron transport equation by the Method of Characteristics using a linear representation of the source within a mesh

International Nuclear Information System (INIS)

Mazumdar, Tanay; Degweker, S.B.

2017-01-01

Highlights: • In Method of Characteristics, the neutron source within a mesh is expanded up to linear term. • This expansion reduces the number of meshes as compared to flat source assumption. • Poor representation of circular geometry with coarser meshes is corrected. • Few benchmark problems are solved to show the advantages of linear expansion of source. • The advantage of the present formalism is quite visible in problems with large flux gradient. - Abstract: A common assumption in the solution of the neutron transport equation by the Method of Characteristics (MOC) is that the source (or flux) is constant within a mesh. This assumption is adequate provided the meshes are small enough so that the spatial variation of flux within a mesh may be ignored. Whether a mesh is small enough or not depends upon the flux gradient across a mesh, which in turn depends on factors like the presence of strong absorbers, localized sources or vacuum boundaries. The flat flux assumption often requires a very large number of meshes for solving the neutron transport equation with acceptable accuracy as was observed in our earlier work on the subject. A significant reduction in the required number of meshes is attainable by using a higher order representation of the flux within a mesh. In this paper, we expand the source within a mesh up to first order (linear) terms, which permits the use of larger sized (and therefore fewer) meshes and thereby reduces the computation time without compromising the accuracy of calculation. Since the division of the geometry into meshes is through an automatic triangulation procedure using the Bowyer-Watson algorithm, representation of circular objects (cylindrical fuel rods) with coarse meshes is poorer and causes geometry related errors. A numerical recipe is presented to make a correction to the automatic triangulation process and thereby eliminate this source of error. A number of benchmark problems are analyzed to emphasize the

Fluid, solid and fluid-structure interaction simulations on patient-based abdominal aortic aneurysm models.

Science.gov (United States)

Kelly, Sinead; O'Rourke, Malachy

2012-04-01

This article describes the use of fluid, solid and fluid-structure interaction simulations on three patient-based abdominal aortic aneurysm geometries. All simulations were carried out using OpenFOAM, which uses the finite volume method to solve both fluid and solid equations. Initially a fluid-only simulation was carried out on a single patient-based geometry and results from this simulation were compared with experimental results. There was good qualitative and quantitative agreement between the experimental and numerical results, suggesting that OpenFOAM is capable of predicting the main features of unsteady flow through a complex patient-based abdominal aortic aneurysm geometry. The intraluminal thrombus and arterial wall were then included, and solid stress and fluid-structure interaction simulations were performed on this, and two other patient-based abdominal aortic aneurysm geometries. It was found that the solid stress simulations resulted in an under-estimation of the maximum stress by up to 5.9% when compared with the fluid-structure interaction simulations. In the fluid-structure interaction simulations, flow induced pressure within the aneurysm was found to be up to 4.8% higher than the value of peak systolic pressure imposed in the solid stress simulations, which is likely to be the cause of the variation in the stress results. In comparing the results from the initial fluid-only simulation with results from the fluid-structure interaction simulation on the same patient, it was found that wall shear stress values varied by up to 35% between the two simulation methods. It was concluded that solid stress simulations are adequate to predict the maximum stress in an aneurysm wall, while fluid-structure interaction simulations should be performed if accurate prediction of the fluid wall shear stress is necessary. Therefore, the decision to perform fluid-structure interaction simulations should be based on the particular variables of interest in a given

Faithful representation of similarities among three-dimensional shapes in human vision.

Science.gov (United States)

Cutzu, F; Edelman, S

1996-01-01

Efficient and reliable classification of visual stimuli requires that their representations reside a low-dimensional and, therefore, computationally manageable feature space. We investigated the ability of the human visual system to derive such representations from the sensory input-a highly nontrivial task, given the million or so dimensions of the visual signal at its entry point to the cortex. In a series of experiments, subjects were presented with sets of parametrically defined shapes; the points in the common high-dimensional parameter space corresponding to the individual shapes formed regular planar (two-dimensional) patterns such as a triangle, a square, etc. We then used multidimensional scaling to arrange the shapes in planar configurations, dictated by their experimentally determined perceived similarities. The resulting configurations closely resembled the original arrangements of the stimuli in the parameter space. This achievement of the human visual system was replicated by a computational model derived from a theory of object representation in the brain, according to which similarities between objects, and not the geometry of each object, need to be faithfully represented. Images Fig. 3 PMID:8876260

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

ART-ML: a new markup language for modelling and representation of biological processes in cardiovascular diseases.

Science.gov (United States)

Karvounis, E C; Exarchos, T P; Fotiou, E; Sakellarios, A I; Iliopoulou, D; Koutsouris, D; Fotiadis, D I

2013-01-01

With an ever increasing number of biological models available on the internet, a standardized modelling framework is required to allow information to be accessed and visualized. In this paper we propose a novel Extensible Markup Language (XML) based format called ART-ML that aims at supporting the interoperability and the reuse of models of geometry, blood flow, plaque progression and stent modelling, exported by any cardiovascular disease modelling software. ART-ML has been developed and tested using ARTool. ARTool is a platform for the automatic processing of various image modalities of coronary and carotid arteries. The images and their content are fused to develop morphological models of the arteries in 3D representations. All the above described procedures integrate disparate data formats, protocols and tools. ART-ML proposes a representation way, expanding ARTool, for interpretability of the individual resources, creating a standard unified model for the description of data and, consequently, a format for their exchange and representation that is machine independent. More specifically, ARTool platform incorporates efficient algorithms which are able to perform blood flow simulations and atherosclerotic plaque evolution modelling. Integration of data layers between different modules within ARTool are based upon the interchange of information included in the ART-ML model repository. ART-ML provides a markup representation that enables the representation and management of embedded models within the cardiovascular disease modelling platform, the storage and interchange of well-defined information. The corresponding ART-ML model incorporates all relevant information regarding geometry, blood flow, plaque progression and stent modelling procedures. All created models are stored in a model repository database which is accessible to the research community using efficient web interfaces, enabling the interoperability of any cardiovascular disease modelling software

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Quantum theory of space charge limited current in solids

Energy Technology Data Exchange (ETDEWEB)

González, Gabriel, E-mail: gabriel.gonzalez@uaslp.mx [Cátedras Conacyt, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000, Mexico and Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000 (Mexico)

2015-02-28

We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.

The SUSY oscillator from local geometry: Dynamics and coherent states

International Nuclear Information System (INIS)

Thienel, H.P.

1994-01-01

The choice of a coordinate chart on an analytical R n (R a n ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

A new experiment-independent mechanism to persistify and serve the detector geometry of ATLAS

Science.gov (United States)

Bianchi, Riccardo Maria; Boudreau, Joseph; Vukotic, Ilija

2017-10-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the-fly on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS software framework “Athena”, which provides the online services and the tools to retrieve the data from the database. This operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geometry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify (in software development in general, and in HEP computing in particular, persistifying means taking an object which lives in memory only - for example because it was built on-the-fly while processing the experimental data, - serializing it and storing it on disk as a persistent object) and serve the geometry of HEP experiments. The new mechanism is composed by a new file format and the modules to make use of it. The new file format allows to store the whole detector description locally in a file, and it is especially optimized to describe large complex detectors with the minimum file size, making use of shared instances and storing compressed representations of geometry transformations. Then, the detector description can be read back in, to fully restore the in-memory geometry tree. Moreover, a dedicated REST API is being designed and developed to serve the geometry in standard exchange formats like JSON, to let users and applications download specific partial geometry information. With this new geometry persistification a new generation of applications could be developed, which can use the actual detector geometry while being platform-independent and experiment-independent.

Pulsar Emission Geometry and Accelerating Field Strength

Science.gov (United States)

DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien

2012-01-01

The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Topics in Cubic Special Geometry

CERN Document Server

Bellucci, Stefano; Roychowdhury, Raju

2011-01-01

We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

Science.gov (United States)

Melezhik, Vladimir S.

2018-02-01

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

CFD prediction of mixing in a steam generator mock-up: Comparison between full geometry and porous medium approaches

International Nuclear Information System (INIS)

Dehbi, A.; Badreddine, H.

2013-01-01

Highlights: • CFD is used to simulate single phase mixing in a model steam generator. • Motive of the work is to compare porous media approach with full geometry representation of tubes. • Porous media approach is found to compare favorably with full representation in steady states. - Abstract: In CFD simulations of single phase flow mixing in a steam generator (SG) during a station blackout severe accident, one is faced with the problem of representing the thousands of SG U-tubes. Typically simplifications are made to render the problem computationally tractable. In particular, one or a number of tubes are lumped in one volume that is treated as a single porous medium which replicates the pressure loss and heat transfer characteristics of the real tube. This approach significantly reduces the computational size of the problem and hence simulation time. In this work, we endeavor to investigate the adequacy of this approach by performing a series of simulations. We first validate the porous medium approach against results of the 1/7th scale Westinghouse SG-S3 test. In a second step, we make two separate simulations of flow in the PSI SG mock-up, i.e. one in which the porous medium model is used for the tube bundle, and another in which the full geometry is represented. In all simulations, the Reynolds Stress (RSM) model of turbulence is used. We show that in steady state conditions, the porous medium treatment yields results which are comparable to those of the full geometry representation (temperature distribution, recirculation ratio, hot plume spread, etc.). Hence, the porous medium approach can be extended with a good degree of confidence to model single phase mixing in the full scale SG

A Numerical Study of the Impact of Radial Baffles in solid Bowl Centrifuges Using computational Fluid Dynamics

OpenAIRE

Romani, Xiana; Nirschl, Hermann

2010-01-01

Centrifugal separation equipment, such as solid bowl centrifuges, is used to carry out an effective separation of fine particles from industrial fluids. Knowledge of the streams and sedimentation behavior inside solid bowl centrifuges is necessary to determine the geometry and the process parameters that lead to an optimal performance. Regarding a given industrial centrifuge geometry, a grid was built to calculate numerically the multiphase flow of water, air, and particles with a computation...

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

Particle and liquid motion in semi-solid aluminium alloys: A quantitative in situ microradioscopy study

International Nuclear Information System (INIS)

Zabler, S.; Ershov, A.; Rack, A.; Garcia-Moreno, F.; Baumbach, T.; Banhart, J.

2013-01-01

Semi-solid melts exhibit a very unpredictable rheology and filling dynamics, when injected into thin-walled components. Optimization of the process requires an insight into the casting process during injection. For this purpose we injected semi-solid an Al–Ge alloy into two different thin channel geometries while recording high resolution radiographs at fast frame rates (up to 1000 images per s). Comparison of a bottleneck channel, which has previously been used for slower experiments, with a right-angle turn geometry reveals a significant influence of the channel shape on the flow behaviour of the particle–liquid mixture. While the bottleneck is quickly sealed with densified solid, turbulences in the right-angle turn apparently permit solid particles and clusters to move conjointly with the liquid and thus achieve a more complete filling. Single particle trajectories and rapid break-up of solid skeletons in such a system have been observed for the first time in situ

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Solar-pumped solid state Nd lasers

Science.gov (United States)

Williams, M. D.; Zapata, L.

1985-01-01

Solid state neodymium lasers are considered candidates for space-based polar-pumped laser for continuous power transmission. Laser performance for three different slab laser configurations has been computed to show the excellent power capability of such systems if heat problems can be solved. Ideas involving geometries and materials are offered as potential solutions to the heat problem.

Modelling and simulation of gas explosions in complex geometries

Energy Technology Data Exchange (ETDEWEB)

Saeter, Olav

1998-12-31

This thesis presents a three-dimensional Computational Fluid Dynamics (CFD) code (EXSIM94) for modelling and simulation of gas explosions in complex geometries. It gives the theory and validates the following sub-models : (1) the flow resistance and turbulence generation model for densely packed regions, (2) the flow resistance and turbulence generation model for single objects, and (3) the quasi-laminar combustion model. It is found that a simple model for flow resistance and turbulence generation in densely packed beds is able to reproduce the medium and large scale MERGE explosion experiments of the Commission of European Communities (CEC) within a band of factor 2. The model for a single representation is found to predict explosion pressure in better agreement with the experiments with a modified k-{epsilon} model. This modification also gives a slightly improved grid independence for realistic gas explosion approaches. One laminar model is found unsuitable for gas explosion modelling because of strong grid dependence. Another laminar model is found to be relatively grid independent and to work well in harmony with the turbulent combustion model. The code is validated against 40 realistic gas explosion experiments. It is relatively grid independent in predicting explosion pressure in different offshore geometries. It can predict the influence of ignition point location, vent arrangements, different geometries, scaling effects and gas reactivity. The validation study concludes with statistical and uncertainty analyses of the code performance. 98 refs., 96 figs, 12 tabs.

Non-uniform tube representation of proteins

DEFF Research Database (Denmark)

Hansen, Mikael Sonne

Treating the full protein structure is often neither computationally nor physically possible. Instead one is forced to consider various reduced models capturing the properties of interest. Previous work have used tubular neighborhoods of the C-alpha backbone. However, assigning a unique radius...... might not correctly capture volume exclusion - of crucial importance when trying to understand a proteins $3$d-structure. We propose a new reduced model treating the protein as a non-uniform tube with a radius reflecting the positions of atoms. The tube representation is well suited considering X......-ray crystallographic resolution ~ 3Å while a varying radius accounts for the different sizes of side chains. Such a non-uniform tube better capture the protein geometry and has numerous applications in structural/computational biology from the classification of protein structures to sequence-structure prediction....

A method for generating large datasets of organ geometries for radiotherapy treatment planning studies

International Nuclear Information System (INIS)

Hu, Nan; Cerviño, Laura; Segars, Paul; Lewis, John; Shan, Jinlu; Jiang, Steve; Zheng, Xiaolin; Wang, Ge

2014-01-01

With the rapidly increasing application of adaptive radiotherapy, large datasets of organ geometries based on the patient’s anatomy are desired to support clinical application or research work, such as image segmentation, re-planning, and organ deformation analysis. Sometimes only limited datasets are available in clinical practice. In this study, we propose a new method to generate large datasets of organ geometries to be utilized in adaptive radiotherapy. Given a training dataset of organ shapes derived from daily cone-beam CT, we align them into a common coordinate frame and select one of the training surfaces as reference surface. A statistical shape model of organs was constructed, based on the establishment of point correspondence between surfaces and non-uniform rational B-spline (NURBS) representation. A principal component analysis is performed on the sampled surface points to capture the major variation modes of each organ. A set of principal components and their respective coefficients, which represent organ surface deformation, were obtained, and a statistical analysis of the coefficients was performed. New sets of statistically equivalent coefficients can be constructed and assigned to the principal components, resulting in a larger geometry dataset for the patient’s organs. These generated organ geometries are realistic and statistically representative

Quantum theory of the solid state part B

CERN Document Server

Callaway, Joseph

1974-01-01

Quantum Theory of the Solid State, Part B describes the concepts and methods of the central problems of the quantum theory of solids. This book discusses the developed machinery applied to impurities, disordered systems, effects of external fields, transport phenomena, and superconductivity. The representation theory, low field diamagnetic susceptibility, electron-phonon interaction, and Landau theory of fermi liquids are also deliberated. This text concludes with an introduction to many-body theory and some applications. This publication is a suitable textbook for students who have completed

On Fock Space Representations of quantized Enveloping Algebras related to Non-Commutative Differential Geometry

CERN Document Server

Jurco, B; Jurco, B; Schlieker, M

1995-01-01

In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding q-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the q-deformed flag manifold.

Complexities of three dimensional part geometry. [Ambiguities in specification of pieces for manufacture

Energy Technology Data Exchange (ETDEWEB)

Stark, R.H.

1977-05-01

This report is a non-technical exposition on the ambiguities in conventional specification of the shape of a part to be manufactured and on various alternatives for representing its geometry for computer processing. It touches lightly on wire-frame and bounded surface representations and on the concept of design by volumes. It concludes that no existing computer-aided design system has yet shown its long-range superiority over he spectrum of parts and of uses to which its information base should be applicable. 9 figures.

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

OPTIMIZATION OF POTASSIUM NITRATE BASED SOLID PROPELLANT GRAINS FORMULATION USING RESPONSE SURFACE METHODOLOGY

Directory of Open Access Journals (Sweden)

Oladipupo Olaosebikan Ogunleye

2015-08-01

Full Text Available This study was designed to evaluate the effect of propellant formulation and geometry on the solid propellant grains internal ballistic performance using core, bates, rod and tubular and end-burn geometries. Response Surface Methodology (RSM was used to analyze and optimize the effect of sucrose, potassium nitrate and carbon on the chamber pressure, temperature, thrust and specific impulse of the solid propellant grains through Central Composite Design (CCD of the experiment. An increase in potassium nitrate increased the specific impulse while an increase in sucrose and carbon decreased specific impulse. The coefficient of determination (R2 for models of chamber pressure, temperature, thrust and specific impulse in terms of composition and geometry were 0.9737, 0.9984, 0.9745 and 0.9589, respectively. The optimum specific impulse of 127.89 s, pressure (462201 Pa, temperature (1618.3 K and thrust (834.83 N were obtained using 0.584 kg of sucrose, 1.364 kg of potassium nitrate and 0.052 kg of carbon as well as bate geometry. There was no significant difference between the calculated and experimented ballistic properties at p < 0.05. The bate grain geometry is more efficient for minimizing the oscillatory pressure in the combustion chamber.

Determination of solid angle

International Nuclear Information System (INIS)

Qiu, S.; Amano, H.; Kasai, A.

1988-01-01

The solid angle in extended alpha source measurement for a series of counting geometries has been obtained by two methods: (1) calculated by means of the Nelson Blachmen series; (2) interpolated from the data table given by Gardner. A particular consequence of the application of the Nelson Blachmen series was deduced which was different from that given by the original author. The applicability of these two methods, as well as an experimentally measured method, is also evaluated. (author)

Multidimensional integral representations problems of analytic continuation

CERN Document Server

Kytmanov, Alexander M

2015-01-01

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem.   This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.

A global high-resolution data set of ice sheet topography, cavity geometry and ocean bathymetry

DEFF Research Database (Denmark)

Schaffer, Janin; Timmermann, Ralph; Arndt, Jan Erik

2016-01-01

of the Southern Ocean (IBCSO) version 1. While RTopo-1 primarily aimed at a good and consistent representation of the Antarctic ice sheet, ice shelves, and sub-ice cavities, RTopo-2now also contains ice topographies of the Greenland ice sheet and outlet glaciers. In particular, we aimed at agood representation....... For the continental shelf off Northeast Greenland and the floating ice tongue of Nioghalvfjerdsfjorden Glacier at about79 N, we incorporated a high-resolution digital bathymetry model considering original multibeam survey datafor the region. Radar data for surface topographies of the floating ice tongues...... for the geometry of Getz, Abbot, andFimbul ice shelf cavities. The data set is available in full and in regional subsets in NetCDF format from thePANGAEA database at doi:10.1594/PANGAEA.856844....

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

On the Importance of Solar Eclipse Geometry in the Interpretation of Ionospheric Observations

Science.gov (United States)

Stankov, S.; Verhulst, T. G. W.

