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Sample records for geometry calculo numerico

  1. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Preliminares

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-12-11

    This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs.

  2. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods; Calculo Numerico de Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Metodos Numericos

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-10-12

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.

  3. Estudio numerico y experimental del proceso de soldeo MIG sobre la aleacion 6063--T5 utilizando el metodo de Taguchi

    Science.gov (United States)

    Meseguer Valdenebro, Jose Luis

    improvement on mechanical properties in aluminum metal joint. Los procesos de soldadura por arco electrico representan unas de las tecnicas mas utilizadas en los procesos de fabricacion de componentes mecanicos en la industria moderna. Los procesos de soldeo por arco se han adaptado a las necesidades actuales, haciendose un modo de fabricacion flexible y versatil. Los resultados obtenidos numericamente en el proceso de soldadura son validados experimentalmente. Los principales metodos numericos mas empleados en la actualidad son tres, metodo por diferencias finitas, metodos por elementos finitos y metodo por volumenes finitos. El metodo numerico mas empleado para el modelado de uniones soldadas, es el metodo por elementos finitos, debido a que presenta una buena adaptacion a las condiciones geometricas y de contorno ademas de que existe una diversidad de programas comerciales que utilizan el metodo por elementos finitos como base de calculo. Este trabajo de investigacion presenta un estudio experimental de una union soldada mediante el proceso MIG de la aleacion de aluminio 6063-T5. El metodo numerico se valida experimentalmente aplicando el metodo de los elementos finitos con el programa de calculo ANSYS. Los resultados experimentales obtenidos son: las curvas de enfriamiento, el tiempo critico de enfriamiento t4/3, geometria del cordon, microdurezas obtenidas en la union soldada, zona afectada termicamente y metal base, dilucion del proceso, areas criticas intersecadas entre las curvas de enfriamiento y la curva TTP. Los resultados numericos son: las curvas del ciclo termico, que representan tanto el calentamiento hasta alcanzar la temperatura maxima y un posterior enfriamiento. Se calculan el tiempo critico de enfriamiento t4/3, el rendimiento termico y se representa la geometria del cordon obtenida experimentalmente. La zona afectada termicamente se obtiene diferenciando las zonas que se encuentran a diferentes temperaturas, las areas criticas intersecadas entre las

  4. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Convergence and Testing; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Convergencia y Comprobaciones

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-12-11

    This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs.

  5. O ambiente e a modelagem matematica no ensino do calculo numerico

    OpenAIRE

    Nilson Sergio Peres Stahl

    2003-01-01

    Resumo: Este trabalho de pesquisa trata da utilização da Modelagem Matemática Aplicada a fenômenos Ambientais como meio de transformação de atitudes docentes e discentes no processo aprendizagem/ensino da disciplina de Cálculo Numérico. A pesquisa se desenvolveu numa instituição privada em que os alunos do quarto ano do curso de licenciatura em Matemática, em 1999, participaram como atores do processo. Foram aplicados 7 projetos enfocando o meio...

  6. Measurement and calculation of dynamic coefficients in hydrodynamic bearings of gas films; Medicion y calculo de coeficientes dinamicos en cojinetes hidrodinamicos de peliculas de gas

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz, Rafael O.; Di Liscia, Marcelo H.; Diaz, Sergio E. [Universidad Simon Bolivar, Sartendejas, Baruta (Venezuela)

    2007-11-15

    dynamic coefficients. [Spanish] La identificacion de los coeficientes dinamicos en cojinetes de aire es fundamental para un adecuado analisis rotodinamico. El presente trabajo muestra el desarrollo de un algoritmo que permite la obtencion directa de los coeficientes dinamicos en cojinetes hidrodinamicos de aire tanto de forma numerica como experimental. El banco de pruebas utilizado consta de dos cojinetes magneticos, los cuales soportan al rotor en sus extremos y a su vez funcionan como actuadores permitiendo inducir orbitas controladas en el rotor. El cojinete de prueba se encuentra ubicado entre los cojinetes magneticos. Las fuerzas dinamicas generadas en el cojinete de aire se registran a partir de tres celdas de carga. El algoritmo fue desarrollado en un codigo comercial de programacion grafica, a traves del cual se pueden colectar, controlar y procesar las senales. El comportamiento no lineal de este tipo de cojinetes dificulta el calculo de los coeficientes dinamicos, por esta razon el procesamiento de las senales en espacio frecuencial facilita de cierta manera su manejo. Por otra parte, el modelo numerico se comparo con los resultados experimentales obteniendo aproximaciones aceptables tanto en magnitud como en comportamiento. El calculo de los coeficientes dinamicos numericos se realizo resolviendo la ecuacion diferencial de Reynolds para un fluido compresible en el espesor de la pelicula de gas, tomando en consideracion el flujo masico del fluido que se introduce, asi como la perdida de presion que sufre el mismo al pasar a traves de los orificios de alimentacion. Los metodos numericos utilizados incluyen la resolucion de la ecuacion diferencial de Reynolds por diferencias finitas, el calculo del perfil de presiones realizando iteraciones sucesivas y el calculo de las fuerzas hidrodinamicas a traves de una integracion numerica de Simpson. Los coeficientes dinamicos numericos fueron hallados aplicando una tecnica de minimos cuadrados a las fuerzas hidrodinamicas

  7. Measurement and calculation of dynamic coefficients in hydrodynamic bearings of gas films; Medicion y calculo de coeficientes dinamicos en cojinetes hidrodinamicos de peliculas de gas

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz, Rafael O.; Di Liscia, Marcelo H.; Diaz, Sergio E. [Universidad Simon Bolivar, Sartendejas, Baruta (Venezuela)

    2007-11-15

    dynamic coefficients. [Spanish] La identificacion de los coeficientes dinamicos en cojinetes de aire es fundamental para un adecuado analisis rotodinamico. El presente trabajo muestra el desarrollo de un algoritmo que permite la obtencion directa de los coeficientes dinamicos en cojinetes hidrodinamicos de aire tanto de forma numerica como experimental. El banco de pruebas utilizado consta de dos cojinetes magneticos, los cuales soportan al rotor en sus extremos y a su vez funcionan como actuadores permitiendo inducir orbitas controladas en el rotor. El cojinete de prueba se encuentra ubicado entre los cojinetes magneticos. Las fuerzas dinamicas generadas en el cojinete de aire se registran a partir de tres celdas de carga. El algoritmo fue desarrollado en un codigo comercial de programacion grafica, a traves del cual se pueden colectar, controlar y procesar las senales. El comportamiento no lineal de este tipo de cojinetes dificulta el calculo de los coeficientes dinamicos, por esta razon el procesamiento de las senales en espacio frecuencial facilita de cierta manera su manejo. Por otra parte, el modelo numerico se comparo con los resultados experimentales obteniendo aproximaciones aceptables tanto en magnitud como en comportamiento. El calculo de los coeficientes dinamicos numericos se realizo resolviendo la ecuacion diferencial de Reynolds para un fluido compresible en el espesor de la pelicula de gas, tomando en consideracion el flujo masico del fluido que se introduce, asi como la perdida de presion que sufre el mismo al pasar a traves de los orificios de alimentacion. Los metodos numericos utilizados incluyen la resolucion de la ecuacion diferencial de Reynolds por diferencias finitas, el calculo del perfil de presiones realizando iteraciones sucesivas y el calculo de las fuerzas hidrodinamicas a traves de una integracion numerica de Simpson. Los coeficientes dinamicos numericos fueron hallados aplicando una tecnica de minimos cuadrados a las fuerzas hidrodinamicas

  8. Calculation of the temperature distribution and thermal stresses in a gas turbine nozzle cooled by air film; Calculo de la distribucion de temperaturas y esfuerzos termicos en una tobera de turbina de gas enfriada por pelicula de aire

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez R, Alejandro; Garcia I, Rafael; Mazur C, Zdislaw [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)

    2004-07-01

    The analysis begins with the generation of a computational geometric model of the gas turbine nozzle using reverse engineering techniques. For the obtaining of the original geometry of the blade, a measurement machine by coordinates and computerized numerical control was used. Next, the computational model is converted into a three-dimensional mesh. In advance, a study of boundary conditions was made of the nozzle material as well as of the turbine operating conditions during non-operating cycles, start-ups and shut-downs. On the other hand, with the boundary conditions imposed to the model, the distributions of the temperature and pressures on the aerofoil profile of the nozzle blade were calculated. These results had to be manipulated to be exported to a finite element software (ANSYS); at this point, another nozzle model was elaborated to be able to import the temperature distribution. With the temperatures correctly imported, the simulations for the calculation of the thermal stresses were made in the nozzle. [Spanish] El analisis inicia con la generacion de un modelo geometrico computacional de la tobera de la turbina de gas utilizando tecnicas de ingenieria inversa. Para la obtencion de la geometria original del alabe, se utilizo una maquina de medicion por coordenadas y control numerico computarizado. A continuacion, el modelo computacional es convertido en una malla tridimensional. Con antelacion, se realizo un estudio de las condiciones de frontera, tanto del material de la tobera como de las condiciones de operacion de la turbina, durante ciclos de paro, arranque y disparo. Por otra parte, con las condiciones de frontera impuestas al modelo, se calcularon las distribuciones de las temperaturas y presiones sobre el perfil aerodinamico de la paleta de la tobera. Estos resultados tuvieron que ser manipulados para ser exportados a un software de elemento finito (ANSYS); en este punto, se elaboro otro modelo de la tobera para poder importar la distribucion de

  9. 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

  10. P{sub N} solutions for the slowing-down and the cell calculation problems in plane geometry; Solucoes P{sub N} para os problemas da moderacao e do calculo de celula em geometria plana

    Energy Technology Data Exchange (ETDEWEB)

    Caldeira, Alexandre David

    1999-07-01

    In this work P{sub N} solutions for the slowing-down and cell problems in slab geometry are developed. To highlight the main contributions of this development, one can mention: the new particular solution developed for the P{sub N} method applied to the slowing-down problem in the multigroup model, originating a new class of polynomials denominated Chandrasekhar generalized polynomials; the treatment of a specific situation, known as a degeneracy, arising from a particularity in the group constants and the first application of the P{sub N} method, for arbitrary N, in criticality calculations at the cell level reported in literature. (author)

  11. Dancoff factors with partial neutrons absorption in cluster geometry by the direct method; Calculo dos fatores de Dancoff com absorcao parcial de neutrons em geometria cluster pelo metodo direto

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, Leticia Jenisch

    2007-07-01

    Accurate analysis of resonance absorption in heterogeneous systems is essential in problems like criticality, breeding ratios and fuel depletion calculations. In compact arrays of fuel rods, resonance absorption is strongly affected by the Dancoff factor, defined in mis study as the probability that a neutron emitted from the surface of a fuel element, enters another fuel element without any collusion in the moderator or cladding. In fact, in the most practical cases of irregular cells, it is observed that inaccuracies in computing both Grey and Black Dancoff factors, i.e. for partially and perfectly absorbing fuel rods, can lead to considerable errors in the calculated values of such integral quantities. For this reason, much effort has been made in the past decades to further improve the models for calculating Dancoff factors, a task that has been accomplished in connection with the development of faster computers. In the WIMS code, Black Dancoff factors based on the above mentioned collusion probability definition are computed in cluster geometry, for each one of the symmetrically distinct fuel pin positions in the cell. Sets of equally-spaced parallel lines are drawn in subroutine PIJ, at a number of discrete equally-incremented azimuthal angles, covering the whole system and forming a mesh over which the in-plane integrations of the Bickley functions are carried out by simple trapezoidal rule, leading to the first-flight collusion matrices. Although fast, the method in PIJ is inefficient, since the constructed mesh does not depended on the system details, so that regions of small relative volumes are crossed out by relatively few lines, which affects the convergence of the calculated probabilities. A new routine (PIJM) was then created to incorporate a more efficient integration scheme considering each system region individually, minimizing convergence problems and reducing the number of neutron track lines required in the in-plane integrations for any given

  12. HADES. A computer code for fast neutron cross section from the Optical Model; HADES. Un programa numerico para el calculo de seccciones eficaces neutronicas mediante el modelo optico

    Energy Technology Data Exchange (ETDEWEB)

    Guasp, J.; Navarro, C.

    1973-07-01

    A FORTRAN V computer code for UNIVAC 1108/6 using a local Optical Model with spin-orbit interaction is described. The code calculates fast neutron cross sections, angular distribution, and Legendre moments for heavy and intermediate spherical nuclei. It allows for the possibility of automatic variation of potential parameters for experimental data fitting. (Author) 55 refs.

  13. Torque calculation in the induction motor with the finite element method; Calculo del par en el motor de induccion con el metodo del elemento finito

    Energy Technology Data Exchange (ETDEWEB)

    Castillo Diaz, Ramon

    2002-06-15

    In this work the method of the finite element is applied to the bi-dimensional analysis of the induction motor in operation in steady state, excited by sine sources of laminar currents and sine sources of voltage. The analysis is focused mainly in the calculation of the electromagnetic torque. The topics of electromagnetic theory are covered and in an idealized model of the induction motor, analytically and numerically with the method of the finite element, in the variant method of Galerkin, the vectorial potential and the torque are calculated. The results obtained with the analytical and numerical methods are compared. Three formulations are developed to calculate the torque with the method of the finite element, using triangular elements of first order, based in the equation of force of Lorentz, the Maxwell tensor and the principle of the virtual work. Finally, a motor of induction of real characteristics is simulated, assuming it is connected to a three-phase voltage source. In this motor it is analyzed the convergence and the evolution in the results obtained of the torque with different discretions, and the torque-velocity performance curve is calculated. [Spanish] En este trabajo se aplica el metodo del elemento finito al analisis bidimensional del motor de induccion en operacion en estado estable, excitado por fuentes de corriente laminar senoidales y fuentes de voltaje senoidales. El analisis se enfoca principalmente en el calculo del par electromagnetico. Se tratan los topicos de teoria electromagnetica involucrados y en un modelo idealizado del motor de induccion, se calculan analitica y numericamente con el metodo del elemento finito, en la variante metodo de Galerkin, el potencial vectorial y el par. Se comparan resultados obtenidos con los metodos analiticos y numericos. Se desarrollan tres formulaciones para calcular el par con el metodo del elemento finito, utilizando elementos triangulares de primer orden, basadas en la ecuacion de fuerza de