2017-12-01

A reliable interpretation of solar eclipse effects on the geospace environment, and on the ionosphere in particular, necessitates a careful consideration of the so-called eclipse geometry. A solar eclipse is a relatively rare astronomical phenomenon, which geometry is rather complex, specific for each event, and fast changing in time. The standard, most popular way to look at the eclipse geometry is via the two-dimensional representation (map) of the solar obscuration on the Earth's surface, in which the path of eclipse totality is drawn together with isolines of the gradually-decreasing eclipse magnitude farther away from this path. Such "surface maps" are widely used to readily explain some of the solar eclipse effects including, for example, the well-known decrease in total ionisation (due to the substantial decrease in solar irradiation), usually presented by the popular and easy to understand ionospheric characteristic of Total Electron Content (TEC). However, many other effects, especially those taking place at higher altitudes, cannot be explained in this fashion. Instead, a complete, four-dimensional (4D) description of the umbra (and penumbra), would be required. This presentation will address the issue of eclipse geometry effects on various ionospheric observations carried out during the total solar eclipse of August 21, 2017. In particular, GPS-based TEC and ionosonde measurements will be analysed and the eclipse effects on the ionosphere will be interpreted with respect to the actual eclipse geometry at ionospheric heights. Whenever possible, a comparison will be made with results from previous events, such as the ones from March 20, 2015 and October 3, 2005.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

An excursion through elementary mathematics, volume ii euclidean geometry

CERN Document Server

Caminha Muniz Neto, Antonio

2018-01-01

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many...

ORIGAMI -- The Oak Ridge Geometry Analysis and Modeling Interface

International Nuclear Information System (INIS)

Burns, T.J.

1996-01-01

A revised ''ray-tracing'' package which is a superset of the geometry specifications of the radiation transport codes MORSE, MASH (GIFT Versions 4 and 5), HETC, and TORT has been developed by ORNL. Two additional CAD-based formats are also included as part of the superset: the native format of the BRL-CAD system--MGED, and the solid constructive geometry subset of the IGES specification. As part of this upgrade effort, ORNL has designed an Xwindows-based utility (ORIGAMI) to facilitate the construction, manipulation, and display of the geometric models required by the MASH code. Since the primary design criterion for this effort was that the utility ''see'' the geometric model exactly as the radiation transport code does, ORIGAMI is designed to utilize the same ''ray-tracing'' package as the revised version of MASH. ORIGAMI incorporates the functionality of two previously developed graphical utilities, CGVIEW and ORGBUG, into a single consistent interface

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

End-Member Formulation of Solid Solutions and Reactive Transport

Energy Technology Data Exchange (ETDEWEB)

Lichtner, Peter C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-09-01

A model for incorporating solid solutions into reactive transport equations is presented based on an end-member representation. Reactive transport equations are solved directly for the composition and bulk concentration of the solid solution. Reactions of a solid solution with an aqueous solution are formulated in terms of an overall stoichiometric reaction corresponding to a time-varying composition and exchange reactions, equivalent to reaction end-members. Reaction rates are treated kinetically using a transition state rate law for the overall reaction and a pseudo-kinetic rate law for exchange reactions. The composition of the solid solution at the onset of precipitation is assumed to correspond to the least soluble composition, equivalent to the composition at equilibrium. The stoichiometric saturation determines if the solid solution is super-saturated with respect to the aqueous solution. The method is implemented for a simple prototype batch reactor using Mathematica for a binary solid solution. Finally, the sensitivity of the results on the kinetic rate constant for a binary solid solution is investigated for reaction of an initially stoichiometric solid phase with an undersaturated aqueous solution.

Mixing and solid suspension in a stirred precipitator

International Nuclear Information System (INIS)

Chang, T.P.

1986-04-01

Full-scale mixing and solid suspension studies have been conducted to determine the optimum agitator design for precipitators used in plutonium processing. Design considerations include the geometry of precipitator vessels, feed locations, flow patterns, and product requirements. Evaluations of various agitator designs are based on their capabilities: (1) to achieve uniform mixing of reactants in minimum time, (2) to suspend slurry uniformly throughout the vessel, and (3) to minimize power consumption without inducing air entrainment. Tests of full-scale agitator designs showed that significant improvements in mixing, solid suspension, and energy consumption were achieved

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

International Nuclear Information System (INIS)

Gill, D. F.; Nease, B. R.; Griesheimer, D. P.

2013-01-01

A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

Energy Technology Data Exchange (ETDEWEB)

Gill, D. F.; Nease, B. R.; Griesheimer, D. P. [Bettis Atomic Power Laboratory, PO Box 79, West Mifflin, PA 15122 (United States)

2013-07-01

A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

Water-equivalent solid sources prepared by means of two distinct methods

International Nuclear Information System (INIS)

Koskinas, Marina F.; Yamazaki, Ione M.; Potiens Junior, Ademar

2014-01-01

The Nuclear Metrology Laboratory at IPEN is involved in developing radioactive water-equivalent solid sources prepared from an aqueous solution of acrylamide using two distinct methods for polymerization. One of them is the polymerization by high dose of 60 Co irradiation; in the other method the solid matrix-polyacrylamide is obtained from an aqueous solution composed by acrylamide, catalyzers and an aliquot of a radionuclide. The sources have been prepared in cylindrical geometry. In this paper, the study of the distribution of radioactive material in the solid sources prepared by both methods is presented. (author)

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

CLASSIFICATION AND COMPUTER SIMULATION OF CONSTRUCTIVE PROBLEM IN THE PLANE GEOMETRY: METHOD OF CIRCLES

Directory of Open Access Journals (Sweden)

Ivan H. Lenchuk

2014-02-01

Full Text Available Presented article concerns construction problems in plane geometry. Solved the problem of the formation of students' stereotypes efficient, economical in time visual representation of algorithms for solving problems on the modern computer screens. Used universal author’s method of fragmented typing tasks on the method of circles. Allocated rod-type problem with its subsequent filling with ingredients. Previously developed educational software (partially, GeoGebra ensure optimal realization of the construction. Their dynamic characteristics and constructive capabilities - quality visual- shaped stages of "evidence" and "research".

[Representation and mathematical analysis of human crystalline lens].

Science.gov (United States)

Tălu, Stefan; Giovanzana, Stefano; Tălu, Mihai

2011-01-01

The surface of human crystalline lens can be described and analyzed using mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the lens. The mathematical models used in lens biomechanics allow the study and the behavior of crystalline lens on variables and complex dynamic loads. Also, the lens biomechanics has the potential to improve the results in the development of intraocular lenses and cataract surgery. The paper presents the most representative mathematical models currently used for the modeling of human crystalline lens, both optically and biomechanically.

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

Modeling of ultrasonic wave propagation in composite laminates with realistic discontinuity representation.

Science.gov (United States)

Zelenyak, Andreea-Manuela; Schorer, Nora; Sause, Markus G R

2018-02-01

This paper presents a method for embedding realistic defect geometries of a fiber reinforced material in a finite element modeling environment in order to simulate active ultrasonic inspection. When ultrasonic inspection is used experimentally to investigate the presence of defects in composite materials, the microscopic defect geometry may cause signal characteristics that are difficult to interpret. Hence, modeling of this interaction is key to improve our understanding and way of interpreting the acquired ultrasonic signals. To model the true interaction of the ultrasonic wave field with such defect structures as pores, cracks or delamination, a realistic three dimensional geometry reconstruction is required. We present a 3D-image based reconstruction process which converts computed tomography data in adequate surface representations ready to be embedded for processing with finite element methods. Subsequent modeling using these geometries uses a multi-scale and multi-physics simulation approach which results in quantitative A-Scan ultrasonic signals which can be directly compared with experimental signals. Therefore, besides the properties of the composite material, a full transducer implementation, piezoelectric conversion and simultaneous modeling of the attached circuit is applied. Comparison between simulated and experimental signals provides very good agreement in electrical voltage amplitude and the signal arrival time and thus validates the proposed modeling approach. Simulating ultrasound wave propagation in a medium with a realistic shape of the geometry clearly shows a difference in how the disturbance of the waves takes place and finally allows more realistic modeling of A-scans. Copyright © 2017 Elsevier B.V. All rights reserved.

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Teschner, J.; Vartanov, G.S.

2012-02-15

We revisit the definition of the 6j-symbols from the modular double of U{sub q}(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

International Nuclear Information System (INIS)

Teschner, J.; Vartanov, G.S.

2012-02-01

We revisit the definition of the 6j-symbols from the modular double of U q (sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

Influence of internal channel geometry of gas turbine blade on flow structure and heat transfer

Science.gov (United States)

Szwaba, Ryszard; Kaczynski, Piotr; Telega, Janusz; Doerffer, Piotr

2017-12-01

This paper presents the study of the influence of channel geometry on the flow structure and heat transfer, and also their correlations on all the walls of a radial cooling passage model of a gas turbine blade. The investigations focus on the heat transfer and aerodynamic measurements in the channel, which is an accurate representation of the configuration used in aeroengines. Correlations for the heat transfer coefficient and the pressure drop used in the design of internal cooling passages are often developed from simplified models. It is important to note that real engine passages do not have perfect rectangular cross sections, but include a corner fillets, ribs with fillet radii and a special orientation. Therefore, this work provides detailed fluid flow and heat transfer data for a model of radial cooling geometry which has very realistic features.

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

A non-linear, finite element, heat conduction code to calculate temperatures in solids of arbitrary geometry

International Nuclear Information System (INIS)

Tayal, M.

1987-01-01

Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated

Three dimensional electrochemical simulation of solid oxide fuel cell cathode based on microstructure reconstructed by marching cubes method

Science.gov (United States)

He, An; Gong, Jiaming; Shikazono, Naoki

2018-05-01

In the present study, a model is introduced to correlate the electrochemical performance of solid oxide fuel cell (SOFC) with the 3D microstructure reconstructed by focused ion beam scanning electron microscopy (FIB-SEM) in which the solid surface is modeled by the marching cubes (MC) method. Lattice Boltzmann method (LBM) is used to solve the governing equations. In order to maintain the geometries reconstructed by the MC method, local effective diffusivities and conductivities computed based on the MC geometries are applied in each grid, and partial bounce-back scheme is applied according to the boundary predicted by the MC method. From the tortuosity factor and overpotential calculation results, it is concluded that the MC geometry drastically improves the computational accuracy by giving more precise topology information.

Geometry of the Mesopotamian "ecliptic"

Science.gov (United States)

Kurtik, G. E.

2018-02-01

The article deals with the history of ecliptic as an element of the mathematical astronomy in Ancient Mesopotamia. It contains data from the cuneiform sources of the 2nd - 1st millennia BC and from the modern studies shedding light on the following three questions: 1) the idea of the celestial sphere in Mesopotamian astronomy; 2) the geometric representations associated with the ecliptic; 3) the positions of the ecliptic relative to the fixed stars and to the Sun. It is shown that although we do not have solid evidences, however, there are serious reasons to believe that in the Seleucid period in the mathematical astronomy and astrology the ecliptic was conceived geometrically as a circle divided into 12 equal parts. It is also shown that in this period the ecliptic was not yet identified with the projection of annual path of the Sun to the celestial sphere.

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

The construction of tridimensional representation of body and external reality in man. The greatest achievement of evolution to date implications for virtual reality.

Science.gov (United States)

Woodbury, M A; Woodbury, M F

1998-01-01

Our 3-D Body Representation constructed during development by our Central Nervous System under the direction of our DNA, consists of a holographic representation arising from sensory input in the cerebellum and projected extraneurally in the brain ventricular fluid which has the chemical structure of liquid crystal. The structure of 3-D holographic Body Representation is then extrapolated by such cognitive instruments as boundarization, geometrization and gestalt organization upon the external environment which is perceived consequently as three dimensional. When the Body Representation collapses as in psychotic panic states. patients become terrified as they suddenly lose the perception of themselves and the world around them as three dimensional, solid in a reliably solid environment but feel suddenly that they are no longer a person but a disorganized blob. In our clinical practice we found serendipitously that the structure of three dimensionality can be restored even without medication by techniques involving stimulation of the body sensory system in the presence of a benevolent psychotherapist. Implications for Virtual Reality will be discussed.

Propellant selection for ramjets with solid fuel

Energy Technology Data Exchange (ETDEWEB)

Schmucker, R H; Lips, H

1976-03-11

Ramjet propulsion using solid propellant for post-boost acceleration of missiles exhibits several favorable properties, brought about by heterogeneous combustion. A simplified theory for calculating the performance of possible propellants is presented, and they are classified with respect to maximum fuel-specific impulse. The optimal choice of fuel, from a system standpoint, must consider volume constraints, and defines the requirements for motor geometry.

Geometry of Quantum States

International Nuclear Information System (INIS)

Hook, D W

2008-01-01

applications of the geometric approach. The first four chapters contain the standard mathematics required to understand the rest of the material presented: specific areas in colour theory, set theory, probability theory, differential geometry and projective geometry are all covered with an eye to the material that follows. Chapter 5 starts the first real discussion of quantum theory in GQS and serves as an elegant, succinct introduction to the geometry which underlies quantum theory. This may be the most worthwhile chapter for the casual reader who wants to understand the key ideas in this field. Chapter 6 builds on the discussion in Chapter 5, introducing a group theoretic approach to understand coherent states and Chapter 7 describes a geometric tool in the form of an approach to complex projective geometry called 'the stellar representation'. Chapter 8 returns to a more purely quantum mechanical discussion as the authors turn to study the space of density matrices. This chapter completes the discussion which started in Chapter 5. Chapter 9 begins the part of the book concerned with applications of the geometric approach. From this point on the book aims, specifically, to prepare the reader for the material in Chapter 15 beginning with a discussion on the purification of mixed quantum states. In the succeeding chapters a definite choice has been made to present a geometric approach to certain quantum information problems. For example, Chapter 10 contains an extremely well formulated discussion of measurement and positive operator-valued measures with several well illustrated examples and Chapter 11 reopens the discussion of density matrices. Entropy and majorization are again revisited in Chapter 12 in much greater detail than in previous chapters. Chapters 13 and 14 concern themselves with a discussion of various metrics and their relation to the problem of distinguishing between probability distributions and their suitability as probability measures. (book review)

Effects of fluorescence excitation geometry on the accuracy of DNA fragment sizing by flow cytometry

Energy Technology Data Exchange (ETDEWEB)

Werner, James H. [Division of Bioscience, Los Alamos National Laboratory, Mail Stop M888, Los Alamos, New Mexico 87545-0001 (United States); Larson, Erica J. [Division of Bioscience, Los Alamos National Laboratory, Mail Stop M888, Los Alamos, New Mexico 87545-0001 (United States); Goodwin, Peter M. [Division of Bioscience, Los Alamos National Laboratory, Mail Stop M888, Los Alamos, New Mexico 87545-0001 (United States); Ambrose, W. Patrick [Division of Bioscience, Los Alamos National Laboratory, Mail Stop M888, Los Alamos, New Mexico 87545-0001 (United States); Keller, Richard A. [Division of Bioscience, Los Alamos National Laboratory, Mail Stop M888, Los Alamos, New Mexico 87545-0001 (United States)

2000-06-01

We report on various excitation geometries used in ultrasensitive flow cytometry that yield a linear relation between the fluorescence intensity measured from individual strained DNA fragments and the lengths of the fragments (in base pairs). This linearity holds for DNA samples that exhibit a wide range of conformations. The variety of DNA conformations leads to a distribution of dipole moment orientations for the dye molecules intercalated into the DNA. It is consequently important to use an excitation geometry such that all dye molecules are detected with similar efficiency. To estimate the conformation and the extent of elongation of the strained fragments in the flow, fluorescence polarization anisotropy and autocorrelation measurements were performed. Significant extension was observed for DNA fragments under the flow conditions frequently used for DNA fragment sizing. Classical calculations of the fluorescence emission collected over a finite solid angle are in agreement with the experimental measurements and have confirmed the relative insensitivity to DNA conformation of an orthogonal excitation geometry. Furthermore, the calculations suggested a modified excitation geometry that has increased our sizing resolution. (c) 2000 Optical Society of America.

Effects of fluorescence excitation geometry on the accuracy of DNA fragment sizing by flow cytometry

International Nuclear Information System (INIS)

Werner, James H.; Larson, Erica J.; Goodwin, Peter M.; Ambrose, W. Patrick; Keller, Richard A.

2000-01-01

We report on various excitation geometries used in ultrasensitive flow cytometry that yield a linear relation between the fluorescence intensity measured from individual strained DNA fragments and the lengths of the fragments (in base pairs). This linearity holds for DNA samples that exhibit a wide range of conformations. The variety of DNA conformations leads to a distribution of dipole moment orientations for the dye molecules intercalated into the DNA. It is consequently important to use an excitation geometry such that all dye molecules are detected with similar efficiency. To estimate the conformation and the extent of elongation of the strained fragments in the flow, fluorescence polarization anisotropy and autocorrelation measurements were performed. Significant extension was observed for DNA fragments under the flow conditions frequently used for DNA fragment sizing. Classical calculations of the fluorescence emission collected over a finite solid angle are in agreement with the experimental measurements and have confirmed the relative insensitivity to DNA conformation of an orthogonal excitation geometry. Furthermore, the calculations suggested a modified excitation geometry that has increased our sizing resolution. (c) 2000 Optical Society of America

Influence of Geometry and Velocity of Rotating Solids on Hydrodynamics of a Confined Volume

Directory of Open Access Journals (Sweden)

Ignacio Carvajal-Mariscal

2017-01-01

Full Text Available Three cylinder-based geometries were evaluated at five different rotating speeds (ω = 20.94, 62.83, 94.25, 125.66, and 157.08 rad·s−1 to obtain the fluid flow pattern in nonsteady conditions. Two of the models were modified at the lower region, also known as tip section, by means of inverted and right truncated cone geometries, respectively. The experimental technique used a visualization cell and a Particle Imaging Velocimetry installation to obtain the vector field at the central plane of the volume. The Line Integral Convolution Method was used to obtain the fluid motion at the plane. In addition, the scalar kinetic energy and the time series were calculated to perform the normal probability plot. This procedure was used to determine the nonlinear fluid flow pattern. It was also used to identify two different flow regimens in physical and numerical results. As the rotation speed increased, the turbulent regions were placed together and moved. The process makes experimental observation difficult. The biphasic and turbulence constitutive equations were solved with the Computational Fluid Dynamics technique. Numerical results were compared with physical experiments for validation. The model with the inverted truncated cone tip presented better stability in the fluid flow pattern along the rotation speed range.

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

On the performance of metrics to predict quality in point cloud representations

Science.gov (United States)

Alexiou, Evangelos; Ebrahimi, Touradj

2017-09-01

Point clouds are a promising alternative for immersive representation of visual contents. Recently, an increased interest has been observed in the acquisition, processing and rendering of this modality. Although subjective and objective evaluations are critical in order to assess the visual quality of media content, they still remain open problems for point cloud representation. In this paper we focus our efforts on subjective quality assessment of point cloud geometry, subject to typical types of impairments such as noise corruption and compression-like distortions. In particular, we propose a subjective methodology that is closer to real-life scenarios of point cloud visualization. The performance of the state-of-the-art objective metrics is assessed by considering the subjective scores as the ground truth. Moreover, we investigate the impact of adopting different test methodologies by comparing them. Advantages and drawbacks of every approach are reported, based on statistical analysis. The results and conclusions of this work provide useful insights that could be considered in future experimentation.