  14. Calculations of reactivity based in the solution of the Neutron transport equation in X Y geometry and Lineal perturbation theory; Calculos de reactividad basados en la solucion de la Ecuacion de transporte de neutrones en geometria XY y Teoria de perturbacion lineal

    Energy Technology Data Exchange (ETDEWEB)

    Valle G, E. del; Mugica R, C.A. [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx

    2005-07-01

    In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)

  15. Geometry from Information Geometry

    CERN Document Server

    Caticha, Ariel

    2015-01-01

    We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.

  16. Aquelarre. A computer code for fast neutron cross sections from the statistical model; AQUELARRE. Un programa numerico para el calculo de secciones eficaces neutronicas mediante el modelo de nucleo compuesto

    Energy Technology Data Exchange (ETDEWEB)

    Guasp, J.

    1974-07-01

    A Fortran V computer code for Univac 1108/6 using the partial statistical (or compound nucleus) model is described. The code calculates fast neutron cross sections for the (n, n'), (n, p), (n, d) and (n, {alpha}) reactions and the angular distributions and Legendre moments for the (n, n) and (n, n') processes in heavy and intermediate spherical nuclei. A local Optical Model with spin-orbit interaction for each level is employed, allowing for the width fluctuation and Moldauer corrections, as well as the inclusion of discrete and continuous levels. (Author) 67 refs.

  17. T.I.G. Welding of stainless steel. Numerical modelling for temperatures calculation in the Haz; Soldadura T.I.G. de acero inoxidable. Modelo numerico para el calculo de temperaturas en la ZAT

    Energy Technology Data Exchange (ETDEWEB)

    Martinez-Conesa, E. J.; Estrems-Amestoy, M.; Miguel-Eguia, V.; Garrido-Hernandez, A.; Guillen-Martinez, J. A.

    2010-07-01

    In this work, a numerical method for calculating the temperature field into the heat affected zone for butt welded joints is presented. The method has been developed for sheet welding and takes into account a bidimensional heat flow. It has built a computer program by MS-Excel books and Visual Basic for Applications (VBA). The model has been applied to the TIG process of AISI 304 stainless steel 2mm thickness sheet. The welding process has been considered without input materials. The numerical method may be used to help the designers to predict the temperature distribution in welded joints. (Author) 12 refs.

  18. Contatto tra i componenti di una protesi di ginocchio: studio numerico e sperimentale

    Directory of Open Access Journals (Sweden)

    D. Tumino

    2012-10-01

    Full Text Available The aim of this work is the analysis of the contact area in a knee prosthesis using two different approaches. In particular, the interface between the femoral component and the polyethylene insert has been studied both numerically and experimentally. The interest in studying the contact area is related to the fact that the wear of the polyethylene insert, due to the high contact pressures, represents one of the major causes of failure of the total knee prosthesis. The possibility to evaluate the contact area at different loads and mutual position between femur and tibia is, therefore, of fundamental importance to study the service life of a prosthesis and to improve its performance. The finite element numerical approach has required the acquisition, through reverse engineering, and CAD modelling of the prosthetic components. Then the FEM simulations have been developed considering two different load conditions. In order to compare the calculated data, the same load configurations have been used for experimental tests based on ultrasonic method. In this case, some preliminary tests were required to calibrate the system depending on the particular characteristics of materials, geometries and surface finish of the prosthesis.The results show a good correlation between the data obtained with the two different approaches and, consequently, a good level of reliability of the procedures developed for the numerical and experimental evaluation of the contact area. The numerical procedure can be used to determine the area for different angles and loads, but especially in the design phase. The ultrasonic technique can be used to validate the numerical data.

  19. Experimental numerical study utilizing CFD in a stratified gasifier operating with biomass; Estudio numerico experimental de un gasificador estratificado que opera con biomasa, utilizando CFD

    Energy Technology Data Exchange (ETDEWEB)

    Rogel Ramirez, Alejandro

    2007-07-01

    The central idea behind this work is the developing of a numeric-experimental model, useful to optimize the biomass stratified gasifier design. Firstly, model validation will be carried up by comparison with reference experimental data available. This study describes a 1-D + 2-D numerical model used to simulate the gasification of pine wood pellets in a stratified downdraft gasifier whereby Eulerian conservation equations are solved for particle and gas phase components, velocities and specific enthalpies. The model takes into account the biomass particle process such as heating up, drying, primary pyrolysis of biomass, secondary pyrolysis of tar, homogeneous reactions and heterogeneous combustion/gasification reactions, and particle size change. This CFD model can be used to predict temperature profiles, gas composition, producer gas lower heating value, and carbon conversion efficiency, and the reactor performance when operating parameters and feed properties are changed. The standard {kappa}-{epsilon} and RNG {kappa}-{epsilon} models were used to simulate the turbulent flow conditions. [Spanish] La idea central del presente trabajo es el desarrollo de un modelo numerico- experimental, para optimizar el diseno de gasificadores estratificados de biomasa. Primeramente, el modelo sera validado utilizando datos experimentales disponibles en la literatura. Este estudio describe un modelo numerico 1-D+2-D, utilizado para simular la gasificacion de 'pelets' de madera de pino en un gasificador estratificado de flujos paralelos, en el que se resuelven ecuaciones de conservacion Eulerianas para los componentes de la fase gaseosa, la fase solida, velocidades y entalpias especificas. El modelo considera procesos como: calentamiento, secado de la biomasa, pirolisis primaria de la madera, pirolisis secundaria de los alquitranes, reacciones homogeneas, reacciones heterogeneas de combustion/gasificacion y cambio en el tamano de la particula. Este modelo CFD puede ser

  20. Calculo de la Barra Antivuelco de un Vehículo Automotor.

    Directory of Open Access Journals (Sweden)

    Javier García de la Figal

    2005-09-01

    Full Text Available El presente trabajo trata acerca del calculo de la barra antivuelco del FORD modelo A, desarrollado por elInstituto de Desarrollo Automotriz, IDA, teniendo en cuenta las fuerzas que la cinta de seguridad de losautomovilistas, ejerce sobre la citada barra, ante un choque que provoca una aceleración de 20 g en elvehículo. El calculo se hace mediante la confección de un modelo de elementos finitos de la barra y lacarrocería, para lo cual se hace uso de un programa profesional de elementos finitos.Se determinan los esfuerzos máximos y los equivalentes, tanto de las partes metálicas del sistema, queson fundamentalmente tubos de acero, como de las partes de material compuesto (poliéster con fibras devidrio E, propios de la carrocería del vehículo. Todo lo cual permite hacer los cálculos y comprobacionesa resistencia de todo el conjunto. Así mismo, se determinan los desplazamientos en todos los sentidos detodos las partes del sistema, para poder realizar los correspondientes análisis de rigidez.El objetivo final de todos los análisis es determinar lo adecuado o no de las soluciones y materialespropuestos para el sistema, bajo la acción de la citada carga de impacto.

  1. 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.

  2. Numerical-experimental analysis of a rin AISI{sub 7}Mg Alloy; Analisis numerico experimental de un rin de aleacion AISi{sub 7}Mg

    Energy Technology Data Exchange (ETDEWEB)

    Sauceda Mesa, Israel; Mata Lucero, Omar; Tirado Delgado, Luis; Ocampo Diaz, Juan de Dios [Universidad Autonoma de Baja California, Mexicali, Baja California (Mexico)

    2005-10-15

    The present work shows the results obtained from an investigation mode on the behaviour of a rin of alloy AISi{sub 7}Mg, which is used in compact Volkswagen's cars. Due to two kind of analysis were realized, firstly an experimental and numerical analysis was done, using a special machine for test the flexionante torque and material fatigue, besides was used an equipment of laser to scanner zone with strength concentrations and the maximum displacement amplitudes. The second analysis was done with the finite element technique, using the software ANSYS and CATIA. The difference between life fatigue cycles obtained from the two analyses was 0.6%. While the time optimize by MEF, was of 85% less than experimental analysis. [Spanish] En el presente trabajo se hicieron investigaciones del comportamiento de un rin de aleacion AISi{sub 7}Mg, el cual es usado en automoviles compactos de volkswagen (VW). Para esto, se realizo analisis experimental y numerico. En el primero se utilizo una maquina para prueba de fatiga de momento flexionante, un equipo de medicion de laser escaner donde se detectaron las zonas de concentraciones de esfuerzos y la maxima amplitud de desplazamiento en el rin. Mientras que en el segundo se obtuvieron los esfuerzos que ocasionaban la fatiga por el elemento finito, utilizando los paquetes de computo Ansys y Catia. La diferencia de los ciclos de vida de fatiga obtenidos entre ambos analisis fue del 0.6%. Mientras que el tiempo que se optimizo por el MEF, fue de un 85% menos que el analisis experimental.

  3. Numerical analysis of flow in a solar heater of air packing with shavings; Analisis numerico del flujo en un calentador solar de aire empacado con viruta

    Energy Technology Data Exchange (ETDEWEB)

    Lopez C, Raymundo; Morales G, Juan R; Diaz C, Alen; Lara V, Araceli; Lizardi R, Arturo [Universidad Autonoma Metropolitana-Azcapotzalco, Mexico, D.F. (Mexico); Vaca M, Mabel [UNAM, Mexico, D.F. (Mexico)

    2000-07-01

    The temperature distribution of air through a solar heater is determined by means of the equations of heat, mass, momentum, and energy conservation. The solution is obtained by means of the numeric model of finite volume, using the CFC2000 software, V. 3.3. The studied flow is laminar. The temperature distribution resulted quite similar for different Reynolds numbers; the greatest difference was less than 4 Celsius degrees, for similar ranges of solar radiation. The influence of the separation that exists between the clear cover and the free surface of the material used as thermal summit (b) was analyzed. A difference up to 41 Celsius degrees for a Reynolds number of 1000 and values of b between 3 and 7 cm. For a Reynolds of 2000, the difference was of 29 Celsius degrees, in the same range of b. [Spanish] Se determinan la distribucion de temperaturas del aire, a lo largo de un calentador solar, aplicando las ecuaciones de conservacion de masa, cantidad de movimiento y energia. La solucion se obtiene con el modelo numerico de volumen finito y la utilizacion del programa de computadora llamado CFC2000 version 3.3. El flujo estudiado es del tipo laminar. La distribucion de temperaturas resulto ser muy semejante para diferentes valores del numero de Reynolds, la diferencia mayor resulto menor a 4 grados Celsius, para rangos similares de radiacion solar. Se analizo la influencia de la separacion que existe entre la cubierta transparente y la superficie libre del material que sirve como almacen termico (b). Se encontro una diferencia maxima de hasta 41 grados celsius para un numero de Reynolds de 1000 y los valores de b entre 3 y 7 cm. Cuando el Reynolds fue de 2000 la diferencia fue de 29 grados Celsius, en el mismo rango de b.

  4. Differential geometry

    CERN Document Server

    Guggenheimer, Heinrich W

    1977-01-01

    This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a

  5. 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

  6. Algorithm for the calculation of a steam generator efficiency; Algoritmo para el calculo de la eficiencia de un generador de vapor

    Energy Technology Data Exchange (ETDEWEB)

    Franco, David; Ambriz, Juan Jose; Romero Paredes, Hernando [Universidad Autonoma Metropolitana-Iztapalapa, Mexico, D. F. (Mexico)

    1994-12-31

    The efficiency calculation of steam generators is not always simple. The purpose of this paper is to propose an algorithm for the calculation of steam generators efficiency, easy to understand and carry out, in the form of a series of steps to be followed. It takes as starting point that the person in charge of applying these calculations has knowledge of the combustion processes and thermodynamic principles that rule such processes. [Espanol] El calculo de la eficiencia de los generadores de vapor no siempre es sencillo, el presente trabajo tiene como objetivo el de proponer un algoritmo de calculo de eficiencia de generadores de vapor, el cual sea facil de entender y de llevar a cabo, en forma de una serie de pasos a seguir. Se toma como punto de partida, que la persona encargada de aplicar estos calculos tenga el conocimiento de los procesos de combustion y principios termodinamicos que rigen tales procesos.

  7. Dosimetry in intravascular brachytherapy; Calculos dosimetricos em braquiterapia intravascular

    Energy Technology Data Exchange (ETDEWEB)

    Campos, Laelia Pumilla Botelho

    2000-03-01

    Among the cardiovascular diseases responsible for deaths in the adult population in almost all countries of the world, the most common is acute myocardial infarction, which generally occurs because of the occlusion of one or more coronary arteries. Several diagnostic techniques and therapies are being tested for the treatment of coronary artery disease. Balloon angioplasty has been a popular treatment which is less invasive than traditional surgeries involving revascularization of the myocardium, thus promising a better quality of life for patients. Unfortunately, the rate of restenosis (re-closing of the vessel) after balloon angioplasty is high (approximately 30-50% within the first year after treatment).Recently, the idea of delivering high radiation doses to coronary arteries to avoid or delay restenosis has been suggested. Known as intravascular brachytherapy, the technique has been used with several radiation sources, and researchers have obtained success in decreasing the rate of restenosis in some patient populations. In order to study the radiation dosimetry in the patient and radiological protection for the attending staff for this therapy, radiation dose distributions for monoenergetic electrons and photons (at nine discrete energies) were calculated for blood vessels of diameter 0.15, o,30 and 0.45 cm with balloon and wire sources using the radiation transport code MCNP4B. Specific calculations were carried out for several candidate radionuclides as well. Two s tent sources (metallic prosthesis that put inside of patient's artery through angioplasty) employing {sup 32} P are also simulated. Advantages and disadvantages of the various radionuclides and source geometries are discussed. The dosimetry developed here will aid in the realization of the benefits obtained in patients for this promising new technology. (author)