Solid targetry at the TESLA Accelerator Installation

CERN Document Server

Comor, J J; Rajcevic, M; Kosutic, D; Spasic, M; Vidovic, A; Duricic, J; Nedeljkovic, N

2002-01-01

According to the concept of the TESLA Accelerator Installation, the channel for production of radioisotopes has to routinely produce sup 2 sup 0 sup 1 Tl, sup 1 sup 1 sup 1 In, sup 6 sup 7 Ga, sup 1 sup 2 sup 3 I and sup 1 sup 8 F, and a number of other radionuclides for experimental purposes. The production of sup 1 sup 2 sup 3 I and sup 1 sup 8 F will be performed in dedicated, commercial target stations, while a versatile solid target irradiation system is designed for the routine and experimental production of all other radioisotopes. The solid target station is designed to accept targets for both the 7 deg. and 90 deg. irradiation geometry. The targets used for the routine production will be prepared by electroplating on a silver substrate. They can be irradiated with a 1.5 kW beam using the 7 deg. geometry. The cooling of these targets is enhanced by fins on the back of the silver substrate designed so that the highest temperature on the surface of the target does not exceed 110 deg. C. The irradiation ...

Acceleration techniques for the direct use of CAD-based geometry in fusion neutronics analysis

International Nuclear Information System (INIS)

Wilson, Paul P.H.; Tautges, Timothy J.; Kraftcheck, Jason A.; Smith, Brandon M.; Henderson, Douglass L.

2010-01-01

The Direct Accelerated Geometry Monte Carlo (DAGMC) software library offers a unique approach to performing neutronics analysis on CAD-based geometries of fusion systems. By employing a number of acceleration techniques, the ray-tracing operations that are fundamental to Monte Carlo radiation transport are implemented efficiently for direct use on the CAD-based solid model, eliminating the need to translate to the native Monte Carlo input language. By forming hierarchical trees of oriented bounding boxes, one for each facet that results from a high-fidelity tessellation of the model, the ray-tracing performance is adequate to permit detailed analysis of large complex systems. In addition to the reduction in human effort and improvement in quality assurance that is found in the translation approaches, the DAGMC approach also permits the analysis of geometries with higher order surfaces that cannot be represented by many native Monte Carlo radiation transport tools. The paper describes the various acceleration techniques and demonstrates the resulting capability in a real fusion neutronics analysis.

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Geometric data transfer between CAD systems: solid models

DEFF Research Database (Denmark)

Kroszynski, Uri; Palstroem, Bjarne; Trostmann, Erik

1989-01-01

The first phase of the ESPRIT project CAD*I resulted in a specification for the exchange of solid models as well as in some pilot implementations of processors based on this specification. The authors summarize the CAD*I approach, addressing the structure of neutral files for solids, entities......, and attributes supporting three kinds of representations: facilities for the transfer of parametric designs; referencing library components; and other general mechanisms. They also describe the current state of the specification and processor implementations and include an example of a CAD*I neutral file....... Results from cycle and intersystem solid model transfer tests are presented, showing the practicality of the CAD*I proposal. B-rep model transfer results are discussed in some detail. The relationship of this work to standardization efforts is outlined...

Factorizations and physical representations

International Nuclear Information System (INIS)

Revzen, M; Khanna, F C; Mann, A; Zak, J

2006-01-01

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the decomposition of M into prime numbers. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (Zak J 1970 Phys. Today 23 51), and related representations termed q 1 q 2 representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Distinguishing Representations as Origin and Representations as Input: Roles for Individual Cells

Directory of Open Access Journals (Sweden)

Jonathan C.W. Edwards

2016-09-01

Full Text Available It is widely perceived that there is a problem in giving a naturalistic account of mental representation that deals adequately with meaning, interpretation or significance (semantic content. It is suggested here that this problem may arise partly from the conflation of two vernacular senses of representation: representation-as-origin and representation-as-input. The flash of a neon sign may in one sense represent a popular drink, but to function as representation it must provide an input to a ‘consumer’ in the street. The arguments presented draw on two principles – the neuron doctrine and the need for a venue for ‘presentation’ or ‘reception’ of a representation at a specified site, consistent with the locality principle. It is also argued that domains of representation cannot be defined by signal traffic, since they can be expected to include ‘null’ elements based on non-firing cells. In this analysis, mental representations-as-origin are distributed patterns of cell firing. Each firing cell is given semantic value in its own right - some form of atomic propositional significance – since different axonal branches may contribute to integration with different populations of signals at different downstream sites. Representations-as-input are patterns of local co-arrival of signals in the form of synaptic potentials in dendrites. Meaning then draws on the relationships between active and null inputs, forming ‘scenarios’ comprising a molecular combination of ‘premises’ from which a new output with atomic propositional significance is generated. In both types of representation, meaning, interpretation or significance pivots on events in an individual cell. (This analysis only applies to ‘occurrent’ representations based on current neural activity. The concept of representations-as-input emphasises the need for a ‘consumer’ of a representation and the dependence of meaning on the co-relationships involved in an

A visual LISP program for voxelizing AutoCAD solid models

Science.gov (United States)

Marschallinger, Robert; Jandrisevits, Carmen; Zobl, Fritz

2015-01-01

AutoCAD solid models are increasingly recognized in geological and geotechnical 3D modeling. In order to bridge the currently existing gap between AutoCAD solid models and the grid modeling realm, a Visual LISP program is presented that converts AutoCAD solid models into voxel arrays. Acad2Vox voxelizer works on a 3D-model that is made up of arbitrary non-overlapping 3D-solids. After definition of the target voxel array geometry, 3D-solids are scanned at grid positions and properties are streamed to an ASCII output file. Acad2Vox has a novel voxelization strategy that combines a hierarchical reduction of sampling dimensionality with an innovative use of AutoCAD-specific methods for a fast and memory-saving operation. Acad2Vox provides georeferenced, voxelized analogs of 3D design data that can act as regions-of-interest in later geostatistical modeling and simulation. The Supplement includes sample geological solid models with instructions for practical work with Acad2Vox.

Characterization of feed channel spacer performance using geometries obtained by X-ray computed tomography

KAUST Repository

Haaksman, Viktor A.

2016-09-09

Spiral-wound membrane modules used in water treatment for water reuse and desalination make use of spacer meshes for keeping the membrane leaves apart and for enhancing the mass transfer. Computational fluid dynamics (CFD) has gained importance in the design of new spacers with optimized hydrodynamic characteristics, but this requires a precise description of the spacer geometry. This study developed a method to obtain accurate three-dimensional (3-D) geometry representations for any given spacer design from X-ray computed tomography (CT) scans. The method revealed that the filaments of industrial spacers have a highly variable cross-section size and shape, which impact the flow characteristics in the feed channel. The pressure drop and friction factors were calculated from numerical simulations on five commercially available feed spacers used in practice. Model solutions compared well to experimental data measured using a flow cell for average velocities up to 0.2 m/s, as used in industrial reverse osmosis and nanofiltration membrane operations. A newly-proposed spacer geometry with alternating strand thickness was tested, which was found to yield a lower pressure drop while being highly efficient in converting the pumping power into membrane shear. Numerical model solutions using CFD with geometries from CT scans were closer to measurements than those obtained using the traditional circular cross-section strand simplification, indicating that CT scans are very well suitable to approximate real feed spacer geometries. By providing detailed insight on the spacer filament shape, CT scans allow better quantification of local distribution of velocity and shear, possibly leading to more accurate estimations of fouling and concentration polarization. © 2016 Elsevier B.V.

Absorbing CAD system geometries into GEANT

International Nuclear Information System (INIS)

Womersley, J.; Dragovitsch, P.; Youssef, S.

1991-01-01

The simulation community has for many years discussed the possibility of direct conversion of geometrical detector models from computer- aided design and engineering systems (CAD systems) to the simulation packages (which we shall assume means GEANT). This would allow fast and simultaneous optimization of the physics performance and structural integrity of detector designs. The benefit that this would offer is the avoidance of such problems as the late discovery of the rather thick cryostats in the D-Zero detector. Recent progress in the absorption of CAD geometries into GEANT models is reviewed, including descriptions of the additions to the I-DEAS solid modeller package developed for the EMPACT SSC proposal, the COGENT CAD-to-GEANT interpreter developed by Quantum Research Services, and the OCTAGON package for representing arbitrary shapes in GEANT. Likely future directions of development are described. 2 refs., 7 figs

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

Science.gov (United States)

Fabanich, William A., Jr.

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Using SpaceClaim/TD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

Science.gov (United States)

Fabanich, William

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.

Topologically distinct classes of valence-bond solid states with their parent Hamiltonians

International Nuclear Information System (INIS)

Tu Honghao; Zhang Guangming; Xiang Tao; Liu Zhengxin; Ng Taikai

2009-01-01

We present a general method to construct one-dimensional translationally invariant valence-bond solid states with a built-in Lie group G and derive their matrix product representations. The general strategies to find their parent Hamiltonians are provided so that the valence-bond solid states are their unique ground states. For quantum integer-spin-S chains, we discuss two topologically distinct classes of valence-bond solid states: one consists of two virtual SU(2) spin-J variables in each site and another is formed by using two SO(2S+1) spinors. Among them, a spin-1 fermionic valence-bond solid state, its parent Hamiltonian, and its properties are discussed in detail. Moreover, two types of valence-bond solid states with SO(5) symmetries are further generalized and their respective properties are analyzed as well.

Multi-representation based on scientific investigation for enhancing students’ representation skills

Science.gov (United States)

Siswanto, J.; Susantini, E.; Jatmiko, B.

2018-03-01

This research aims to implementation learning physics with multi-representation based on the scientific investigation for enhancing students’ representation skills, especially on the magnetic field subject. The research design is one group pretest-posttest. This research was conducted in the department of mathematics education, Universitas PGRI Semarang, with the sample is students of class 2F who take basic physics courses. The data were obtained by representation skills test and documentation of multi-representation worksheet. The Results show gain analysis value of .64 which means some medium improvements. The result of t-test (α = .05) is shows p-value = .001. This learning significantly improves students representation skills.

Solid-phase PCR for rapid multiplex detection of Salmonella spp. at the subspecies level, with amplification efficiency comparable to conventional PCR

DEFF Research Database (Denmark)

Chin, Wai Hoe; Sun, Yi; Høgberg, Jonas

2017-01-01

Solid-phase PCR (SP-PCR) has attracted considerable interest in different research fields since it allows parallel DNA amplification on the surface of a solid substrate. However, the applications of SP-PCR have been hampered by the low efficiency of the solid-phase amplification. In order to incr...... diagnosis, high-throughput DNA sequencing, and single-nucleotide polymorphism analysis. Graphical abstract Schematic representation of solid-phase PCR....

Radiometric determination of dilute inhomogeneous solids loading in pneumatic conveying systems

International Nuclear Information System (INIS)

Yong Yan; Byrne, Ben; Coulthard, John

1994-01-01

The application of γ-ray attenuation methods to non-intrusive measurement of the solids content in pneumatic flow lines is discussed. An instrument employing a broad single-beam interrogation geometry and a single-element detector with uniform sensitivity profile is described. It is designed primarily for metering pulverized coal, where the solids concentration is typically very low, and also often highly inhomogeneous. A detailed analysis of the factors affecting measurement accuracy is presented, together with results obtained from laboratory tests. (author)

Representation in Memory.

Science.gov (United States)

Rumelhart, David E.; Norman, Donald A.

This paper reviews work on the representation of knowledge from within psychology and artificial intelligence. The work covers the nature of representation, the distinction between the represented world and the representing world, and significant issues concerned with propositional, analogical, and superpositional representations. Specific topics…

Combustion of metal agglomerates in a solid rocket core flow

Science.gov (United States)

Maggi, Filippo; Dossi, Stefano; DeLuca, Luigi T.

2013-12-01

The need for access to space may require the use of solid propellants. High thrust and density are appealing features for different applications, spanning from boosting phase to other service applications (separation, de-orbiting, orbit insertion). Aluminum is widely used as a fuel in composite solid rocket motors because metal oxidation increases enthalpy release in combustion chamber and grants higher specific impulse. Combustion process of metal particles is complex and involves aggregation, agglomeration and evolution of reacting particulate inside the core flow of the rocket. It is always stated that residence time should be enough in order to grant complete metal oxidation but agglomerate initial size, rocket grain geometry, burning rate, and other factors have to be reconsidered. New space missions may not require large rocket systems and metal combustion efficiency becomes potentially a key issue to understand whether solid propulsion embodies a viable solution or liquid/hybrid systems are better. A simple model for metal combustion is set up in this paper. Metal particles are represented as single drops trailed by the core flow and reacted according to Beckstead's model. The fluid dynamics is inviscid, incompressible, 1D. The paper presents parametric computations on ideal single-size particles as well as on experimental agglomerate populations as a function of operating rocket conditions and geometries.

Attention and Representational Momentum

OpenAIRE

Hayes, Amy; Freyd, Jennifer J

1995-01-01

Representational momentum, the tendency for memory to be distorted in the direction of an implied transformation, suggests that dynamics are an intrinsic part of perceptual representations. We examined the effect of attention on dynamic representation by testing for representational momentum under conditions of distraction. Forward memory shifts increase when attention is divided. Attention may be involved in halting but not in maintaining dynamic representations.

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

A general three-dimensional parametric geometry of the native aortic valve and root for biomechanical modeling.

Science.gov (United States)

Haj-Ali, Rami; Marom, Gil; Ben Zekry, Sagit; Rosenfeld, Moshe; Raanani, Ehud

2012-09-21

The complex three-dimensional (3D) geometry of the native tricuspid aortic valve (AV) is represented by select parametric curves allowing for a general construction and representation of the 3D-AV structure including the cusps, commissures and sinuses. The proposed general mathematical description is performed by using three independent parametric curves, two for the cusp and one for the sinuses. These curves are used to generate different surfaces that form the structure of the AV. Additional dependent curves are also generated and utilized in this process, such as the joint curve between the cusps and the sinuses. The model's feasibility to generate patient-specific parametric geometry is examined against 3D-transesophageal echocardiogram (3D-TEE) measurements from a non-pathological AV. Computational finite-element (FE) mesh can then be easily constructed from these surfaces. Examples are given for constructing several 3D-AV geometries by estimating the needed parameters from echocardiographic measurements. The average distance (error) between the calculated geometry and the 3D-TEE measurements was only 0.78±0.63mm. The proposed general 3D parametric method is very effective in quantitatively representing a wide range of native AV structures, with and without pathology. It can also facilitate a methodical quantitative investigation over the effect of pathology and mechanical loading on these major AV parameters. Copyright © 2012 Elsevier Ltd. All rights reserved.

Chemical thermodynamic representation of

International Nuclear Information System (INIS)

Lindemer, T.B.; Besmann, T.M.

1984-01-01

The entire data base for the dependence of the nonstoichiometry, x, on temperature and chemical potential of oxygen (oxygen potential) was retrieved from the literature and represented. This data base was interpreted by least-squares analysis using equations derived from the classical thermodynamic theory for the solid solution of a solute in a solvent. For hyperstoichiometric oxide at oxygen potentials more positive than -266700 + 16.5T kJ/mol, the data were best represented by a [UO 2 ]-[U 3 O 7 ] solution. For O/U ratios above 2 and oxygen potentials below this boundary, a [UO 2 ]-[U 2 O 4 . 5 ] solution represented the data. The data were represented by a [UO 2 ]-[U 1 / 3 ] solution. The resulting equations represent the experimental ln(PO 2 ) - ln(x) behavior and can be used in thermodynamic calculations to predict phase boundary compositions consistent with the literature. Collectively, the present analysis permits a mathematical representation of the behavior of the total data base

LGBT Representations on Facebook : Representations of the Self and the Content

OpenAIRE

Chu, Yawen

2017-01-01

The topic of LGBT rights has been increasingly discussed and debated over recent years. More and more scholars show their interests in the field of LGBT representations in media. However, not many studies involved LGBT representations in social media. This paper explores LGBT representations on Facebook by analysing posts on an open page and in a private group, including both representations of the self as the identity of sexual minorities, content that is displayed on Facebook and the simila...

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Calculating corrections in F-theory from refined BPS invariants and backreacted geometries

Energy Technology Data Exchange (ETDEWEB)

Poretschkin, Maximilian

2015-07-01

This thesis presents various corrections to F-theory compactifications which rely on the computation of refined Bogomol'nyi-Prasad-Sommerfield (BPS) invariants and the analysis of backreacted geometries. Detailed information about rigid supersymmetric theories in five dimensions is contained in an index counting refined BPS invariants. These BPS states fall into representations of SU(2){sub L} x SU(2){sub R}, the little group in five dimensions, which has an induced action on the cohomology of the moduli space of stable pairs. In the first part of this thesis, we present the computation of refined BPS state multiplicities associated to M-theory compactifications on local Calabi-Yau manifolds whose base is given by a del Pezzo or half K3 surface. For geometries with a toric realization we use an algorithm which is based on the Weierstrass normal form of the mirror geometry. In addition we use the refined holomorphic anomaly equation and the gap condition at the conifold locus in the moduli space in order to perform the direct integration and to fix the holomorphic ambiguity. In a second approach, we use the refined Goettsche formula and the refined modular anomaly equation that govern the (refined) genus expansion of the free energy of the half K3 surface. By this procedure, we compute the refined BPS invariants of the half K3 from which the results of the remaining del Pezzo surfaces are obtained by flop transitions and blow-downs. These calculations also make use of the high symmetry of the del Pezzo surfaces whose homology lattice contains the root lattice of exceptional Lie algebras. In cases where both approaches are applicable, we successfully check the compatibility of these two methods. In the second part of this thesis, we apply the results obtained from the calculation of the refined invariants of the del Pezzo respectively the half K3 surfaces to count non-perturbative objects in F-theory. The first application is given by BPS states of the E

Topological vertex, string amplitudes and spectral functions of hyperbolic geometry

Energy Technology Data Exchange (ETDEWEB)

Guimaraes, M.E.X.; Rosa, T.O. [Universidade Federal Fluminense, Instituto de Fisica, Av. Gal. Milton Tavares de Souza, s/n, CEP 24210-346, Niteroi, RJ (Brazil); Luna, R.M. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil)

2014-05-15

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of a hyperbolic three-geometry associated with q-series in the computation of the string amplitudes. (orig.)

Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells.

Science.gov (United States)

Nagaosa, Naoto; Morimoto, Takahiro

2017-07-01

The concept of topology is becoming more and more relevant to the properties and functions of electronic materials including various transport phenomena and optical responses. A pedagogical introduction is given here to the basic ideas and their applications to optoelectronic processes in solids. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Apseudo-fluid representation of vertical liquid–coarse solids flow

Directory of Open Access Journals (Sweden)

ZORANA ARSENIJEVIC

2005-05-01

Full Text Available The pseudo–fluid concept has been applied for the prediction of the pressure gradient and voidage in vertical liquid-coarse solids flow. Treating the flowing mixture as a single homogenous fluid, the correlation for the friction coefficient of the suspension–wall was developed, as was the correlation between the true voidage and the apparent (volumetric voidage in the transport tube. Experiments were performed using water and spherical glass particles 1.20, 1.94 and 2.98 mm in diameter in a transport tube of 24 mm in diameter. The loading ratio (Gp/Gf was varied between 0.05 and 1.05 and the fluid superficial velocity was between 0.4 Ut and 4.95 Ut where Ut represents the single particle terminal velocity. The voidage ranged from 0.648 to 0.951 for these ratios. Experimental data for the pressure gradient and voidage from the literature agree well with the proposed correlations.

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Effect of Geometry on Electrokinetic Characterization of Solid Surfaces.