  8. PCRELAP5: data calculation program for RELAP 5 code; PCRELAP5: programa de calculo dos dados de entrada para o codigo RELAP5

    Energy Technology Data Exchange (ETDEWEB)

    Silvestre, Larissa Jacome Barros

    2016-07-01

    Nuclear accidents in the world led to the establishment of rigorous criteria and requirements for nuclear power plant operations by the international regulatory bodies. By using specific computer programs, simulations of various accidents and transients likely to occur at any nuclear power plant are required for certifying and licensing a nuclear power plant. Based on this scenario, some sophisticated computational tools have been used such as the Reactor Excursion and Leak Analysis Program (RELAP5), which is the most widely used code for the thermo-hydraulic analysis of accidents and transients in nuclear reactors in Brazil and worldwide. A major difficulty in the simulation by using RELAP5 code is the amount of information required for the simulation of thermal-hydraulic accidents or transients. The preparation of the input data requires a great number of mathematical operations to calculate the geometry of the components. Thus, for those calculations performance and preparation of RELAP5 input data, a friendly mathematical preprocessor was designed. The Visual Basic for Application (VBA) for Microsoft Excel demonstrated to be an effective tool to perform a number of tasks in the development of the program. In order to meet the needs of RELAP5 users, the RELAP5 Calculation Program (Programa de Calculo do RELAP5 - PCRELAP5) was designed. The components of the code were codified; all entry cards including the optional cards of each one have been programmed. In addition, an English version for PCRELAP5 was provided. Furthermore, a friendly design was developed in order to minimize the time of preparation of input data and errors committed by users. In this work, the final version of this preprocessor was successfully applied for Safety Injection System (SIS) of Angra 2. (author)

  9. 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.

  10. 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

  11. Differential geometry

    CERN Document Server

    Graustein, William C

    2006-01-01

    This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of

  12. 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.

  13. 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...

  14. Subtracted geometry

    Science.gov (United States)

    Saleem, Zain Hamid

    In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.

  15. 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,

  16. 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

  17. 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

  18. Architectural geometry

    NARCIS (Netherlands)

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes

    2015-01-01

    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

  19. Architectural geometry

    NARCIS (Netherlands)

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes

    2015-01-01

    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

  20. 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...

  1. Differential geometry

    CERN Document Server

    Kreyszig, Erwin

    1991-01-01

    An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.

  2. 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...

  3. Differential geometry

    CERN Document Server

    Ciarlet, Philippe G

    2007-01-01

    This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

  4. Calculation of electromagnetic fields in electric machines by means of the finite element. Computational aspects; Calculo de campos electromagneticos en maquinas electricas mediante elemento finito. Aspectos computacionales

    Energy Technology Data Exchange (ETDEWEB)

    Rosales, Mario; De la Torre, Octavio [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)

    1989-12-31

    In this article are described the computational characteristics of the Package CALIIE 2D of the Instituto de Investigaciones Electricas (IIE), for the calculation of bi-dimensional electromagnetic fields. The computational implementation of the package is based in the electromagnetic and numerical statements formerly published in this series. [Espanol] En este articulo se describen las caracteristicas computacionales del paquete CALIIE 2D del Instituto de Investigaciones Electricas (IIE), para calcular campos electromagneticos bidimensionales. La implantacion computacional del paquete se basa en los planteamientos electromagneticos y numericos antes publicados en esta serie.

  5. Development of applications in Internet for the calculation of solar control devices; Desarrollo de una aplicacion en Internet para el calculo de dispositivos de control solar

    Energy Technology Data Exchange (ETDEWEB)

    Perez V, Jesus B; Robles G, Saul; Villa M, Hector A; Cabanillas L, Rafael E [Universidad de Sonora, Hermosillo, Sonora (Mexico)

    2000-07-01

    In this work the development of an interactive software, visible over the World Wide Web, is presented to support the basic calculation required to control the solar gain inside buildings and houses. The site has two main parts: one part describes in a very required parameters to design devices for the control of the illumination inside the buildings, like overhangs and wingwalls for shading. The other part has the routines and procedures to calculate the sun position for any date and position over the earth, and the horizontal and vertical protection angles. The part to implement the calculations has been developed as a Java applet which can run on any platform and let the users, in an interactive way, to get the results. This software makes possible that any Internet user can run the application from his/her own computer without having to compile of use sophisticated procedures as it happens with traditional languages. With this web site it is intended to cover the necessity of having simple and reliable means for architects and civil engineers to support the use of solar energy and the saving of energy in bioclimatic design of buildings. [Spanish] En este trabajo se presenta el desarrollo de un sitio interactivo visible en el World Wide Web (WWW) que pretende servir de apoyo para los calculos basicos de control de asoleamiento en viviendas y edificios. El sitio esta conformado por dos partes principales: una parte cubre el aspecto informativo, donde en forma sencilla y clara, se explican los conceptos y parametros necesarios para disenar los dispositivos de control, alerones y parteluces. La otra parte contiene los procedimientos y las rutinas de calculo para la determinacion de la posicion solar para cualquier fecha del ano desde cualquier punto sobre la tierra, asi como los angulos de sombreado vertical y horizontal. Para la realizacion de los calculos se ha construido un applet de Java, el cual puede ejecutarse desde cualquier plataforma de computacion y

  6. Data acquisition system and calculation for the evaluation of polluting emissions in stacks; Sistema de adquisicion de datos y calculo para la evaluacion de emisiones contaminantes en chimeneas

    Energy Technology Data Exchange (ETDEWEB)

    Leon Enriquez, Javier

    1999-06-01

    The present thesis work, was developed in Visual C++5, to replace the present procedure of calculation in Excel and to avoid the manual processing of the data obtained during the evaluation of polluting from stacks, with movable laboratories that make dilutions in the originating gaseous sample of the stack. Six projects in Visual C++5 were designed. The first five include the formulas and procedures of calculation to obtain the total particulate emission suspended originating of stationary sources (stacks), indicated in the Code of Federal Regulations (CFR) part 60, emitted by the Environmental Protection Agency of the United Sates (EPA). The last one, includes the calculations necessary to read archives generated by a card of data acquisition and to consider the factor of dilution of the gaseous sample. A standard business card for the data acquisition is used during the monitoring process of the variables that requires the sixth mentioned project previously. The results of the monitoring of variables and result of the calculations are stored in archives that conform a data base of the made work, which allows future, to compare the results of the measurements and calculations in different evaluations from a same user. The made work can be used by evaluators companies of polluting emissions in stacks that count on dilution equipment during the evaluation. [Spanish] El presente trabajo de tesis, fue desarrollado en visual C++5, para sustituir el procedimiento actual de calculo en Excel y evitar el procesamiento manual de los datos obtenidos durante la evaluacion de emisiones contaminantes en chimeneas, con laboratorios moviles que realizan diluciones en la muestra gaseosa proveniente de la chimenea. Se disenaron 6 proyectos en visual C++5. Los primeros cinco incluyen las formulas y procedimientos de calculo para obtener la emision de particulas suspendidas totales provenientes de fuentes fijas (chimeneas), indicadores en el Codigo de Regulaciones Federales (CFR

  7. Global Differential Geometry

    CERN Document Server

    Bär, Christian; Schwarz, Matthias

    2012-01-01

    This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.

  8. Geometry in Medias Res

    Science.gov (United States)

    Cukier, Mimi; Asdourian, Tony; Thakker, Anand

    2012-01-01

    Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

  9. Real Algebraic Geometry

    CERN Document Server

    Mahé, Louis; Roy, Marie-Françoise

    1992-01-01

    Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...

  10. Digital Differential Geometry Processing

    Institute of Scientific and Technical Information of China (English)

    Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng

    2006-01-01

    The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

  11. Numerical study of a parallel plates ice storage unity; Estudo numerico de uma unidade de armazenamento de gelo de placas paralelas

    Energy Technology Data Exchange (ETDEWEB)

    Saraiva, Luis Edson [Passo Fundo Univ., RS (Brazil). Fac. de Engenharia e Arquitetura; Ismail, Kamal Abdel El-Radi [Universidade Estadual de Campinas, SP (Brazil). Faculdade de Engenharia Mecanica

    1998-07-01

    The objective of this paper is to present a numerical model to predict the thermal performance of parallel plate PCM storage units. The physical model is composed of a tank of rectangular geometry with cold plates through which the coolant passes and warm plates for water circulation. The PCM used is water. During the charging process (late night time) coolant circulation provides ice. This ice is to be used during the discharging cycle when water circulations in the warm plates provides cold water 7 deg C for air conditioning applications. The numerical model is based upon one-dimensional formulation of the phase-change heat transfer problem associated with an energy balance equation between the circulating coolant and the PCM. These coupled equations, written in enthalpic form, are solved using control-volume formulation to furnish the solidified mass, temperature distribution along the plates, heat transfer and effectiveness of the system. (author)

  12. 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...

  13. Riemann-Finsler geometry

    Institute of Scientific and Technical Information of China (English)

    GUO Enli; MO Xiaohuan

    2006-01-01

    In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.

  14. Characteristic parameters of drift chambers calculation; Calculo de los parametros caracteristicos de camaras de deriva

    Energy Technology Data Exchange (ETDEWEB)

    Duran, I.; Martinez-Laso, L.

    1989-07-01

    We present here the methods we used to analyse the characteristic parameters of drift chambers. The algorithms to calculate the electric potential in any point for any drift chamber geometry are presented. We include the description of the programs used to calculate the electric field, the drift paths, the drift velocity and the drift time. The results and the errors are discussed. (Author) 7 refs.

  15. 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

  16. Introduction to projective geometry

    CERN Document Server

    Wylie, C R

    2008-01-01

    This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w

  17. Affine and Projective Geometry

    CERN Document Server

    Bennett, M K

    1995-01-01

    An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory

  18. Symplectic geometries on supermanifolds

    CERN Document Server

    Lavrov, P M

    2007-01-01

    Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.

  19. Generalized Kahler geometry

    CERN Document Server

    Gualtieri, Marco

    2010-01-01

    Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.

  20. Methods for euclidean geometry

    CERN Document Server

    Byer, Owen; Smeltzer, Deirdre L

    2010-01-01

    Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.

  1. 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.

  2. 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

  3. Fundamental concepts of geometry

    CERN Document Server

    Meserve, Bruce E

    1983-01-01

    Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

  4. 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

  5. Euclidean geometry and transformations

    CERN Document Server

    Dodge, Clayton W

    1972-01-01

    This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

  6. Introduction to finite geometries

    CERN Document Server

    Kárteszi, F

    1976-01-01

    North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geo

  7. Euclidean Geometry via Programming.

    Science.gov (United States)

    Filimonov, Rossen; Kreith, Kurt

    1992-01-01

    Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…

  8. Supersymmetric Sigma Model Geometry

    OpenAIRE

    Ulf Lindström

    2012-01-01

    This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.

  9. 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.

  10. Supersymmetric Sigma Model geometry

    CERN Document Server

    Lindström, Ulf

    2012-01-01

    This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.

  11. 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.

  12. Foundations of algebraic geometry

    CERN Document Server

    Weil, A

    1946-01-01

    This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.

  13. Dual doubled geometry

    NARCIS (Netherlands)

    Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.

    2011-01-01

    We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam

  14. 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.

  15. Riemann-Finsler Geometry with Applications to Information Geometry

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.

  16. Statistical discrete geometry

    CERN Document Server

    Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana

    2016-01-01

    Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.

  17. Non-Euclidean geometry

    CERN Document Server

    Bonola, Roberto

    2010-01-01

    This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such

  18. ALICE Geometry Database

    CERN Document Server

    Santo, J

    1999-01-01

    The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.

  19. 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 a

  20. 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

  1. Elementary differential geometry

    CERN Document Server

    Pressley, Andrew

    2001-01-01

    Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...

  2. What Is Geometry?

    Science.gov (United States)

    Chern, Shiing-Shen

    1990-01-01

    Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)

  3. An expedition to geometry

    CERN Document Server

    Kumaresan, S

    2005-01-01

    Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.

  4. 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...

  5. Gingerbread-House Geometry.

    Science.gov (United States)

    Emenaker, Charles E.

    1999-01-01

    Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

  6. Geometry of differential equations

    CERN Document Server

    Khovanskiĭ, A; Vassiliev, V

    1998-01-01

    This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.

  7. Facilitating Understandings of Geometry.

    Science.gov (United States)

    Pappas, Christine C.; Bush, Sara

    1989-01-01

    Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

  8. 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...

  9. Invitation to geometry

    CERN Document Server

    Melzak, Z A

    2008-01-01

    Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.

  10. 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.

  11. Derived logarithmic geometry I

    OpenAIRE

    Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi

    2016-01-01

    In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.

  12. The geometry of geodesics

    CERN Document Server

    Busemann, Herbert

    2005-01-01

    A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

  13. 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...

  14. Observer dependent geometries

    CERN Document Server

    Hohmann, Manuel

    2014-01-01

    From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.

  15. 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....

  16. 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

  17. Higher prequantum geometry

    CERN Document Server

    Schreiber, Urs

    2016-01-01

    This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.

  18. Brans-Dicke geometry

    CERN Document Server

    Punzi, Raffaele; Wohlfarth, Mattias N R

    2008-01-01

    We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.

  19. Brans-Dicke geometry

    Energy Technology Data Exchange (ETDEWEB)

    Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de

    2008-12-11

    We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.

  20. SOC and Fractal Geometry

    Science.gov (United States)

    McAteer, R. T. J.