Science.gov (United States)

Kumar, Abhijeet; Kleinen, Jochen; Venzmer, Joachim; Gambaryan-Roisman, Tatiana

2017-08-01

An analytical approach is presented to describe pressure-driven streaming current (I str ) and streaming potential (U str ) generation in geometrically complex samples, for which the classical Helmholtz-Smoluchowski (H-S) equation is known to be inaccurate. The new approach is valid under the same prerequisite conditions that are used for the development of the H-S equation, that is, the electrical double layers (EDLs) are sufficiently thin and surface conductivity and electroviscous effects are negligible. The analytical methodology is developed using linear velocity profiles to describe liquid flow inside of EDLs and using simplifying approximations to describe macroscopic flow. At first, a general expression is obtained to describe the I str generated in different cross sections of an arbitrarily shaped sample. Thereafter, assuming that the generated U str varies only along the pressure-gradient direction, an expression describing the variation of generated U str along the sample length is obtained. These expressions describing I str and U str generation constitute the theoretical foundation of this work, which is first applied to a set of three nonuniform cross-sectional capillaries and thereafter to a square array of cylindrical fibers (model porous media) for both parallel and transverse fiber orientation cases. Although analytical solutions cannot be obtained for real porous substrates because of their random structure, the new theory provides useful insights into the effect of important factors such as fiber orientation, sample porosity, and sample dimensions. The solutions obtained for the model porous media are used to device strategies for more accurate zeta potential determination of porous fiber plugs. The new approach could be thus useful in resolving the long-standing problem of sample geometry dependence of zeta potential measurements.

Object representation and magnetic moments in thin alkali films

Science.gov (United States)

Garrett, Douglas C.

2008-10-01

This thesis is broken into two parts a computer vision part and a solid state physics part. In the computer vision part of the thesis (chapters 1 through 5), the concept of an architecture is discussed with a review of what is known about the brain's visual architecture as it applies to object representation. With this in mind we review the two main types of architectures that are used in computer vision for object representation. A specific object representation is then implemented and optimized to solve a problem in object tracking. This representation is then used to derive the fiducial points of a face using two distinct methods. One using evolutionary algorithms and another by a Bayesian analysis of the feature responses drawn from a gallery of faces. The evolved fiducial representation is tested as a facial detection system. It is shown that the Bayesian analysis of facial images gives an entropy measure that can be used to further improve detection results in the facial detection system. In addition, two similarity metrics are explored in the context of facial detection. It is found that a normalized vector dot product substantially outperforms the Euclidean distance measure. The solid state part of the thesis is composed of two self contained chapters. An effort has been made to reduce the redundancies between the material but some will necessarily remain (i.e., short descriptions of the experimental setup). Both chapters deal with the phenomenon of magnetism of atomic impurities in and on thin metal host films. The important difference between the chapters, besides the results, lies in the experimental technique used to measure the magnetism. In chapter 6, thin films of Pb are covered in situ with sub monolayers of V, Mo and Co in the range between 0.01 and 1 monolayers. If the surface impurities are magnetic they will reduce the superconducting transition temperature of the Pb film. From the reduction of Tc the magnetic dephasing rate of the surface

Application of three-dimensional simulation at lecturing on descriptive geometry

Directory of Open Access Journals (Sweden)

Tel'noy Viktor Ivanovich

2014-05-01

Full Text Available Teaching descriptive geometry has its own characteristics. Need not only to inform students of a certain amount of knowledge on the subject, but also to develop their spatial imagination as well as the right to develop the skills of logical thinking. Practice of teaching the discipline showed that students face serious difficulties in the process of its study. This is due to the relatively low level of their schooling in geometry and technical drawing, and lacking in high spatial imagination. They find it difficult to imagine the geometrical image of the object of study and mentally convert it on the plane. Because of this, there is a need to find ways to effectively teach the discipline «Descriptive Geometry» at university. In the context of global informatization and computerization of the educational process, implementation of graphically programs for the development of design documentation and 3D modeling is one of the most promising applications of information technology in the process of solving these problems. With the help of three-dimensional models the best visibility in the classroom is achieved. When conducting lectures on descriptive geometry it is requested to use three-dimensional modeling not only as didactic means (demonstrativeness means, but also as a method of teaching (learning tool to deal with various graphics tasks. Bearing this in mind, the essence of the implementation of 3D modeling is revealed with the aim of better understanding of the algorithms for solving both positional and metric tasks using spatial representation of graphic constructions. It is shown that the possibility to consider the built model from different angles is of particular importance, as well as the use of transparency properties for illustrating the results of solving geometric problems. Using 3D models together with their display on the plane, as well as text information promotes better assimilation and more lasting memorization of the

Boolean representations of simplicial complexes and matroids

CERN Document Server

Rhodes, John

2015-01-01

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context.   Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean represent...

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Representation Elements of Spatial Thinking

Science.gov (United States)

Fiantika, F. R.

2017-04-01

This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss the concept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, the function of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.

Mixing and solid suspension of up-down agitators in a slab tank

International Nuclear Information System (INIS)

Ramsey, C.J.

1989-01-01

Seven different up-down agitators were studied for their ability to produce mixing and solid suspension in a slab tank. Mixing times were measured as the time needed to disperse injected dye. The solid suspension studies determined the minimum stroke frequency of the agitators needed for complete off-bottom suspension. The effects of stroke frequency, n; amplitude, a; blade width, w; blade clearance, c; and liquid depth, h, and weight percent solids, X, were studied. The most effective geometry, in terms of mixing, solid suspension and design simplicity, was a single flat blade with minimum off-bottom clearance and a blade width/tank thickness ratio, w/T, of 0.74 at the maximum stroke amplitude studied. 15 refs., 7 figs

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

Symmetries and Laplacians introduction to harmonic analysis, group representations and applications

CERN Document Server

Gurarie, D

1992-01-01

Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...

Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

Science.gov (United States)

Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

2012-01-01

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

Evaluation of the water equivalence of solid phantoms using gamma ray transmission measurements

International Nuclear Information System (INIS)

Hill, R.F.; Brown, S.; Baldock, C.

2008-01-01

Gamma ray transmission measurements have been used to evaluate the water equivalence of solid phantoms. Technetium-99m was used in narrow beam geometry and the transmission of photons measured, using a gamma camera, through varying thickness of the solid phantom material and water. Measured transmission values were compared with Monte Carlo calculated transmission data using the EGSnrc Monte Carlo code to score fluence in a geometry similar to that of the measurements. The results indicate that the RMI457 Solid Water, CMNC Plastic Water and PTW RW3 solid phantoms had similar transmission values as compared to water to within ±1.5%. However, Perspex had a greater deviation in the transmission values up to ±4%. The agreement between the measured and EGSnrc calculated transmission values agreed to within ±1% over the range of phantom thickness studied. The linear attenuation coefficients at the gamma ray energy of 140.5 keV were determined from the measured and EGSnrc calculated transmission data and compared with predicted values derived from data provided by the National Institute of Standards and Technology (NIST) using the XCOM program. The coefficients derived from the measured data were up to 6% lower than those predicted by the XCOM program, while the coefficients determined from the Monte Carlo calculations were between measured and XCOM values. The results indicate that a similar process can be followed to determine the water equivalency of other solid phantoms and at other photon energies

Fluid-solid boundary conditions for multiparticle collision dynamics

International Nuclear Information System (INIS)

Whitmer, Jonathan K; Luijten, Erik

2010-01-01

The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

Viscoelastic response of HTPB based solid fuel to horizontal and vertical storage slumping conditions and it's affect on service life

International Nuclear Information System (INIS)

Nawaz, Q.; Nizam, F.

2011-01-01

Frequent use of solid fuels as thrust generating energy source in modern day space vehicle systems has created a need to assess their serviceability for long term storage under various conditions. Solid fuel grain, the most important part of any solid fuel system, responds visco elastically to any loading condition. For the assessment of the service life of any solid fuel system, the solid fuel grain has to be structurally evaluated in applied storage conditions. Structural integrity of the grain is exceptionally significant to guarantee the successful operation of the solid fuel system. In this work, numerical simulations have been performed to assess the mechanical stresses and strains induced in an HTPB based solid fuel grain during service life employing ABAQUS standard FEA software using 4-node bilinear quadrilateral elements. For finite element analysis (FEA), typical 2-D and p/nth axisymmetric section of 5-point (n) star grain geometry is considered. Mechanical loads include the horizontal or vertical 1-g (solid fuel weight) storage condition. The simulation results are compared with the analytical results for the same grain geometry. Analytically measured slump deflections in grain segment at various storage times have been found in good relation with the FEA based simulation results. This proves the validity of the procedure adopted and is helpful in assessment of the service life of solid fuel systems. (author)

Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations

International Nuclear Information System (INIS)

Ferrie, Christopher; Emerson, Joseph

2008-01-01

Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus. (fast track communication)

Software Geometry in Simulations

Science.gov (United States)

Alion, Tyler; Viren, Brett; Junk, Tom

2015-04-01

The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

Computer aided surface representation. Progress report, June 1, 1989--May 31, 1990

Energy Technology Data Exchange (ETDEWEB)

Barnhill, R.E.

1990-02-19

The central research problem of this project is the effective representation, computation, and display of surfaces interpolating to information in three or more dimensions. If the given information is located on another surface, then the problem is to construct a ``surface defined on a surface``. Sometimes properties of an already defined surface are desired, which is ``geometry processing``. Visualization of multivariate surfaces is possible by means of contouring higher dimensional surfaces. These problems and more are discussed below. The broad sweep from constructive mathematics through computational algorithms to computer graphics illustrations is utilized in this research. The breadth and depth of this research activity makes this research project unique.

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

Poetic representation

DEFF Research Database (Denmark)

Wulf-Andersen, Trine Østergaard

2012-01-01

, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...

Crystallization features of normal alkanes in confined geometry.

Science.gov (United States)

Su, Yunlan; Liu, Guoming; Xie, Baoquan; Fu, Dongsheng; Wang, Dujin

2014-01-21

How polymers crystallize can greatly affect their thermal and mechanical properties, which influence the practical applications of these materials. Polymeric materials, such as block copolymers, graft polymers, and polymer blends, have complex molecular structures. Due to the multiple hierarchical structures and different size domains in polymer systems, confined hard environments for polymer crystallization exist widely in these materials. The confined geometry is closely related to both the phase metastability and lifetime of polymer. This affects the phase miscibility, microphase separation, and crystallization behaviors and determines both the performance of polymer materials and how easily these materials can be processed. Furthermore, the size effect of metastable states needs to be clarified in polymers. However, scientists find it difficult to propose a quantitative formula to describe the transition dynamics of metastable states in these complex systems. Normal alkanes [CnH2n+2, n-alkanes], especially linear saturated hydrocarbons, can provide a well-defined model system for studying the complex crystallization behaviors of polymer materials, surfactants, and lipids. Therefore, a deeper investigation of normal alkane phase behavior in confinement will help scientists to understand the crystalline phase transition and ultimate properties of many polymeric materials, especially polyolefins. In this Account, we provide an in-depth look at the research concerning the confined crystallization behavior of n-alkanes and binary mixtures in microcapsules by our laboratory and others. Since 2006, our group has developed a technique for synthesizing nearly monodispersed n-alkane containing microcapsules with controllable size and surface porous morphology. We applied an in situ polymerization method, using melamine-formaldehyde resin as shell material and nonionic surfactants as emulsifiers. The solid shell of microcapsules can provide a stable three-dimensional (3-D

A dissipative particle dynamics method for arbitrarily complex geometries

Science.gov (United States)

Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em

2018-02-01

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor-corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid-solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier-Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry - the "Brown Pacman" microfluidic device - to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its

The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...

Understanding representations in design

DEFF Research Database (Denmark)

Bødker, Susanne

1998-01-01

Representing computer applications and their use is an important aspect of design. In various ways, designers need to externalize design proposals and present them to other designers, users, or managers. This article deals with understanding design representations and the work they do in design....... The article is based on a series of theoretical concepts coming out of studies of scientific and other work practices and on practical experiences from design of computer applications. The article presents alternatives to the ideas that design representations are mappings of present or future work situations...... and computer applications. It suggests that representations are primarily containers of ideas and that representation is situated at the same time as representations are crossing boundaries between various design and use activities. As such, representations should be carriers of their own contexts regarding...

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

Covariant representations of nuclear *-algebras

International Nuclear Information System (INIS)

Moore, S.M.

1978-01-01

Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries

OpenAIRE

Li, Dong

2012-01-01

In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...

Standard model of knowledge representation

Science.gov (United States)

Yin, Wensheng

2016-09-01

Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.

The representation of manipulable solid objects in a relational database

Science.gov (United States)

Bahler, D.

1984-01-01

This project is concerned with the interface between database management and solid geometric modeling. The desirability of integrating computer-aided design, manufacture, testing, and management into a coherent system is by now well recognized. One proposed configuration for such a system uses a relational database management system as the central focus; the various other functions are linked through their use of a common data repesentation in the data manager, rather than communicating pairwise to integrate a geometric modeling capability with a generic relational data managemet system in such a way that well-formed questions can be posed and answered about the performance of the system as a whole. One necessary feature of any such system is simplification for purposes of anaysis; this and system performance considerations meant that a paramount goal therefore was that of unity and simplicity of the data structures used.

SU-E-I-79: Source Geometry Dependence of Gamma Well-Counter Measurements

Energy Technology Data Exchange (ETDEWEB)

Park, M; Belanger, A; Kijewski, M [Brigham and Women’s Hospital and Harvard Medical School, Boston, MA (United States)

2015-06-15

Purpose: To determine the effect of liquid sample volume and geometry on counting efficiency in a gamma well-counter, and to assess the relative contributions of sample geometry and self-attenuation. Gamma wellcounters are standard equipment in clinical and preclinical studies, for measuring patient blood radioactivity and quantifying animal tissue uptake for tracer development and other purposes. Accurate measurements are crucial. Methods: Count rates were measured for aqueous solutions of 99m- Tc at four liquid volume values in a 1-cm-diam tube and at six volume values in a 2.2-cm-diam vial. Total activity was constant for all volumes, and data were corrected for decay. Count rates from a point source in air, supported by a filter paper, were measured at seven heights between 1.3 and 5.7 cm from the bottom of a tube. Results: Sample volume effects were larger for the tube than for the vial. For the tube, count efficiency relative to a 1-cc volume ranged from 1.05 at 0.05 cc to 0.84 at 3 cc. For the vial, relative count efficiency ranged from 1.02 at 0.05 cc to 0.87 at 15 cc. For the point source, count efficiency relative to 1.3 cm from the tube bottom ranged from 0.98 at 1.8 cm to 0.34 at 5.7 cm. The relative efficiency of a 3-cc liquid sample in a tube compared to a 1-cc sample is 0.84; the average relative efficiency for the solid sample in air between heights in the tube corresponding to the surfaces of those volumes (1.3 and 4.8 cm) is 0.81, implying that the major contribution to efficiency loss is geometry, rather than attenuation. Conclusion: Volume-dependent correction factors should be used for accurate quantitation radioactive of liquid samples. Solid samples should be positioned at the bottom of the tube for maximum count efficiency.

Analytic evaluation of the weighting functions for remote sensing of blackbody planetary atmospheres : the case of limb viewing geometry

Science.gov (United States)

Ustinov, Eugene A.

2006-01-01

In a recent publication (Ustinov, 2002), we proposed an analytic approach to evaluation of radiative and geophysical weighting functions for remote sensing of a blackbody planetary atmosphere, based on general linearization approach applied to the case of nadir viewing geometry. In this presentation, the general linearization approach is applied to the limb viewing geometry. The expressions, similar to those obtained in (Ustinov, 2002), are obtained for weighting functions with respect to the distance along the line of sight. Further on, these expressions are converted to the expressions for weighting functions with respect to the vertical coordinate in the atmosphere. Finally, the numerical representation of weighting functions in the form of matrices of partial derivatives of grid limb radiances with respect to the grid values of atmospheric parameters is used for a convolution with the finite field of view of the instrument.

Chemical thermodynamic representations of and

International Nuclear Information System (INIS)

Besmann, T.M.; Lindemer, T.B.

1985-01-01

All available oxygen potential-temperature-composition data for the calcium fluorite-structure sup(**) phase were retrieved from the literature and utilized in the development of a binary solid solution representation of the phase. The data and phase relations are found to be best described by a solution of [Pusub(4/3)O 2 ] and [PuO 2 ] with a temperature dependent interaction energy. The fluorite-structure is assumed to be represented by a combination of the binaries and , and thus treated as a solution of [Pusub(4/3)O 2 ], [PuO 2 ], [UO 2 ], and either [U 2 Osub(4.5)] or [U 3 O 7 ]. The resulting equations well reproduce the large amount of oxygen potential-temperature-composition data for the mixed oxide system, all of which were also retrieved from the literature. These models are the first that appear to display the appropriate oxygen potential-temperature-composition and phase relation behavior over the entire range of existence for the phases. (orig.)

Noncommutative geometry

CERN Document Server

Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry Revealed

CERN Document Server

Berger, Marcel

2010-01-01

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

The Past Is Present: Representations of Parents, Friends, and Romantic Partners Predict Subsequent Romantic Representations.

Science.gov (United States)

Furman, Wyndol; Collibee, Charlene

2018-01-01

This study examined how representations of parent-child relationships, friendships, and past romantic relationships are related to subsequent romantic representations. Two-hundred 10th graders (100 female; M age  = 15.87 years) from diverse neighborhoods in a Western U.S. city were administered questionnaires and were interviewed to assess avoidant and anxious representations of their relationships with parents, friends, and romantic partners. Participants then completed similar questionnaires and interviews about their romantic representations six more times over the next 7.5 years. Growth curve analyses revealed that representations of relationships with parents, friends, and romantic partners each uniquely predicted subsequent romantic representations across development. Consistent with attachment and behavioral systems theory, representations of romantic relationships are revised by representations and experiences in other relationships. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Generation of Mid-Ocean Ridge Geometries by Strain Induced Damage

Science.gov (United States)

Hieronymus, C. F.

2001-12-01

Motivated by the success of wax models in which spreading segments, transform faults, and overlapping spreading centers form in a thin plate of solid wax under tension overlying a reservoir of molten wax, the dynamics of an elastic plate with damage is investigated. The effects of the underlying medium are neglected. A thin elastic plate with localized weaknesses in the elastic moduli is exposed to a deviatoric stress field. Stresses and strains are concentrated near the boundaries and inside the weak zones. Weakening of the material is assumed to occur where stress and strain are high, i.e. in regions of high elastic energy. The weak zones typically develop into linear bands of reduced elastic strength resembling fractures and shear zones. Different dependencies of the elastic moduli on damage result in different geometries of weak zones. An initially circular weakness has two locations of normal stress concentration; reduction of bulk and shear modulus there results in formation of an opening mode fracture with low resistance to any type of deformation. Two such fractures offset from each other and propagating toward each other interact by overlapping and curving toward each other. This overlapping geometry, which is observed along the East Pacific Rise, is stable; the fractures do not cut each other off. Introduction of a second type of damage causes the overlapping region between the two fractures to fail, and the more commonly observed transform offset develops. With another type of damage-strain dependency, oblique spreading occurs along lines 45o from the applied stress. Such patterns form frequently in certain types of wax, but are not observed along mid-ocean ridges. The model results suggest that it is the rheology of the solid plate, not the dynamics of the underlying mantle that control the morphology of the spreading ridge. Standard damage theory uses only a single damage parameter. The fact that the failure modes described above are limited to systems

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap

International Nuclear Information System (INIS)

Greiter, Martin; Rachel, Stephan

2007-01-01

To begin with, we introduce several exact models for SU(3) spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU(3) if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and, hence, a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of valence bond solid states to argue that models of antiferromagnetic chains of SU(n) spins, in general, possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λ which is divisible by n. If λ and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λ and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

2007-09-15

We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Optimization of Casting Design Parameters on Fabrication of Reliable Semi-Solid Aluminum Suspension Control Arm

Science.gov (United States)

Ragab, Kh. A.; Bouaicha, A.; Bouazara, M.

2017-09-01

The semi-solid casting process has the advantage of providing reliable mechanical aluminum parts that work continuously in dynamic as control arm of the suspension system in automotive vehicles. The quality performance of dynamic control arm is related to casting mold and gating system designs that affect the fluidity of semi-solid metal during filling the mold. Therefore, this study focuses on improvement in mechanical performance, depending on material characterization, and casting design optimization, of suspension control arms made of A357 aluminum semi-solid alloys. Mechanical and design analyses, applied on the suspension arm, showed the occurrence of mechanical failures at unexpected weak points. Metallurgical analysis showed that the main reason lies in the difficult flow of semi-solid paste through the thin thicknesses of a complex geometry. A design modification procedure is applied to the geometry of the suspension arm to avoid this problem and to improve its quality performance. The design modification of parts was carried out by using SolidWorks design software, evaluation of constraints with ABAQUS, and simulation of flow with ProCast software. The proposed designs showed that the modified suspension arm, without ribs and with a central canvas designed as Z, is considered as a perfect casting design showing an increase in the structural strength of the component. In this case, maximum von Mises stress is 199 MPa that is below the yield strength of the material. The modified casting mold design shows a high uniformity and minim turbulence of molten metal flow during semi-solid casting process.

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

The effect of interfaces on solid-state reactions between oxides

International Nuclear Information System (INIS)

Johnson, M.T.; Carter, C.B.

1998-01-01

A thin-film geometry has been used to study fundamental solid-state reaction processes occurring at interfaces in two spinel-forming oxide systems. In the first system, NiO/Al 2 O 3 , epitactic NiO films were deposited on various orientations of single-crystal α-Al 2 O 3 . In this case, the reaction kinetics were studied and correlated with the interfacial structure (or substrate orientation). In the second, In 2 O 3 /MgO, solid-state reactions were studied under the influence of an electric field. The electric field provides a driving force for mass transport that affects both the reaction process and the morphological stability of an interface

Volta-Based Cells Materials Chemical Multiple Representation to Improve Ability of Student Representation

Science.gov (United States)

Helsy, I.; Maryamah; Farida, I.; Ramdhani, M. A.

2017-09-01

This study aimed to describe the application of teaching materials, analyze the increase in the ability of students to connect the three levels of representation and student responses after application of multiple representations based teaching materials chemistry. The method used quasi one-group pretest-posttest design to 71 students. The results showed the application of teaching materials carried 88% with very good category. A significant increase ability to connect the three levels of representation of students after the application of multiple representations based teaching materials chemistry with t-value > t-crit (11.402 > 1.991). Recapitulation N-gain pretest and posttest showed relatively similar for all groups is 0.6 criterion being achievement. Students gave a positive response to the application of multiple representations based teaching materials chemistry. Students agree teaching materials used in teaching chemistry (88%), and agrees teaching materials to provide convenience in connecting the three levels of representation (95%).

Interconnection between the geometry and the structure of unit cells of substances in inorganic chemistry

International Nuclear Information System (INIS)

Eliseev, A.A.; Kuz'micheva, G.M.

1979-01-01

Regularity of interconnection between the geometry and the structure of elementary cells of inorganic compounds is investigated. Structural motives on the basis of NaCl structure for all phases of rare earth chalcogenides are built. It is shown that compounds (phases of variable content), detected on 23 (out of 48 possible) state diagrams of rare earths chalcogen binary systems are closely bound both from the viewpoint of geometric dimensions of elementary cells and structural motives. It is shown that using ion representations the number of formula units in the cell of a new rare earth chalcogenide can be calculated and its structural motif can be built

Convection in Slab and Spheroidal Geometries

Science.gov (United States)

Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

2000-01-01

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Initiation to global Finslerian geometry

CERN Document Server

Akbar-Zadeh, Hassan

2006-01-01

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

Algebraic geometry in India

Indian Academy of Sciences (India)

algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

Introduction to computer data representation

CERN Document Server

Fenwick, Peter

2014-01-01

Introduction to Computer Data Representation introduces readers to the representation of data within computers. Starting from basic principles of number representation in computers, the book covers the representation of both integer and floating point numbers, and characters or text. It comprehensively explains the main techniques of computer arithmetic and logical manipulation. The book also features chapters covering the less usual topics of basic checksums and 'universal' or variable length representations for integers, with additional coverage of Gray Codes, BCD codes and logarithmic repre

Introduction to combinatorial geometry

International Nuclear Information System (INIS)

Gabriel, T.A.; Emmett, M.B.

1985-01-01

The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Embedded data representations

DEFF Research Database (Denmark)

Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre

2017-01-01

We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...

Geometry of multihadron production

Energy Technology Data Exchange (ETDEWEB)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

Geometry of multihadron production

International Nuclear Information System (INIS)

Bjorken, J.D.

1994-10-01

This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

Categorification and higher representation theory

CERN Document Server

Beliakova, Anna

2017-01-01

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse te...

Geometry of higher-dimensional black hole thermodynamics

International Nuclear Information System (INIS)

Aaman, Jan E.; Pidokrajt, Narit

2006-01-01

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

Differential geometry of groups in string theory

International Nuclear Information System (INIS)

Schmidke, W.B. Jr.

1990-09-01

Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1|1). The quantum group GL q (1|1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL q (1|1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S 1 )/S 1 . We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs

Topotactic synthesis of vanadium nitride solid foams

International Nuclear Information System (INIS)

Oyama, S.T.; Kapoor, R.; Oyama, H.T.; Hofmann, D.J.; Matijevic, E.

1993-01-01

Vanadium nitride has been synthesized with a surface area of 120 m 2 g -1 by temperature programmed nitridation of a foam-like vanadium oxide (35 m 2 g -1 ), precipitated from vanadate solutions. The nitridation reaction was established to be topotactic and pseudomorphous by x-ray powder diffraction and scanning electron microscopy. The crystallographic relationship between the nitride and oxide was {200}//{001}. The effect of precursor geometry on the product size and shape was investigated by employing vanadium oxide solids of different morphologies

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

Inference-based procedural modeling of solids

KAUST Repository

Biggers, Keith

2011-11-01

As virtual environments become larger and more complex, there is an increasing need for more automated construction algorithms to support the development process. We present an approach for modeling solids by combining prior examples with a simple sketch. Our algorithm uses an inference-based approach to incrementally fit patches together in a consistent fashion to define the boundary of an object. This algorithm samples and extracts surface patches from input models, and develops a Petri net structure that describes the relationship between patches along an imposed parameterization. Then, given a new parameterized line or curve, we use the Petri net to logically fit patches together in a manner consistent with the input model. This allows us to easily construct objects of varying sizes and configurations using arbitrary articulation, repetition, and interchanging of parts. The result of our process is a solid model representation of the constructed object that can be integrated into a simulation-based environment. © 2011 Elsevier Ltd. All rights reserved.

Reactivity indexes for different geometries of palladium leads

Energy Technology Data Exchange (ETDEWEB)

Gomez-Carrillo, S C; Bolcatto, P G [Departamento de Fisica, Facultad de Ingenieria Quimica, Universidad Nacional de Litoral, Santiago del Estero 2829 S3000AOM Santa Fe Argentina (Argentina); Ortega, J, E-mail: scgomez@fiq.unl.edu.a [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid (Spain)

2009-05-01

Electronic transport through metallic break junctions or molecules is clearly dependent not only on the electronic structure of the central nanodevice connecting the leads, but also the shape and crystalline orientation of the contacts which can define the possible conduction channels. In this work we examine different geometries of contacts of palladium characterizing them through global and local reactivity indexes as electrophilicity, chemical hardness and Fukui functions. In molecules, these indicators are essentially defined by the energies of the frontier molecular orbitals and in solids they are related with the local and partial density of states. We use for this purpose an ab-initio based code (FIREBALL), applied to plane contacts with (001) fcc faces and also pyramidal tips grown following a (001) and (111) packaging. The results allow us to have an insight about the chemical features of this type of nanojunctions.

Quiver representations

CERN Document Server

Schiffler, Ralf

2014-01-01

This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.

Complex differential geometry

CERN Document Server

Zheng, Fangyang

2002-01-01

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

Computational synthetic geometry

CERN Document Server

Bokowski, Jürgen

1989-01-01

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

Designs and finite geometries

CERN Document Server

1996-01-01

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

d-geometries revisited

CERN Document Server

Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

2013-01-01

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

Representational Classroom Practices that Contribute to Students' Conceptual and Representational Understanding of Chemical Bonding

Science.gov (United States)

Hilton, Annette; Nichols, Kim

2011-11-01

Understanding bonding is fundamental to success in chemistry. A number of alternative conceptions related to chemical bonding have been reported in the literature. Research suggests that many alternative conceptions held by chemistry students result from previous teaching; if teachers are explicit in the use of representations and explain their content-specific forms and functions, this might be avoided. The development of an understanding of and ability to use multiple representations is crucial to students' understanding of chemical bonding. This paper draws on data from a larger study involving two Year 11 chemistry classes (n = 27, n = 22). It explores the contribution of explicit instruction about multiple representations to students' understanding and representation of chemical bonding. The instructional strategies were documented using audio-recordings and the teacher-researcher's reflection journal. Pre-test-post-test comparisons showed an improvement in conceptual understanding and representational competence. Analysis of the students' texts provided further evidence of the students' ability to use multiple representations to explain macroscopic phenomena on the molecular level. The findings suggest that explicit instruction about representational form and function contributes to the enhancement of representational competence and conceptual understanding of bonding in chemistry. However, the scaffolding strategies employed by the teacher play an important role in the learning process. This research has implications for professional development enhancing teachers' approaches to these aspects of instruction around chemical bonding.

Geometry success in 20 minutes a day

CERN Document Server

LLC, LearningExpress

2014-01-01

Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

Evolved Representation and Computational Creativity

Directory of Open Access Journals (Sweden)

Ashraf Fouad Hafez Ismail

2001-01-01

Full Text Available Advances in science and technology have influenced designing activity in architecture throughout its history. Observing the fundamental changes to architectural designing due to the substantial influences of the advent of the computing era, we now witness our design environment gradually changing from conventional pencil and paper to digital multi-media. Although designing is considered to be a unique human activity, there has always been a great dependency on design aid tools. One of the greatest aids to architectural design, amongst the many conventional and widely accepted computational tools, is the computer-aided object modeling and rendering tool, commonly known as a CAD package. But even though conventional modeling tools have provided designers with fast and precise object handling capabilities that were not available in the pencil-and-paper age, they normally show weaknesses and limitations in covering the whole design process.In any kind of design activity, the design worked on has to be represented in some way. For a human designer, designs are for example represented using models, drawings, or verbal descriptions. If a computer is used for design work, designs are usually represented by groups of pixels (paintbrush programs, lines and shapes (general-purpose CAD programs or higher-level objects like ‘walls’ and ‘rooms’ (purpose-specific CAD programs.A human designer usually has a large number of representations available, and can use the representation most suitable for what he or she is working on. Humans can also introduce new representations and thereby represent objects that are not part of the world they experience with their sensory organs, for example vector representations of four and five dimensional objects. In design computing on the other hand, the representation or representations used have to be explicitly defined. Many different representations have been suggested, often optimized for specific design domains

Incorporation of sweep in a transonic fan design using a 3D blade-row geometry package intended for aero-structural-manufacturing optimization

OpenAIRE

Abdelhamid, Hazen Fahmy

1997-01-01

Approved for public release; distribution is unlimited A new 3D blade row geometry package was developed and implemented. In the new representation the blade is described by six Bezier surfaces two of which represent the pressure and suction surfaces with sixteen points each. The leading and trailing edges are each represented by two Bezier surfaces. Only one extra parameter is required (in addition to the pressure and suction surfaces parameters) to define each of the leading and trailing...

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Introduction to tropical geometry

CERN Document Server

Maclagan, Diane

2015-01-01

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

Geometry Euclid and beyond

CERN Document Server

Hartshorne, Robin

2000-01-01

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

Atomistic Modeling of the Fluid-Solid Interface in Simple Fluids

Science.gov (United States)

Hadjiconstantinou, Nicolas; Wang, Gerald

2017-11-01

Fluids can exhibit pronounced structuring effects near a solid boundary, typically manifested in a layered structure that has been extensively shown to directly affect transport across the interface. We present and discuss several results from molecular-mechanical modeling and molecular-dynamics (MD) simulations aimed at characterizing the structure of the first fluid layer directly adjacent to the solid. We identify a new dimensionless group - termed the Wall number - which characterizes the degree of fluid layering, by comparing the competing effects of wall-fluid interaction and thermal energy. We find that in the layering regime, several key features of the first layer layer - including its distance from the solid, its width, and its areal density - can be described using mean-field-energy arguments, as well as asymptotic analysis of the Nernst-Planck equation. For dense fluids, the areal density and the width of the first layer can be related to the bulk fluid density using a simple scaling relation. MD simulations show that these results are broadly applicable and robust to the presence of a second confining solid boundary, different choices of wall structure and thermalization, strengths of fluid-solid interaction, and wall geometries.

Volume-based Representation of the Magnetic Field

CERN Document Server

Amapane, N; Drollinger, V; Karimäki, V; Klyukhin, V; Todorov, T

2005-01-01

Simulation and reconstruction of events in high-energy experiments require the knowledge of the value of the magnetic field at any point within the detector. The way this information is extracted from the actual map of the magnetic field and served to simulation and reconstruction applications has a large impact on accuracy and performance in terms of speed. As an example, the CMS high level trigger performs on-line tracking of muons within the magnet yoke, where the field is discontinuous and largely inhomogeneous. In this case the high level trigger execution time is dominated by the time needed to access the magnetic field map.For this reason, an optimized approach for the access to the CMS field was developed, based on a dedicated representation of thedetector geometry. The detector is modeled in terms of volumes, constructed in such a way that their boundaries correspond to the fiel d discontinuities due to changes in the magnetic permeability of the materials. The field within each volume is therefore c...

Canonical differential geometry of string backgrounds

International Nuclear Information System (INIS)

Schuller, Frederic P.; Wohlfarth, Mattias N.R.

2006-01-01

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes

Operator representations of frames

DEFF Research Database (Denmark)

Christensen, Ole; Hasannasab, Marzieh

2017-01-01

of the properties of the operator T requires more work. For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show......The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis...... that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ. The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded...

Group and representation theory

CERN Document Server

Vergados, J D

2017-01-01

This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...

Microencapsulated Phase Change Materials in Solar-Thermal Conversion Systems: Understanding Geometry-Dependent Heating Efficiency and System Reliability.

Science.gov (United States)

Zheng, Zhaoliang; Chang, Zhuo; Xu, Guang-Kui; McBride, Fiona; Ho, Alexandra; Zhuola, Zhuola; Michailidis, Marios; Li, Wei; Raval, Rasmita; Akhtar, Riaz; Shchukin, Dmitry

2017-01-24

The performance of solar-thermal conversion systems can be improved by incorporation of nanocarbon-stabilized microencapsulated phase change materials (MPCMs). The geometry of MPCMs in the microcapsules plays an important role for improving their heating efficiency and reliability. Yet few efforts have been made to critically examine the formation mechanism of different geometries and their effect on MPCMs-shell interaction. Herein, through changing the cooling rate of original emulsions, we acquire MPCMs within the nanocarbon microcapsules with a hollow structure of MPCMs (h-MPCMs) or solid PCM core particles (s-MPCMs). X-ray photoelectron spectroscopy and atomic force microscopy reveals that the capsule shell of the h-MPCMs is enriched with nanocarbons and has a greater MPCMs-shell interaction compared to s-MPCMs. This results in the h-MPCMs being more stable and having greater heat diffusivity within and above the phase transition range than the s-MPCMs do. The geometry-dependent heating efficiency and system stability may have important and general implications for the fundamental understanding of microencapsulation and wider breadth of heating generating systems.

Wild hummingbirds rely on landmarks not geometry when learning an array of flowers.

Science.gov (United States)

Hurly, T Andrew; Fox, Thomas A O; Zwueste, Danielle M; Healy, Susan D

2014-09-01

Rats, birds or fish trained to find a reward in one corner of a small enclosure tend to learn the location of the reward using both nearby visual features and the geometric relationships of corners and walls. Because these studies are conducted under laboratory and thereby unnatural conditions, we sought to determine whether wild, free-living rufous hummingbirds (Selasphorus rufus) learning a single reward location within a rectangular array of flowers would similarly employ both nearby visual landmarks and the geometric relationships of the array. Once subjects had learned the location of the reward, we used test probes in which one or two experimental landmarks were moved or removed in order to reveal how the birds remembered the reward location. The hummingbirds showed no evidence that they used the geometry of the rectangular array of flowers to remember the reward. Rather, they used our experimental landmarks, and possibly nearby, natural landmarks, to orient and navigate to the reward. We believe this to be the first test of the use of rectangular geometry by wild animals, and we recommend further studies be conducted in ecologically relevant conditions in order to help determine how and when animals form complex geometric representations of their local environments.

Controllable Solid Propulsion Combustion and Acoustic Knowledge Base Improvements

Science.gov (United States)

McCauley, Rachel; Fischbach, Sean; Fredrick, Robert

2012-01-01

Controllable solid propulsion systems have distinctive combustion and acoustic environments that require enhanced testing and analysis techniques to progress this new technology from development to production. In a hot gas valve actuating system, the movement of the pintle through the hot gas exhibits complex acoustic disturbances and flow characteristics that can amplify induced pressure loads that can damage or detonate the rocket motor. The geometry of a controllable solid propulsion gas chamber can set up unique unsteady flow which can feed acoustic oscillations patterns that require characterization. Research in this area aids in the understanding of how best to design, test, and analyze future controllable solid rocket motors using the lessons learned from past government programs as well as university research and testing. This survey paper will give the reader a better understanding of the potentially amplifying affects propagated by a controllable solid rocket motor system and the knowledge of the tools current available to address these acoustic disturbances in a preliminary design. Finally the paper will supply lessons learned from past experiences which will allow the reader to come away with understanding of what steps need to be taken when developing a controllable solid rocket propulsion system. The focus of this survey will be on testing and analysis work published by solid rocket programs and from combustion and acoustic books, conference papers, journal articles, and additionally from subject matter experts dealing currently with controllable solid rocket acoustic analysis.

The Beauty of Geometry

Science.gov (United States)

Morris, Barbara H.

2004-01-01

This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

3D surface parameterization using manifold learning for medial shape representation

Science.gov (United States)

Ward, Aaron D.; Hamarneh, Ghassan

2007-03-01

The choice of 3D shape representation for anatomical structures determines the effectiveness with which segmentation, visualization, deformation, and shape statistics are performed. Medial axis-based shape representations have attracted considerable attention due to their inherent ability to encode information about the natural geometry of parts of the anatomy. In this paper, we propose a novel approach, based on nonlinear manifold learning, to the parameterization of medial sheets and object surfaces based on the results of skeletonization. For each single-sheet figure in an anatomical structure, we skeletonize the figure, and classify its surface points according to whether they lie on the upper or lower surface, based on their relationship to the skeleton points. We then perform nonlinear dimensionality reduction on the skeleton, upper, and lower surface points, to find the intrinsic 2D coordinate system of each. We then center a planar mesh over each of the low-dimensional representations of the points, and map the meshes back to 3D using the mappings obtained by manifold learning. Correspondence between mesh vertices, established in their intrinsic 2D coordinate spaces, is used in order to compute the thickness vectors emanating from the medial sheet. We show results of our algorithm on real brain and musculoskeletal structures extracted from MRI, as well as an artificial multi-sheet example. The main advantages to this method are its relative simplicity and noniterative nature, and its ability to correctly compute nonintersecting thickness vectors for a medial sheet regardless of both the amount of coincident bending and thickness in the object, and of the incidence of local concavities and convexities in the object's surface.