    2013-06-01

    When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.

  1. Optimum geometry for boiler soot blowers nozzles; Geometria optima de toberas para deshollinadores de caldera

    Energy Technology Data Exchange (ETDEWEB)

    Espinoza Garza, Jesus; Garcia Tinoco, Guillermo J.; Martinez Flores, Jose Oscar [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)

    1989-12-31

    For boiler soot blowing converging-diverging nozzles are employed, whose function is to convert thermal energy of a gas into kinetic energy to remove the deposits that adhere to the heat exchanger surfaces. In this paper are described the experimental equipment and the methods for flow, dynamic pressure, discharge velocity and air expansion factor calculation in each nozzle, as a function of its design geometry, utilizing air from a five stage centrifugal compressor. The graphic analysis of the results, concludes that the most efficient nozzles are not the ones than develop the greatest velocity, but the ones of highest dynamic pressure at the outlet. The nozzle geometry that allows obtaining the maximum dynamic air pressure at the discharge is A{sub 2}/A{sub g}=1.3676 [Espanol] Para el deshollinado de calderas se utilizan las toberas convergentes-divergentes, cuya funcion es convertir la energia termica de un gas en energia cinetica para remover los depositos que se adhieren a las superficies de intercambio de calor. En este trabajo se describen el equipo experimental y los metodos de calculo para flujo, presion dinamica, velocidad a la descarga y factor de expansion del aire en cada tobera, como funcion de su geometria de diseno. Durante la experimentacion se evaluaron siete disenos diferentes de toberas, empleando aire de un compresor centrifugo de cinco etapas. Del analisis grafico de los resultados, se concluye que las toberas mas eficientes no son las que desarrollan mayor velocidad sino las de mayor presion dinamica de la salida. La geometria de tobera que permite obtener la maxima presion dinamica del aire a la descarga es A{sub 2}/A{sub g} = 1.3676.

  2. 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...

  3. Students Discovering Spherical Geometry Using Dynamic Geometry Software

    Science.gov (United States)

    Guven, Bulent; Karatas, Ilhan

    2009-01-01

    Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

  4. Students Discovering Spherical Geometry Using Dynamic Geometry Software

    Science.gov (United States)

    Guven, Bulent; Karatas, Ilhan

    2009-01-01

    Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

  5. Emergent Complex Network Geometry

    CERN Document Server

    Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra

    2014-01-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...

  6. 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...

  7. Supersymmetry and noncommutative geometry

    CERN Document Server

    Beenakker, Wim; Suijlekom, Walter D van

    2016-01-01

    In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...

  8. Universality of geometry

    CERN Document Server

    Wetterich, C

    2012-01-01

    In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.

  9. Geometry of hypersurfaces

    CERN Document Server

    Cecil, Thomas E

    2015-01-01

    This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...

  10. 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...

  11. Integral Geometry and Holography

    CERN Document Server

    Czech, Bartlomiej; McCandlish, Samuel; Sully, James

    2015-01-01

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...

  12. 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...

  13. 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.

  14. The Geometry of Conventionality

    CERN Document Server

    Weatherall, James Owen

    2013-01-01

    Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.

  15. A programmer's geometry

    CERN Document Server

    Bowyer, Adrian

    1983-01-01

    A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.

  16. 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

  17. Non-Riemannian geometry

    CERN Document Server

    Eisenhart, L P

    1927-01-01

    The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o

  18. Universal correlators from geometry

    Energy Technology Data Exchange (ETDEWEB)

    Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl

    2004-11-01

    Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)

  19. Universal Correlators from Geometry

    Science.gov (United States)

    Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine

    2004-11-01

    Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.

  20. Universal Correlators from Geometry

    CERN Document Server

    Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine

    2004-01-01

    Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.

  1. Geometry and physics

    Science.gov (United States)

    Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

    2010-01-01

    We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

  2. Sliding vane geometry turbines

    Science.gov (United States)

    Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R

    2014-12-30

    Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.

  3. Diophantine geometry an introduction

    CERN Document Server

    Hindry, Marc

    2000-01-01

    This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

  4. Towards relativistic quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

    2015-12-17

    We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

  5. Advanced geometries and regimes

    Energy Technology Data Exchange (ETDEWEB)

    Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)

    2013-07-26

    We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.

  6. Emergent Hyperbolic Network Geometry

    Science.gov (United States)

    Bianconi, Ginestra; Rahmede, Christoph

    2017-02-01

    A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.

  7. Spacetime and Euclidean Geometry

    CERN Document Server

    Brill, D R; Brill, Dieter; Jacobson, Ted

    2004-01-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".

  8. Spacetime and Euclidean geometry

    Science.gov (United States)

    Brill, Dieter; Jacobson, Ted

    2006-04-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

  9. Towards a Nano Geometry?

    DEFF Research Database (Denmark)

    Booss-Bavnbek, Bernhelm

    2011-01-01

    This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...

  10. Origami, Geometry and Art

    Science.gov (United States)

    Wares, Arsalan; Elstak, Iwan

    2017-01-01

    The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

  11. 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 ...

  12. History of analytic geometry

    CERN Document Server

    Boyer, Carl B

    2012-01-01

    Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.

  13. Origami, Geometry and Art

    Science.gov (United States)

    Wares, Arsalan; Elstak, Iwan

    2017-01-01

    The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

  14. An introduction to Minkowski geometries

    Science.gov (United States)

    Farnsworth, David L.

    2016-07-01

    The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.

  15. Cylindrical geometry hall thruster

    Science.gov (United States)

    Raitses, Yevgeny; Fisch, Nathaniel J.

    2002-01-01

    An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.

  16. Renyi Entropy and Geometry

    CERN Document Server

    Lee, Jeongseog; Safdi, Benjamin R

    2014-01-01

    Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...

  17. Spectral Geometry and Causality

    CERN Document Server

    Kopf, T

    1996-01-01

    For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of...

  18. 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.

  19. Algebra, Arithmetic, and Geometry

    CERN Document Server

    Tschinkel, Yuri

    2009-01-01

    The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont

  20. Geometry of Quantum States

    Science.gov (United States)

    Bengtsson, Ingemar; Zyczkowski, Karol

    2007-12-01

    Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.

  1. Differential geometry and thermodynamics

    CERN Document Server

    Quevedo, H

    2003-01-01

    In this work we present the first steps of a new approach to the study of thermodynamics in the context of differential geometry. We introduce a fundamental differential 1-form and a metric on a pseudo-Euclidean manifold coordinatized by means of the extensive thermodynamic variables. The study of the connection and the curvature of these objects is initialized in this work by using Cartan structure equations. (Author)

  2. Geometry and Destiny

    CERN Document Server

    Krauss, L M; Krauss, Lawrence M.; Turner, Michael S.

    1999-01-01

    The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.

  3. Inflation from quantum geometry.

    Science.gov (United States)

    Bojowald, Martin

    2002-12-23

    Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.

  4. Complex geometries in wood

    DEFF Research Database (Denmark)

    Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob

    2009-01-01

    The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....