Teaching Spatial Geometry in a Virtual World

DEFF Research Database (Denmark)

Förster, Klaus-Tycho

2017-01-01

Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

Trends and developments in computational geometry

NARCIS (Netherlands)

Berg, de M.

1997-01-01

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry

On Behavioral Equivalence of Rational Representations

NARCIS (Netherlands)

Trentelman, Harry L.; Willems, JC; Hara, S; Ohta, Y; Fujioka, H

2010-01-01

This article deals with the equivalence of representations of behaviors of linear differential systems In general. the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel representations and image representations Two kernel

Functional representations for quantized fields

International Nuclear Information System (INIS)

Jackiw, R.

1988-01-01

This paper provides information on Representing transformations in quantum theory bosonic quantum field theories: Schrodinger Picture; Represnting Transformations in Bosonic Quantum Field Theory; Two-Dimensional Conformal Transformations, Schrodinger picture representation, Fock space representation, Inequivalent Schrodinger picture representations; Discussion, Self-Dual and Other Models; Field Theory in de Sitter Space. Fermionic Quantum Field Theories: Schroedinger Picture; Schrodinger Picture Representation for Two-Dimensional; Conformal Transformations; Fock Space Dynamics in the Schrodinger Picture; Fock Space Evaluation of Anomalous Current and Conformal Commutators

Efficient three-dimensional reconstruction of aquatic vegetation geometry: Estimating morphological parameters influencing hydrodynamic drag

Science.gov (United States)

Liénard, Jean; Lynn, Kendra; Strigul, Nikolay; Norris, Benjamin K.; Gatziolis, Demetrios; Mullarney, Julia C.; Bryan, Karin, R.; Henderson, Stephen M.

2016-09-01

Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam's Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new 'sector-slice' algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies.

The protection of warranties and representations

International Nuclear Information System (INIS)

Spence, C.D.; Thusoo, N.

1999-01-01

Most acquisition contracts within the oil and gas industry consist of representations and warranties. The legal distinction between representations and warranties was explained as follows: a representation is a statement of fact made by the representor before making the contract, but a warranty is a statement of fact which forms part of the terms of the contract. The paper outlines the nature of a representation or warranty and explains why certain warranties are not given. The protection offered by representations and warranties in breach of contract cases is also explained. Suggestions are offered for increasing protection by representations and warranties. 22 refs

An approach for management of geometry data

Science.gov (United States)

Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

1980-01-01

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

Motivation for Using Generalized Geometry in the Time Dependent Transport Code TDKENO

Energy Technology Data Exchange (ETDEWEB)

Dustin Popp; Zander Mausolff; Sedat Goluoglu

2016-04-01

We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operation is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).

Recent Advances in Registration, Integration and Fusion of Remotely Sensed Data: Redundant Representations and Frames

Science.gov (United States)

Czaja, Wojciech; Le Moigne-Stewart, Jacqueline

2014-01-01

In recent years, sophisticated mathematical techniques have been successfully applied to the field of remote sensing to produce significant advances in applications such as registration, integration and fusion of remotely sensed data. Registration, integration and fusion of multiple source imagery are the most important issues when dealing with Earth Science remote sensing data where information from multiple sensors, exhibiting various resolutions, must be integrated. Issues ranging from different sensor geometries, different spectral responses, differing illumination conditions, different seasons, and various amounts of noise need to be dealt with when designing an image registration, integration or fusion method. This tutorial will first define the problems and challenges associated with these applications and then will review some mathematical techniques that have been successfully utilized to solve them. In particular, we will cover topics on geometric multiscale representations, redundant representations and fusion frames, graph operators, diffusion wavelets, as well as spatial-spectral and operator-based data fusion. All the algorithms will be illustrated using remotely sensed data, with an emphasis on current and operational instruments.

Harmonic Analysis and Group Representation

CERN Document Server

Figa-Talamanca, Alessandro

2011-01-01

This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.

"WGL," a Web Laboratory for Geometry

Science.gov (United States)

Quaresma, Pedro; Santos, Vanda; Maric, Milena

2018-01-01

The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…

Analytische Geometrie

Science.gov (United States)

Kemnitz, Arnfried

Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

ONETRAN, 1-D Transport in Planar, Cylindrical, Spherical Geometry for Homogeneous, Inhomogeneous Problem, Anisotropic Source

International Nuclear Information System (INIS)

1982-01-01

1 - Description of problem or function: ONETRAN solves the one- dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (K-eff and eigenvalue searches) problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. Standard inner (within-group) iteration cycles are accelerated by system re-balance, coarse mesh re-balance, or Chebyshev acceleration. Outer iteration cycles are accelerated by coarse-mesh re-balance. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. On CDC machines MAXCOR can be about 25 000 words and peripheral storage is used for most group-dependent data

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry.

Science.gov (United States)

Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M

2010-06-01

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.

Algebraic Geometry and Number Theory Summer School

CERN Document Server

Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

2017-01-01

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

Dynamic analysis of structures with solid-fluid interaction

International Nuclear Information System (INIS)

Nahavandi, A.N.; Pedrido, R.R.; Cloud, R.L.

1977-01-01

This study develops a finite element model for interaction between an elastic solid and fluid medium (flow-induced vibrations in nuclear reactor components). Plane triangular finite elements have been used separately for fluid, solid, and solid-fluid continuua and the equivalent mass, damping, and stiffness matrices and interaction load arrays for all elements are derived and assembled into global matrices. The global matrix differential equation of motion developed is solved in time to obtain the pressure and velocity distributions in the fluid, as well as the displacements in the solid. Two independent computer programs are used to obtain the dynamic solution. The first program is a finite element program developed for solid-fluid interaction studies. This program uses the modal superposition technique in which the eigenvalues and eigenvectors for the system are found and used to uncouple the equations. This approach allows an analytic solution in each integration time step. The second program is WECAN finite element program in which a new element library subroutine for solid-fluid interaction was incorporated. This program can employ a NASTRAN direct integration scheme based on a central difference formula for the acceleration and velocity terms and an implicit representation of the displacement term. This reduces the problem to a matrix equation whose right hand side is updated in every time step and is solved by a variation of the Gaussian elimination method known as the wave front technique. Results have been obtained for the case of water, between two flat elastic parallel plates, initially at rest and accelerated suddenly by applying a step pressure. The results obtained from the above-mentioned two independent finite element programs are in full agreement. This verification provides the confidence needed to initiate parametric studies. Both rigid wall (no solid-fluid interaction) and flexible wall (including solid-fluid interaction) cases were examined

The Idea of Order at Geometry Class.

Science.gov (United States)

Rishel, Thomas

The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

Science.gov (United States)

Guven, Bulent

2012-01-01

This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

Disformal transformation in Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)

2016-08-15

Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)

Computation of higher spherical harmonics moments of the angular flux for neutron transport problems in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.; Sharma, A.

2000-01-01

The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson

Polynomial representations of GLn

CERN Document Server

Green, James A; Erdmann, Karin

2007-01-01

The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

Polynomial representations of GLN

CERN Document Server

Green, James A

1980-01-01

The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

Semantic representation of reported measurements in radiology.

Science.gov (United States)

Oberkampf, Heiner; Zillner, Sonja; Overton, James A; Bauer, Bernhard; Cavallaro, Alexander; Uder, Michael; Hammon, Matthias

2016-01-22

In radiology, a vast amount of diverse data is generated, and unstructured reporting is standard. Hence, much useful information is trapped in free-text form, and often lost in translation and transmission. One relevant source of free-text data consists of reports covering the assessment of changes in tumor burden, which are needed for the evaluation of cancer treatment success. Any change of lesion size is a critical factor in follow-up examinations. It is difficult to retrieve specific information from unstructured reports and to compare them over time. Therefore, a prototype was implemented that demonstrates the structured representation of findings, allowing selective review in consecutive examinations and thus more efficient comparison over time. We developed a semantic Model for Clinical Information (MCI) based on existing ontologies from the Open Biological and Biomedical Ontologies (OBO) library. MCI is used for the integrated representation of measured image findings and medical knowledge about the normal size of anatomical entities. An integrated view of the radiology findings is realized by a prototype implementation of a ReportViewer. Further, RECIST (Response Evaluation Criteria In Solid Tumors) guidelines are implemented by SPARQL queries on MCI. The evaluation is based on two data sets of German radiology reports: An oncologic data set consisting of 2584 reports on 377 lymphoma patients and a mixed data set consisting of 6007 reports on diverse medical and surgical patients. All measurement findings were automatically classified as abnormal/normal using formalized medical background knowledge, i.e., knowledge that has been encoded into an ontology. A radiologist evaluated 813 classifications as correct or incorrect. All unclassified findings were evaluated as incorrect. The proposed approach allows the automatic classification of findings with an accuracy of 96.4 % for oncologic reports and 92.9 % for mixed reports. The ReportViewer permits

Value Representations

DEFF Research Database (Denmark)

Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves

2011-01-01

Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...

Geometry and symmetry

CERN Document Server

Yale, Paul B

2012-01-01

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

Distinguished figures in descriptive geometry and its applications for mechanism science from the middle ages to the 17th century

CERN Document Server

2016-01-01

This book consists of chapters that focus specifically on single figures that worked on Descriptive Geometry and also in Mechanisms Sciences and contain biographical notes, a survey of their work and their achievements, together with a modern interpretation of their legacy. Since Vitruvius in ancient times, and with Brunelleschi in the Renaissance, the two disciplines began to share a common direction which, over the centuries, took shape through less well-known figures until the more recent times in which Gaspard Monge worked. Over the years, a gap has been created between Descriptive Geometry and Mechanism Science, which now appear to belong to different worlds. In reality, however, there is a very close relationship between the two disciplines, with a link based on extremely solid foundations. Without the theoretical foundations of Geometry it would not be possible to draw and design mechanical parts such as gears, while in Kinematics it would be less easy to design and predict the reciprocal movements of ...

Optimizing solar-cell grid geometry

Science.gov (United States)

Crossley, A. P.

1969-01-01

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

Geometry and Cloaking Devices

Science.gov (United States)

Ochiai, T.; Nacher, J. C.

2011-09-01

Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

Global affine differential geometry of hypersurfaces

CERN Document Server

Li, An-Min; Zhao, Guosong; Hu, Zejun

2015-01-01

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.

The relationship between experimental geometry, heat rate, and ultrasound wave speed measurement while observing phase changes in highly attenuative materials

Science.gov (United States)

Moore, David G.; Stair, Sarah L.; Jack, David A.

2018-04-01

Ultrasound techniques are capable of monitoring changes in the time-of-flight as a material is exposed to different thermal environments. The focus of the present study is to identify the phase of a material via ultrasound compression wave measurements in a through transmission experimental setup as the material is heated from a solid to a liquid and then allowed to re-solidify. The present work seeks to expand upon the authors' previous research, which proved this through transmission phase monitoring technique was possible, by considering different experimental geometries. The relationship between geometry, the measured speed of sound, and the temperature profile is presented. The use of different volumes helps in establishing a baseline understanding of which aspects of the experiment are geometry dependent and which are independent. The present study also investigates the relationship between the heating rate observed in the experiment and the measured speed of sound. The trends identified between the experimental geometry, heat rate and ultrasound wave speed measurement assist in providing a baseline understanding of the applicability of this technique to various industries, including the polymer industry and the oil industry.

Spectral dimension of quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2014-01-01

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Creating and using a type of free-form geometry in Monte Carlo particle transport

International Nuclear Information System (INIS)

Wessol, D.E.; Wheeler, F.J.

1993-01-01

While the reactor physicists were fine-tuning the Monte Carlo paradigm for particle transport in regular geometries, the computer scientists were developing rendering algorithms to display extremely realistic renditions of irregular objects ranging from the ubiquitous teakettle to dynamic Jell-O. Even though the modeling methods share a common basis, the initial strategies each discipline developed for variance reduction were remarkably different. Initially, the reactor physicist used Russian roulette, importance sampling, particle splitting, and rejection techniques. In the early stages of development, the computer scientist relied primarily on rejection techniques, including a very elegant hierarchical construction and sampling method. This sampling method allowed the computer scientist to viably track particles through irregular geometries in three-dimensional space, while the initial methods developed by the reactor physicists would only allow for efficient searches through analytical surfaces or objects. As time goes by, it appears there has been some merging of the variance reduction strategies between the two disciplines. This is an early (possibly first) incorporation of geometric hierarchical construction and sampling into the reactor physicists' Monte Carlo transport model that permits efficient tracking through nonuniform rational B-spline surfaces in three-dimensional space. After some discussion, the results from this model are compared with experiments and the model employing implicit (analytical) geometric representation

Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

International Nuclear Information System (INIS)

Thierry-Mieg, Jean

2006-01-01

In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space

SimpleGeO - new developments in the interactive creation and debugging of geometries for Monte Carlo simulations

International Nuclear Information System (INIS)

Theis, Christian; Feldbaumer, Eduard; Forkel-Wirth, Doris; Jaegerhofer, Lukas; Roesler, Stefan; Vincke, Helmut; Buchegger, Karl Heinz

2010-01-01

Nowadays radiation transport Monte Carlo simulations have become an indispensable tool in various fields of physics. The applications are diversified and range from physics simulations, like detector studies or shielding design, to medical applications. Usually a significant amount of time is spent on the quite cumbersome and often error prone task of implementing geometries, before the actual physics studies can be performed. SimpleGeo is an interactive solid modeler which allows for the interactive creation and visualization of geometries for various Monte Carlo particle transport codes in 3D. Even though visual validation of the geometry is important, it might not reveal subtle errors like overlapping or undefined regions. These might eventually corrupt the execution of the simulation or even lead to incorrect results, the latter being sometimes hard to identify. In many cases a debugger is provided by the Monte Carlo package, but most often they lack interactive visual feedback, thus making it hard for the user to localize and correct the error. In this paper we describe the latest developments in SimpleGeo, which include debugging facilities that support immediate visual feedback, and apply various algorithms based on deterministic, Monte Carlo or Quasi Monte Carlo methods. These approaches allow for a fast and robust identification of subtle geometry errors that are also marked visually. (author)

A geometry calibration method for rotation translation trajectory

International Nuclear Information System (INIS)

Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng

2013-01-01

In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)

(Self)-representations on youtube

DEFF Research Database (Denmark)

Simonsen, Thomas Mosebo

This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can...... be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how certain forms of representation can be identified as representations of the self (Turkle 1995, Scannell...... 1996, Walker 2005) and further how these forms must be comprehended within a context of technological constrains, institutional structures and social as well as economical practices on YouTube (Burgess and Green 2009, Van Dijck 2009). It is argued that these different contexts play a vital part...

3-D world modeling based on combinatorial geometry for autonomous robot navigation

International Nuclear Information System (INIS)

Goldstein, M.; Pin, F.G.; De Saussure, G.; Weisbin, C.R.

1987-01-01

In applications of robotics to surveillance and mapping at nuclear facilities the scene to be described is three-dimensional. Using range data a 3-D model of the environment can be built. First, each measured point on the object surface is surrounded by a solid sphere with a radius determined by the range to that point. Then the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of the spheres. Using this representation distances to boundary surfaces can be efficiently calculated. This feature is particularly useful for navigation purposes. The efficiency of the proposed approach is illustrated by a simulation of a spherical robot navigating in a 3-D room with static obstacles

Sinusoidal Representation of Acoustic Signals

Science.gov (United States)

Honda, Masaaki

Sinusoidal representation of acoustic signals has been an important tool in speech and music processing like signal analysis, synthesis and time scale or pitch modifications. It can be applicable to arbitrary signals, which is an important advantage over other signal representations like physical modeling of acoustic signals. In sinusoidal representation, acoustic signals are composed as sums of sinusoid (sine wave) with different amplitudes, frequencies and phases, which is based on the timedependent short-time Fourier transform (STFT). This article describes the principles of acoustic signal analysis/synthesis based on a sinusoid representation with focus on sine waves with rapidly varying frequency.

Geometry modeling for SAM-CE Monte Carlo calculations

International Nuclear Information System (INIS)

Steinberg, H.A.; Troubetzkoy, E.S.

1980-01-01

Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described

From Spheric to Aspheric Solid Polymer Lenses: A Review

Directory of Open Access Journals (Sweden)

Kuo-Yung Hung

2011-01-01

Full Text Available This paper presents a new approach in the use of MEMS technology to fabricate micro-optofluidic polymer solid lenses in order to achieve the desired profile, focal length, numerical aperture, and spot size. The resulting polymer solid lenses can be applied in optical data storage systems, imaging systems, and automated optical inspection systems. In order to meet the various needs of different applications, polymer solid lenses may have a spherical or aspherical shape. The method of fabricating polymer solid lenses is different from methods used to fabricate tunable lenses with variable focal length or needing an external control system to change the lens geometry. The current trend in polymer solid lenses is toward the fabrication of microlenses with a high numerical aperture, small clear aperture (<2 mm, and high transmittance. In this paper we focus on the use of thermal energy and electrostatic force in shaping the lens profile, including both spherical and aspherical lenses. In addition, the paper discusses how to fabricate a lens with a high numerical aperture of 0.6 using MEMS and also compares the optical characteristics of polymer lens materials, including SU-8, Norland Optical Adhesive (NOA, and cyclic olefin copolymer (COC. Finally, new concepts and applications related to micro-optofluidic lenses and polymer materials are also discussed.

A compact representation of drawing movements with sequences of parabolic primitives.

Directory of Open Access Journals (Sweden)

Felix Polyakov

2009-07-01

-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry.

Teaching geometry in schools: An investigative rather than instructive process

Directory of Open Access Journals (Sweden)

Rasheed Sanni

2007-10-01

Full Text Available Research has documented the prevalence of lessons  characterised by homework check,  followed by teacher lecture and demonstration, followed in turn, by learner practice sequence of classroom instructional activities in  our classrooms. This sequence of classroom activities does not allow for the development of sound mathematics practices and mathematical proficiency. Meanwhile, curriculum reforms in South Africa as well as in other parts  of the world recommend classroom activities where teachers create opportunities for, listen to  and extend learners.  This paper presents  a sequence of activities to be used in the teaching of geometry and surface areas of solid shapes in a grade 8 classroom. The sequence portrays the teaching of these concepts as an investigative rather than instructive process.

Representations of Reductive Groups : in Honor of the 60th Birthday of David A. Vogan, Jr.

CERN Document Server

Trapa, Peter

2015-01-01

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups.  His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014.  This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored.  Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Son...

Molecular motion in restricted geometries

Indian Academy of Sciences (India)

Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

Remarks on the history of the terms "object representation" and "self representation".

Science.gov (United States)

May, Ulrike

2005-01-01

This paper reconstructs the history of the term "object representation" and "self representation". It seeks to show that "Objektrepräsentanz" was introduced by Fenichel in 1926, following on from Radó, in order to be able to integrate identification (and the superego) into metapsychology. Freud himself never used "Objektrepräsentanz". Fenichel's pioneering role is not discernible in the English literature mainly because of the diverging approaches used in the translation of this term (object representative versus object representation). It is generally acknowledged that "self representation" was first used by Hartmann but this paper suggests that it actually played a more crucial role in Jacobson's work than it did in Hartmann's. In addition, this paper sees the terms of self and object representation as a reflection of the paradigm change in the 1920s that ensued after the publication of Freud's "The Ego and the Id". In tracing the history of the terms, the significance of the Berlin Psychoanalytical Institute in the 1920s emerges as do the Berlin roots of the works written in the USA in the 1950s and 1960s by Edith Jacobson. She received her analytical training in Berlin. Fenichel was her analyst, Radó was one of her teachers, and she was closely involved with the work of her fellow analysts there.

Young children reorient by computing layout geometry, not by matching images of the environment.

Science.gov (United States)

Lee, Sang Ah; Spelke, Elizabeth S

2011-02-01

Disoriented animals from ants to humans reorient in accord with the shape of the surrounding surface layout: a behavioral pattern long taken as evidence for sensitivity to layout geometry. Recent computational models suggest, however, that the reorientation process may not depend on geometrical analyses but instead on the matching of brightness contours in 2D images of the environment. Here we test this suggestion by investigating young children's reorientation in enclosed environments. Children reoriented by extremely subtle geometric properties of the 3D layout: bumps and ridges that protruded only slightly off the floor, producing edges with low contrast. Moreover, children failed to reorient by prominent brightness contours in continuous layouts with no distinctive 3D structure. The findings provide evidence that geometric layout representations support children's reorientation.

Neutron cross sections of cryogenic materials: a synthetic kernel for molecular solids

International Nuclear Information System (INIS)

Granada, J.R.; Gillette, V.H.; Petriw, S.; Cantargi, F.; Pepe, M.E.; Sbaffoni, M.M.

2004-01-01

A new synthetic scattering function aimed at the description of the interaction of thermal neutrons with molecular solids has been developed. At low incident neutron energies, both lattice modes and molecular rotations are specifically accounted for, through an expansion of the scattering law in few phonon terms. Simple representations of the molecular dynamical modes are used, in order to produce a fairly accurate description of neutron scattering kernels and cross sections with a minimum set of input data. As the neutron energies become much larger than that corresponding to the characteristic Debye temperature and to the rotational energies of the molecular solid, the 'phonon formulation' transforms into the traditional description for molecular gases. (orig.)

On the aerodynamics of variable-geometry oval-trajectory Darrieus wind turbines

Energy Technology Data Exchange (ETDEWEB)

Ponta, F.L.; Seminara, J.J.; Otero, A.D. [College of Engineering, University of Buenos Aires, Paseo Colon 850, Buenos Aires C1063ACV (Argentina)

2007-01-15

A new computational model for the aerodynamics of vertical-axis wind turbines is introduced. It is based on the double-multiple streamtube concept and it incorporates the capacity of dealing with rotors whose blades follow oval-trajectories at variable setting-angles. We applied this model to the study of the aerodynamics of an innovative concept in extra-large wind-power plants: the VGOT (variable-geometry oval-trajectory) Darrieus wind turbine. Due to the especial geometric characteristics of the VGOT Darrieus, it was necessary to propose three new non-dimensional parameters to quantify its performance under different wind-conditions: the equivalent power coefficient, the equivalent solidity coefficient and the trajectory efficiency. We show some numerical results testing several rotor configurations working under different wind scenarios. (author)

Multiple representations in physics education

CERN Document Server

Duit, Reinders; Fischer, Hans E

2017-01-01

This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementati...

W-geometry

International Nuclear Information System (INIS)

Hull, C.M.

1993-01-01

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

Projective geometry solved problems and theory review

CERN Document Server

Fortuna, Elisabetta; Pardini, Rita

2016-01-01

This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of ...

Head First 2D Geometry

CERN Document Server

Fallow), Stray

2009-01-01

Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

An alternative approach for the determination of the full-peak detection efficiency in case of a close-in detection geometry

International Nuclear Information System (INIS)

Wispelaere, A. de; Corte, F. de

2006-01-01

The aim of this work is to propose an alternative method for the determination of ε p in the case of measurements restricted to one single sample-detector distance. It is based on an iterative procedure, linking the measurement of calibrated multi-γ point sources at this particular detector distance (the resulting ε p -function being disturbed by true-coincidence effects) with measurement of some coincidence-free single-γ point sources (leading to peak-to-total ratios P/T that, combined with detection efficiencies, yield correction factors for true-coincidence effects). The thus obtained ε p versus E γ curve for point-source geometry can then be converted to the actual extended sample geometry, based on the effective solid angle concept

Quantification of Porcine Vocal Fold Geometry.

Science.gov (United States)

Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L

2016-07-01

The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Lectures on discrete geometry

CERN Document Server

2002-01-01

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

Discrete and computational geometry

CERN Document Server

Devadoss, Satyan L

2011-01-01

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

Alternative approach to nuclear data representation

International Nuclear Information System (INIS)

Pruet, J.; Brown, D.; Beck, B.; McNabb, D.P.

2006-01-01

This paper considers an approach for representing nuclear data that is qualitatively different from the approach currently adopted by the nuclear science community. Specifically, we examine a representation in which complicated data is described through collections of distinct and self-contained simple data structures. This structure-based representation is compared with the ENDF and ENDL formats, which can be roughly characterized as dictionary-based representations. A pilot data representation for replacing the format currently used at LLNL is presented. Examples are given as is a discussion of promises and shortcomings associated with moving from traditional dictionary-based formats to a structure-rich or class-like representation

On the phase space representations. 1

International Nuclear Information System (INIS)

Polubarinov, I.V.

1978-01-01

The Dirac representation theory deals usually with the amplitude formalism of the quantum theory. An introduction is given into a theory of some other representations, which are applicable in the density matrix formalism and can naturally be called phase space representations (PSR). They use terms of phase space variables (x and p simultaneously) and give a description, close to the classical phase space description. Definitions and algebraic properties are given in quantum mechanics for such PSRs as the Wigner representation, coherent state representation and others. Completeness relations of a matrix type are used as a starting point. The case of quantum field theory is also outlined

A prediction for bubbling geometries

OpenAIRE

Okuda, Takuya

2007-01-01

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

Mobilities and Representations

DEFF Research Database (Denmark)

Thelle, Mikkel

2017-01-01

to consider how they and their peers are currently confronting representations of mobility. This is particularly timely given the growing academic focus on practices, material mediation, and nonrepresentational theories, as well as on bodily reactions, emotions, and feelings that, according to those theories......As the centerpiece of the eighth T2M yearbook, the following interview about representations of mobility signals a new and exciting focus area for Mobility in History. In future issues we hope to include reviews that grapple more with how mobilities have been imagined and represented in the arts......, literature, and film. Moreover, we hope the authors of future reviews will reflect on the ways they approached those representations. Such commentaries would provide valuable methodological insights, and we hope to begin that effort with this interview. We have asked four prominent mobility scholars...

Post-representational cartography

Directory of Open Access Journals (Sweden)

Rob Kitchin

2010-03-01

Full Text Available Over the past decade there has been a move amongst critical cartographers to rethink maps from a post-representational perspective – that is, a vantage point that does not privilege representational modes of thinking (wherein maps are assumed to be mirrors of the world and automatically presumes the ontological security of a map as a map, but rather rethinks and destabilises such notions. This new theorisation extends beyond the earlier critiques of Brian Harley (1989 that argued maps were social constructions. For Harley a map still conveyed the truth of a landscape, albeit its message was bound within the ideological frame of its creator. He thus advocated a strategy of identifying the politics of representation within maps in order to circumnavigate them (to reveal the truth lurking underneath, with the ontology of cartographic practice remaining unquestioned.

Generalized oscillator representations for Calogero Hamiltonians

International Nuclear Information System (INIS)

Tyutin, I V; Voronov, B L

2013-01-01

This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

Geometry -----------~--------------RESONANCE

Indian Academy of Sciences (India)

Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

Intermediate algebra & analytic geometry

CERN Document Server

Gondin, William R

1967-01-01

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

Equivalence of rational representations of behaviors

NARCIS (Netherlands)

Gottimukkala, Sasanka; Fiaz, Shaik; Trentelman, H.L.

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel

Specialized mechanisms for theory of mind: are mental representations special because they are mental or because they are representations?

Science.gov (United States)

Cohen, Adam S; Sasaki, Joni Y; German, Tamsin C

2015-03-01

Does theory of mind depend on a capacity to reason about representations generally or on mechanisms selective for the processing of mental state representations? In four experiments, participants reasoned about beliefs (mental representations) and notes (non-mental, linguistic representations), which according to two prominent theories are closely matched representations because both are represented propositionally. Reaction times were faster and accuracies higher when participants endorsed or rejected statements about false beliefs than about false notes (Experiment 1), even when statements emphasized representational format (Experiment 2), which should have favored the activation of representation concepts. Experiments 3 and 4 ruled out a counterhypothesis that differences in task demands were responsible for the advantage in belief processing. These results demonstrate for the first time that understanding of mental and linguistic representations can be dissociated even though both may carry propositional content, supporting the theory that mechanisms governing theory of mind reasoning are narrowly specialized to process mental states, not representations more broadly. Extending this theory, we discuss whether less efficient processing of non-mental representations may be a by-product of mechanisms specialized for processing mental states. Crown Copyright © 2014. Published by Elsevier B.V. All rights reserved.

A generalized wavelet extrema representation

Energy Technology Data Exchange (ETDEWEB)

Lu, Jian; Lades, M.

1995-10-01

The wavelet extrema representation originated by Stephane Mallat is a unique framework for low-level and intermediate-level (feature) processing. In this paper, we present a new form of wavelet extrema representation generalizing Mallat`s original work. The generalized wavelet extrema representation is a feature-based multiscale representation. For a particular choice of wavelet, our scheme can be interpreted as representing a signal or image by its edges, and peaks and valleys at multiple scales. Such a representation is shown to be stable -- the original signal or image can be reconstructed with very good quality. It is further shown that a signal or image can be modeled as piecewise monotonic, with all turning points between monotonic segments given by the wavelet extrema. A new projection operator is introduced to enforce piecewise inonotonicity of a signal in its reconstruction. This leads to an enhancement to previously developed algorithms in preventing artifacts in reconstructed signal.

Applanation optical coherence elastography: noncontact measurement of intraocular pressure, corneal biomechanical properties, and corneal geometry with a single instrument

Science.gov (United States)

Singh, Manmohan; Han, Zhaolong; Nair, Achuth; Schill, Alexander; Twa, Michael D.; Larin, Kirill V.

2017-02-01

Current clinical tools provide critical information about ocular health such as intraocular pressure (IOP). However, they lack the ability to quantify tissue material properties, which are potent markers for ocular tissue health and integrity. We describe a single instrument to measure the eye-globe IOP, quantify corneal biomechanical properties, and measure corneal geometry with a technique termed applanation optical coherence elastography (Appl-OCE). An ultrafast OCT system enabled visualization of corneal dynamics during noncontact applanation tonometry and direct measurement of micro air-pulse induced elastic wave propagation. Our preliminary results show that the proposed Appl-OCE system can be used to quantify IOP, corneal biomechanical properties, and corneal geometry, which builds a solid foundation for a unique device that can provide a more complete picture of ocular health.

ATR-IR spectroscopic cell for in situ studies at solid-liquid interface at elevated temperatures and pressures

NARCIS (Netherlands)

Koichumanova, Kamila; Visan, Aura; Geerdink, Bert; Lammertink, Rob G.H.; Mojet, Barbara; Seshan, Kulathuiyer; Lefferts, Leonardus

2017-01-01

An in situ ATR-IR spectroscopic cell suitable for studies at solid-liquid interface is described including the design and experimental details in continuous flow mode at elevated temperatures (230 °C) and pressures (30 bar). The design parameters considered include the cell geometry, the procedure

Qualitative aspects of representational competence among college chemistry students: Multiple representations and their role in the understanding of ideal gases

Science.gov (United States)

Madden, Sean Patrick

This study examined the role of multiple representations of chemical phenomena, specifically, the temperature-pressure relationship of ideal gases, in the problem solving strategies of college chemistry students. Volunteers included students enrolled in a first semester general chemistry course at a western university. Two additional volunteers from the same university were asked to participate and serve as models of greater sophistication. One was a senior chemistry major; another was a junior science writing major. Volunteers completed an initial screening task involving multiple representations of concentration and dilution concepts. Based on the results of this screening instrument a smaller set of subjects were asked to complete a think aloud session involving multiple representations of the temperature-pressure relationship. Data consisted of the written work of the volunteers and transcripts from videotaped think aloud sessions. The data were evaluated by the researcher and two other graduate students in chemical education using a coding scheme (Kozma, Schank, Coppola, Michalchik, and Allen. 2000). This coding scheme was designed to identify essential features of representational competence and differences in uses of multiple representations. The results indicate that students tend to have a strong preference for one type of representation. Students scoring low on representational competence, as measured by the rubric, ignored important features of some representations or acknowledged them only superficially. Students scoring higher on representational competence made meaningful connections among representations. The more advanced students, those who rated highly on representational competence, tended to use their preferred representation in a heuristic manner to establish meaning for other representations. The more advanced students also reflected upon the problem at greater length before beginning work. Molecular level sketches seemed to be the most

Representational Machines

DEFF Research Database (Denmark)

Photography not only represents space. Space is produced photographically. Since its inception in the 19th century, photography has brought to light a vast array of represented subjects. Always situated in some spatial order, photographic representations have been operatively underpinned by social...... to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...... possibilities, and genre distinctions. Presenting several distinct ways of producing space photographically, this book opens a new and important field of inquiry for photography research....

Facilitating Mathematical Practices through Visual Representations

Science.gov (United States)

Murata, Aki; Stewart, Chana

2017-01-01

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

Science.gov (United States)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

Projective Geometry

Indian Academy of Sciences (India)

mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

Morphing methods to parameterize specimen-specific finite element model geometries.

Science.gov (United States)

Sigal, Ian A; Yang, Hongli; Roberts, Michael D; Downs, J Crawford

2010-01-19

Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens. We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties. Copyright 2009 Elsevier Ltd. All rights reserved.

Procedural Media Representation

OpenAIRE

Henrysson, Anders

2002-01-01

We present a concept for using procedural techniques to represent media. Procedural methods allow us to represent digital media (2D images, 3D environments etc.) with very little information and to render it photo realistically. Since not all kind of content can be created procedurally, traditional media representations (bitmaps, polygons etc.) must be used as well. We have adopted an object-based media representation where an object can be represented either with a procedure or with its trad...

The abstract representations in speech processing.

Science.gov (United States)

Cutler, Anne

2008-11-01

Speech processing by human listeners derives meaning from acoustic input via intermediate steps involving abstract representations of what has been heard. Recent results from several lines of research are here brought together to shed light on the nature and role of these representations. In spoken-word recognition, representations of phonological form and of conceptual content are dissociable. This follows from the independence of patterns of priming for a word's form and its meaning. The nature of the phonological-form representations is determined not only by acoustic-phonetic input but also by other sources of information, including metalinguistic knowledge. This follows from evidence that listeners can store two forms as different without showing any evidence of being able to detect the difference in question when they listen to speech. The lexical representations are in turn separate from prelexical representations, which are also abstract in nature. This follows from evidence that perceptual learning about speaker-specific phoneme realization, induced on the basis of a few words, generalizes across the whole lexicon to inform the recognition of all words containing the same phoneme. The efficiency of human speech processing has its basis in the rapid execution of operations over abstract representations.

Interactions between visual working memory representations.

Science.gov (United States)

Bae, Gi-Yeul; Luck, Steven J

2017-11-01

We investigated whether the representations of different objects are maintained independently in working memory or interact with each other. Observers were shown two sequentially presented orientations and required to reproduce each orientation after a delay. The sequential presentation minimized perceptual interactions so that we could isolate interactions between memory representations per se. We found that similar orientations were repelled from each other whereas dissimilar orientations were attracted to each other. In addition, when one of the items was given greater attentional priority by means of a cue, the representation of the high-priority item was not influenced very much by the orientation of the low-priority item, but the representation of the low-priority item was strongly influenced by the orientation of the high-priority item. This indicates that attention modulates the interactions between working memory representations. In addition, errors in the reported orientations of the two objects were positively correlated under some conditions, suggesting that representations of distinct objects may become grouped together in memory. Together, these results demonstrate that working-memory representations are not independent but instead interact with each other in a manner that depends on attentional priority.

Second International workshop Geometry and Symbolic Computation

CERN Document Server

Walczak, Paweł; Geometry and its Applications

2014-01-01

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...

Face-to-Face Packing of 2,3,9,10-Tetrasubstituted Pentacene Derivatives Revealed through a Solid State [4 + 4] Thermal Cycloaddition and Molecular Dynamic Simulation.

Science.gov (United States)

Pal, Bikash; Lin, Bo-Chao; Dela Cerna, Mark Vincent Carreon; Hsu, Chao-Ping; Lin, Chih-Hsiu

2016-08-05

2,3,9,10-Substituted pentacene tetraesters and pentacene diester-dinitriles were synthesized. These pentacene derivatives underwent an unusual solid state [4 + 4] thermal dimerization with good efficiency and complete stereoselectivity. This observation indicates this series of pentacene derivatives adopt π-π stacking geometry with large mutual overlap in solid state. This notion was confirmed by molecualr dynamic simulation.

Representation

National Research Council Canada - National Science Library

Little, Daniel

2006-01-01

...). The reason this is so is due to hierarchies that we take for granted. By hierarchies I mean that there is a layer of representation of us as individuals, as military professional, as members of a military unit and as citizens of an entire nation...

L-functions and the oscillator representation

CERN Document Server

Rallis, Stephen

1987-01-01

These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N

Quantitative optimization of solid freeform deposition of aqueous hydrogels

International Nuclear Information System (INIS)

Kang, K H; Hockaday, L A; Butcher, J T

2013-01-01

Many soft tissues exhibit complex anatomical geometry that is challenging to replicate for regenerative medicine applications. Solid freeform fabrication (SFF) has emerged as an attractive approach for creating 3D tissues, but a detailed understanding of how specific fabrication parameters affect accuracy and viability has not been established to date. In this study, we evaluate the effects of printing parameters of the Fab-Home 3D printing system on accuracy using alginate, photocrosslinkable polyethylene-glycol diacrylate (PEG-DA) and gelatin as commonly used model hydrogel materials. Print accuracy and resolution along the length, width and height were determined based on quantitative image analysis. The effects of extrusion parameters on cell viability were assessed using porcine aortic valve interstitial cells (PAVIC) as a model cell type. We observed that pressure, pathheight and pathspace all significantly affected print accuracy and resolution. Printing conditions did not affect PAVIC viability within the ranges applied. We predicted that optimal pressure, pathheight and pathspace values would be increased linearly with increasing nozzle diameter, and we confirmed that the predicted values generate accurate 3D geometries while poorly chosen parameters yield inaccurate, unpredictable geometries. This systematic optimization strategy therefore improves the accuracy of 3D printing platforms for biofabrication and tissue engineering applications. (paper)

Spectrum recovery method based on sparse representation for segmented multi-Gaussian model

Science.gov (United States)

Teng, Yidan; Zhang, Ye; Ti, Chunli; Su, Nan

2016-09-01

Hyperspectral images can realize crackajack features discriminability for supplying diagnostic characteristics with high spectral resolution. However, various degradations may generate negative influence on the spectral information, including water absorption, bands-continuous noise. On the other hand, the huge data volume and strong redundancy among spectrums produced intense demand on compressing HSIs in spectral dimension, which also leads to the loss of spectral information. The reconstruction of spectral diagnostic characteristics has irreplaceable significance for the subsequent application of HSIs. This paper introduces a spectrum restoration method for HSIs making use of segmented multi-Gaussian model (SMGM) and sparse representation. A SMGM is established to indicating the unsymmetrical spectral absorption and reflection characteristics, meanwhile, its rationality and sparse property are discussed. With the application of compressed sensing (CS) theory, we implement sparse representation to the SMGM. Then, the degraded and compressed HSIs can be reconstructed utilizing the uninjured or key bands. Finally, we take low rank matrix recovery (LRMR) algorithm for post processing to restore the spatial details. The proposed method was tested on the spectral data captured on the ground with artificial water absorption condition and an AVIRIS-HSI data set. The experimental results in terms of qualitative and quantitative assessments demonstrate that the effectiveness on recovering the spectral information from both degradations and loss compression. The spectral diagnostic characteristics and the spatial geometry feature are well preserved.

Network geometry with flavor: From complexity to quantum geometry

Science.gov (United States)

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

???????????? SolidWorks/SolidWorks Flow Simulation/SolidWorks Simulation ??? ?????????? ???????? ?? ????????????? ???

OpenAIRE

????????????, ?. ?.; ????????, ?. ?.; ?????, ?. ?.

2012-01-01

? ?????? ???????? ??????? ??????? ???????? ?? ???????????? ??????????? ????????? SolidWorks/SolidWorks Flow Simulation (COSMOSFloWorks)/SolidWorks Simulation ??? ?????????? ???????? ?? ????????????? ???. ??? ???????? ????????? ???????? ?????????? ?? ?????? ???????? ??????? ? ????????????? ?????? ? ????????????? ????????????? ?????????? ???????????? SolidWorks Flow Simulation (COSMOSFloWorks). ??? ???????????? ??????????? ????????????? ?????? ?? ????????? ??????????? ??????? ?? ??????????? ...

The Persistification of the ATLAS Geometry

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00068562; The ATLAS collaboration; Bianchi, Riccardo-Maria

2016-01-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the- y on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS so ware framework “Athena”, which provides the online services and the tools to retrieve the data from the database. is operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geom- etry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. e new mechanism is composed by a new le format and a REST API. e new le format allows to store the whole detector description locally in a at le, and it is especially optimized to descri...

Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

International Nuclear Information System (INIS)

Maertens, H.D.

1982-01-01

The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de

Visual perception and verbal descriptions as sources for generating mental representations: Evidence from representational neglect.

Science.gov (United States)

Denis, Michel; Beschin, Nicoletta; Logie, Robert H; Della Sala, Sergio

2002-03-01

In the majority of investigations of representational neglect, patients are asked to report information derived from long-term visual knowledge. In contrast, studies of perceptual neglect involve reporting the contents of relatively novel scenes in the immediate environment. The present study aimed to establish how representational neglect might affect (a) immediate recall of recently perceived, novel visual layouts, and (b) immediate recall of novel layouts presented only as auditory verbal descriptions. These conditions were contrasted with reports from visual perception and a test of immediate recall of verbal material. Data were obtained from 11 neglect patients (9 with representational neglect), 6 right hemisphere lesion control patients with no evidence of neglect, and 15 healthy controls. In the perception, memory following perception, and memory following layout description conditions, the neglect patients showed poorer report of items depicted or described on the left than on the right of each layout. The lateralised error pattern was not evident in the non-neglect patients or healthy controls, and there was no difference among the three groups on immediate verbal memory. One patient showed pure representational neglect, with ceiling performance in the perception condition, but with lateralised errors for memory following perception or following verbal description. Overall, the results indicate that representational neglect does not depend on the presence of perceptual neglect, that visual perception and visual mental representations are less closely linked than has been thought hitherto, and that visuospatial mental representations have similar functional characteristics whether they are derived from visual perception or from auditory linguistic descriptive inputs.

Young Children's Representations of Groups of Objects: The Relationship between Abstraction and Representation.

Science.gov (United States)

Kato, Yasuhiko; Kamii, Constance; Ozaki, Kyoko; Nagahiro, Mariko

2002-01-01

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

Implosions and hypertoric geometry

DEFF Research Database (Denmark)

Dancer, A.; Kirwan, F.; Swann, A.

2013-01-01

The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

Solid phase stability of molybdenum under compression: Sound velocity measurements and first-principles calculations

Energy Technology Data Exchange (ETDEWEB)

Zhang, Xiulu [Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, P.O. Box 919-102, 621900 Mianyang, Sichuan (China); Laboratory for Extreme Conditions Matter Properties, Southwest University of Science and Technology, 621010 Mianyang, Sichuan (China); Liu, Zhongli [Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, P.O. Box 919-102, 621900 Mianyang, Sichuan (China); College of Physics and Electric Information, Luoyang Normal University, 471022 Luoyang, Henan (China); Jin, Ke; Xi, Feng; Yu, Yuying; Tan, Ye; Dai, Chengda; Cai, Lingcang [Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, P.O. Box 919-102, 621900 Mianyang, Sichuan (China)

2015-02-07

The high-pressure solid phase stability of molybdenum (Mo) has been the center of a long-standing controversy on its high-pressure melting. In this work, experimental and theoretical researches have been conducted to check its solid phase stability under compression. First, we performed sound velocity measurements from 38 to 160 GPa using the two-stage light gas gun and explosive loading in backward- and forward-impact geometries, along with the high-precision velocity interferometry. From the sound velocities, we found no solid-solid phase transition in Mo before shock melting, which does not support the previous solid-solid phase transition conclusion inferred from the sharp drops of the longitudinal sound velocity [Hixson et al., Phys. Rev. Lett. 62, 637 (1989)]. Then, we searched its structures globally using the multi-algorithm collaborative crystal structure prediction technique combined with the density functional theory. By comparing the enthalpies of body centered cubic structure with those of the metastable structures, we found that bcc is the most stable structure in the range of 0–300 GPa. The present theoretical results together with previous ones greatly support our experimental conclusions.

Hohenberg-Kohn theorem and non-V-representable densities

International Nuclear Information System (INIS)

Englisch, H.; Englisch, R.

1983-01-01

In the density-functional formalism of Hohenberg and Kohn, the variation is only allowed over the one-particle densities which are pure-state-V-representable (PS-V-representable). Levy and Lieb proved that not every ensemble-V-representable (E-V-representable) density is PS-V-representable. Since we show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states, Levy's and Lieb's result is not a counterexample to the universality of the Hohenberg-Kohn theorem. The question whether every N-representable density is E-V-representable has remained open so far. Presenting examples of non-E-V-representable densities we answer this question in the negative. Thus the value of Levy's functional for the calculation of ground-state energies is obvious, since this functional only requires the N-representability of the densities. Therefore we transfer two approaches for the calculation of excited-state energies into the framework of Levy's formalism. (orig.)

The response matrix method for the representation of the border conditions in the three-dimensional difussion codes

International Nuclear Information System (INIS)

Grant, C.R.

1981-01-01

It could take a considerable amount of memory and processing time to represent a reactor in its simulation by means of a diffusion code and considering areas in which nuclear and geometrical properties are invariant, such as reflector, water columns, etc. To avoid an explicit representation of these zones, a method employing a matrix was developed consisting in expressing the net currents of each group as a function of the total flux. Estimates are made for different geometries, introducing the PUMA difussion code of materials. Several tests made proved a very sound reliability of the results obtained in 2 and 5 groups. (author) [es

A vector space approach to geometry

CERN Document Server

Hausner, Melvin

2010-01-01

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

Integral geometry and valuations

CERN Document Server

Solanes, Gil

2014-01-01

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

CBM RICH geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

2016-07-01

The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

Riemannian geometry

CERN Document Server

Petersen, Peter

2016-01-01

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

Representation theory of lattice current algebras

International Nuclear Information System (INIS)

Alekseev, A.Yu.; Eidgenoessische Technische Hochschule, Zurich; Faddeev, L.D.; Froehlich, L.D.; Schomerus, V.; Kyoto Univ.

1996-04-01

Lattice current algebras were introduced as a regularization of the left-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U q (G). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts. (orig.)

Kaehler geometry and SUSY mechanics

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen

2001-01-01

We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

GPS: Geometry, Probability, and Statistics

Science.gov (United States)

Field, Mike

2012-01-01

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

Cohen-Macaulay representations

CERN Document Server

Leuschke, Graham J

2012-01-01

This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Au...

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

OpenMC: A state-of-the-art Monte Carlo code for research and development

International Nuclear Information System (INIS)

Romano, Paul K.; Horelik, Nicholas E.; Herman, Bryan R.; Nelson, Adam G.; Forget, Benoit; Smith, Kord

2015-01-01

Highlights: • OpenMC is an open source Monte Carlo particle transport code. • Solid geometry and continuous-energy physics allow high-fidelity simulations. • Development has focused on high performance and modern I/O techniques. • OpenMC is capable of scaling up to hundreds of thousands of processors. • Other features include plotting, CMFD acceleration, and variance reduction. - Abstract: This paper gives an overview of OpenMC, an open source Monte Carlo particle transport code recently developed at the Massachusetts Institute of Technology. OpenMC uses continuous-energy cross sections and a constructive solid geometry representation, enabling high-fidelity modeling of nuclear reactors and other systems. Modern, portable input/output file formats are used in OpenMC: XML for input, and HDF5 for output. High performance parallel algorithms in OpenMC have demonstrated near-linear scaling to over 100,000 processors on modern supercomputers. Other topics discussed in this paper include plotting, CMFD acceleration, variance reduction, eigenvalue calculations, and software development processes

Operator representation for effective realistic interactions

Energy Technology Data Exchange (ETDEWEB)

Weber, Dennis; Feldmeier, Hans; Neff, Thomas [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany)

2013-07-01

We present a method to derive an operator representation from the partial wave matrix elements of effective realistic nucleon-nucleon potentials. This method allows to employ modern effective interactions, which are mostly given in matrix element representation, also in nuclear many-body methods requiring explicitly the operator representation, for example ''Fermionic Molecular Dynamics'' (FMD). We present results for the operator representation of effective interactions obtained from the Argonne V18 potential with the Uenitary Correlation Operator Method'' (UCOM) and the ''Similarity Renormalization Group'' (SRG). Moreover, the operator representation allows a better insight in the nonlocal structure of the potential: While the UCOM transformed potential only shows a quadratic momentum dependence, the momentum dependence of SRG transformed potentials is beyond such a simple polynomial form.

ABJM Wilson loops in arbitrary representations

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Honda, Masazumi [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

2013-06-15

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

ABJM Wilson loops in arbitrary representations

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi

2013-06-01

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

NMR Study of Solvation Effect on Geometry of Proton-Bound Homodimers of Increasing Size

KAUST Repository

Gurinov, Andrei A.

2017-10-24

Hydrogen bond geometries in the proton-bound homodimers of quinoline and acridine derivatives in an aprotic polar solution have been experimentally studied using 1H NMR at 120 K. The reported results show that increase of the dielec-tric permittivity of the medium results in contraction of the N…N distance. The degree of contraction depends on the homodimer\\'s size and its substituent-specific solvation features. Neither of these effects can be reproduced using conven-tional implicit solvent models employed in computational studies. In general, the N…N distance in the homodimers of pyridine, quinoline, and acridine derivatives decreases in the sequence gas phase > solid state > polar solvent.

NMR Study of Solvation Effect on Geometry of Proton-Bound Homodimers of Increasing Size

KAUST Repository

Gurinov, Andrei A.; Denisov, Gleb S.; Borissova, Alexandra O.; Goloveshkin, Alexander S.; Greindl, Julian; Limbach, Hans-Heinrich; Shenderovich, Ilya G.

2017-01-01

Hydrogen bond geometries in the proton-bound homodimers of quinoline and acridine derivatives in an aprotic polar solution have been experimentally studied using 1H NMR at 120 K. The reported results show that increase of the dielec-tric permittivity of the medium results in contraction of the N…N distance. The degree of contraction depends on the homodimer's size and its substituent-specific solvation features. Neither of these effects can be reproduced using conven-tional implicit solvent models employed in computational studies. In general, the N…N distance in the homodimers of pyridine, quinoline, and acridine derivatives decreases in the sequence gas phase > solid state > polar solvent.

Introduction into integral geometry and stereology

DEFF Research Database (Denmark)

Kiderlen, Markus

Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...

A knowledge representation model for the optimisation of electricity generation mixes

International Nuclear Information System (INIS)

Chee Tahir, Aidid; Bañares-Alcántara, René

2012-01-01

Highlights: ► Prototype energy model which uses semantic representation (ontologies). ► Model accepts both quantitative and qualitative based energy policy goals. ► Uses logic inference to formulate equations for linear optimisation. ► Proposes electricity generation mix based on energy policy goals. -- Abstract: Energy models such as MARKAL, MESSAGE and DNE-21 are optimisation tools which aid in the formulation of energy policies. The strength of these models lie in their solid theoretical foundations built on rigorous mathematical equations designed to process numerical (quantitative) data related to economics and the environment. Nevertheless, a complete consideration of energy policy issues also requires the consideration of the political and social aspects of energy. These political and social issues are often associated with non-numerical (qualitative) information. To enable the evaluation of these aspects in a computer model, we hypothesise that a different approach to energy model optimisation design is required. A prototype energy model that is based on a semantic representation using ontologies and is integrated to engineering models implemented in Java has been developed. The model provides both quantitative and qualitative evaluation capabilities through the use of logical inference. The semantic representation of energy policy goals is used (i) to translate a set of energy policy goals into a set of logic queries which is then used to determine the preferred electricity generation mix and (ii) to assist in the formulation of a set of equations which is then solved in order to obtain a proposed electricity generation mix. Scenario case studies have been developed and tested on the prototype energy model to determine its capabilities. Knowledge queries were made on the semantic representation to determine an electricity generation mix which fulfilled a set of energy policy goals (e.g. CO 2 emissions reduction, water conservation, energy supply

Mental Representation and Motor Imagery Training

Directory of Open Access Journals (Sweden)

Thomas eSchack

2014-05-01

Full Text Available Research in sports, dance and rehabilitation has shown that Basic Action Concepts (BACs are fundamental building blocks of mental action representations. BACs are based on chunked body postures related to common functions for realizing action goals. In this paper, we outline issues in research methodology and an experimental method, SDA-M (structural dimensional analysis of mental representation, to assess action-relevant representational structures that reflect the organization of BACs. The SDA-M reveals a strong relationship between cognitive representation and performance if complex actions are performed. We show how the SDA-M can improve motor imagery training and how it contributes to our understanding of coaching processes. The SDA-M capitalizes on the objective measurement of individual mental movement representations before training and the integration of these results into the motor imagery training. Such motor imagery training based on mental representations has been applied successfully in professional sports such as golf, volleyball, gymnastics, windsurfing, and recently in the rehabilitation of patients who have suffered a stroke.

Off-shell representations of maximally-extended supersymmetry

International Nuclear Information System (INIS)

Cox, P.H.

1985-01-01

A general theorem on the necessity of off-shell central charges in representations of maximally-extended supersymmetry (number of spinor charges - 4 x largest spin) is presented. A procedure for building larger and higher-N representations is also explored; a (noninteracting) N=8, maximum spin 2, off-shell representation is achieved. Difficulties in adding interactions for this representation are discussed

The impact of surface geometry, cavitation, and condensation on wetting transitions: posts and reentrant structures

Science.gov (United States)

Panter, J. R.; Kusumaatmaja, H.

2017-03-01

The fundamental impacts of surface geometry on the stability of wetting states, and the transitions between them are elucidated for square posts and reentrant structures in three dimensions. We identify three principal outcomes of particular importance for future surface design of liquid-repellent surfaces. Firstly, we demonstrate and quantify how capillary condensation and vapour cavitation affect wetting state stabilities. At high contact angles, cavitation is enhanced about wide, closely-spaced square posts, leading to the existence of suspended states without an associated collapsed state. At low contact angles, narrow reentrant pillars suppress condensation and enable the suspension of even highly wetting liquids. Secondly, two distinct collapse mechanisms are observed for 3D reentrant geometries, base contact and pillar contact, which are operative at different pillar heights. As well as morphological differences in the interface of the penetrating liquid, each mechanism is affected differently by changes in the contact angle with the solid. Finally, for highly-wetting liquids, condensates are shown to critically modify the transition pathways in both the base contact and pillar contact modes.

Spatially variant morphological restoration and skeleton representation.

Science.gov (United States)

Bouaynaya, Nidhal; Charif-Chefchaouni, Mohammed; Schonfeld, Dan

2006-11-01

The theory of spatially variant (SV) mathematical morphology is used to extend and analyze two important image processing applications: morphological image restoration and skeleton representation of binary images. For morphological image restoration, we propose the SV alternating sequential filters and SV median filters. We establish the relation of SV median filters to the basic SV morphological operators (i.e., SV erosions and SV dilations). For skeleton representation, we present a general framework for the SV morphological skeleton representation of binary images. We study the properties of the SV morphological skeleton representation and derive conditions for its invertibility. We also develop an algorithm for the implementation of the SV morphological skeleton representation of binary images. The latter algorithm is based on the optimal construction of the SV structuring element mapping designed to minimize the cardinality of the SV morphological skeleton representation. Experimental results show the dramatic improvement in the performance of the SV morphological restoration and SV morphological skeleton representation algorithms in comparison to their translation-invariant counterparts.

SCAP-82, Single Scattering, Albedo Scattering, Point-Kernel Analysis in Complex Geometry

International Nuclear Information System (INIS)

Disney, R.K.; Vogtman, S.E.

1987-01-01

1 - Description of problem or function: SCAP solves for radiation transport in complex geometries using the single or albedo scatter point kernel method. The program is designed to calculate the neutron or gamma ray radiation level at detector points located within or outside a complex radiation scatter source geometry or a user specified discrete scattering volume. Geometry is describable by zones bounded by intersecting quadratic surfaces within an arbitrary maximum number of boundary surfaces per zone. Anisotropic point sources are describable as pointwise energy dependent distributions of polar angles on a meridian; isotropic point sources may also be specified. The attenuation function for gamma rays is an exponential function on the primary source leg and the scatter leg with a build- up factor approximation to account for multiple scatter on the scat- ter leg. The neutron attenuation function is an exponential function using neutron removal cross sections on the primary source leg and scatter leg. Line or volumetric sources can be represented as a distribution of isotropic point sources, with un-collided line-of-sight attenuation and buildup calculated between each source point and the detector point. 2 - Method of solution: A point kernel method using an anisotropic or isotropic point source representation is used, line-of-sight material attenuation and inverse square spatial attenuation between the source point and scatter points and the scatter points and detector point is employed. A direct summation of individual point source results is obtained. 3 - Restrictions on the complexity of the problem: - The SCAP program is written in complete flexible dimensioning so that no restrictions are imposed on the number of energy groups or geometric zones. The geometric zone description is restricted to zones defined by boundary surfaces defined by the general quadratic equation or one of its degenerate forms. The only restriction in the program is that the total

Surrogate Modeling for Geometry Optimization

DEFF Research Database (Denmark)

Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

2009-01-01

A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.