  5. Integral geometry and holography

    Science.gov (United States)

    Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-01

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

  6. Hilbert, completeness and geometry

    Directory of Open Access Journals (Sweden)

    Giorgio Venturi

    2011-11-01

    Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.

  7. 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...

  8. Generalised Geometry and Flux Vacua

    CERN Document Server

    Larfors, Magdalena

    2015-01-01

    This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.

  9. Introductory non-Euclidean geometry

    CERN Document Server

    Manning, Henry Parker

    1963-01-01

    This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.

  10. Geometry for the Secondary School

    Science.gov (United States)

    Moalem, D.

    1977-01-01

    A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)

  11. Linear connections on matrix geometries

    CERN Document Server

    Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad

    1994-01-01

    A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.

  12. Geometry success in 20 mins

    CERN Document Server

    Editors, LearningExpress

    2010-01-01

    Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of 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 is an invaluable resource for both students and adults.

  13. Teaching of Geometry in Bulgaria

    Science.gov (United States)

    Bankov, Kiril

    2013-01-01

    Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…

  14. Elementary algebraic geometry

    CERN Document Server

    Kendig, Keith

    2015-01-01

    Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th

  15. 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

  16. Local analytic geometry

    CERN Document Server

    Abhyankar, Shreeram Shankar

    1964-01-01

    This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from

  17. Kinematic geometry of gearing

    CERN Document Server

    Dooner, David B

    2012-01-01

    Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat

  18. From geometry to topology

    CERN Document Server

    Flegg, H Graham

    2001-01-01

    This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.

  19. Geometry of conics

    CERN Document Server

    Akopyan, A V

    2007-01-01

    The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca

  20. Geometry I essentials

    CERN Document Server

    REA, The Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric

  1. Thickness calculation software of the thermal insulation in facilities using thermal solar energy; Software para el calculo de espesores del aislante termico en instalaciones de aprovechamiento de energia solar termica

    Energy Technology Data Exchange (ETDEWEB)

    Portillo Jimenez, Canek [Universidad Autonoma de Sinaloa, Culiacan, Sinaloa (Mexico)]. E-mail: cnk@uas.uasnet.mx

    2010-11-15

    It is presented a software application for calculating the thickness of the thermal insulation used in various facilities where there are thermal systems using solar energy. The software facilitates the calculation of the thermal cover thickness over components such as pipes (flat or round), storage and other devices that require thermal protection, installed in outdoors or indoors. The software was programmed in Visual Basic by following the technical specifications of the current regulations in the field. Application examples are performed, obtaining certain results that are discussed briefly. [Spanish] Se presenta un software de aplicacion para el calculo de los espesores de los aislantes termicos, utilizados en diferentes instalaciones donde existen sistemas de aprovechamiento termico de energia solar. El software facilita el calculo del grosor del recubrimiento termico en componentes tales como: tuberias (planas o circulares), depositos acumuladores y otros aparatos que necesiten proteccion termica, instalados en exteriores o en interiores. El software fue programado en Visual Basic siguiendo las especificaciones tecnicas de la normatividad vigente en la materia. Se realizan ejemplos de aplicacion, donde se obtienen ciertos resultados de los cuales se hace una breve discusion.

  2. Computational Fluid Dynamics.

    Science.gov (United States)

    1986-06-01

    the second local aspect of that work. Furthermore, this work also incorporates the effects of the errors resulting from the numerical integration of...space of all functions which are square integrable and H, H - -O denote the usual Sobolev spaces. To approximate the solution to the weak problem (2...into Spanish and appeared in Metodos Numericos Para Calculo y Diseno en Ingeniera 1 (1985), 67-80. [5] J. P. Fink and W. C. Rheinboldt, "Folds on the

  3. Computational Fluid Dynamics at ICMA (Institute for Computational Mathematics and Applications)

    Science.gov (United States)

    1988-10-18

    the numeri- cal integration of the reduced basis ODE systems. 3. Two-Fluid, Two-Phase Flow Additional theoretical results on the nature of the void...space of all functions which are square integrable and HI’, I denote the usual Sobolev spaces. To approximate the solution to the weak problem (2...Pittsburgh, InsL for Comp. Math. and Appl., Technical Report ICMA-82-38, May 1982. Translated into Spanish and appeared in Metodos Numericos Para Calculo y

  4. Linear geometry thyratron

    Science.gov (United States)

    Byron, S.

    1985-03-01

    The low pressure gas-filled thyratron is scalable in the long dimension. Internally the tube is formed as a tetrode, with an auxiliary grid placed between the cathode and the control grid. A dc or pulsed power source drives the auxiliary grid both to insure uniform cathode emission and to provide a grid-cathode plasma prior to commutation. The high voltage holdoff structure consists of the anode, the control grid and its electrostatic shielding baffles, and a main quartz insulator. A small gas flow supply and exhaust system is used that eliminates the need for a hydrogen reservoir and permits other gases, such as helium, to be used. The thyratron provides a low inductance, high current, long lifetime switch configuration: useful for switch-on applications involving large scale lasers and other similar loads that are distributed in a linear geometry.

  5. Critique of information geometry

    Energy Technology Data Exchange (ETDEWEB)

    Skilling, John, E-mail: skilling@eircom.net [Maximum Entropy Data Consultants Ltd, Kenmare (Ireland)

    2014-12-05

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  6. Real algebraic geometry

    CERN Document Server

    Bochnak, Jacek; Roy, Marie-Françoise

    1998-01-01

    This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

  7. Covariant Macroscopic Quantum Geometry

    CERN Document Server

    Hogan, Craig J

    2012-01-01

    A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.

  8. Advanced geometries and regimes

    Science.gov (United States)

    Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Stockem, A.; Fiuza, F.; Silva, L. O.; Antici, P.; Margarone, D.; Korn, G.

    2013-08-01

    We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project. At the request of the Proceedings Editors and Dr. Stepan Bulanov, University of California, Berkeley, the above article has been updated to include three additional authors: A. Stockem, F. Fiuza, and L. O. Silva. All additional authors have consented to their name being added to the paper. Furthermore, the updated article PDF contains amendments to a number of references as detailed within the pages attached to the end of the updated article PDF file. The updated article was re-published on 8 August 2013.

  9. Magnetism in curved geometries

    Science.gov (United States)

    Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys

    2016-09-01

    Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

  10. Klein geometries, parabolic geometries and differential equations of finite type

    CERN Document Server

    Abadoglu, Ender

    2009-01-01

    We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).

  11. 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

  12. Computer program for the calculation of stresses in rotary equipment discs; Programas de computo para el calculo de esfuerzos en discos de equipo rotatorio

    Energy Technology Data Exchange (ETDEWEB)

    Gutierrez Delgado, Wilson; Kubiak, Janusz; Serrano Romero, Luis Enrique [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)

    1990-12-31

    In the preliminary design and diagnosis of rotary machines is very common to utilize simple calculation methods for the mechanical and thermal stresses, dynamic and thermodynamic analysis and flow of fluids in this machines (Gutierrez et al., 1989). The analysis with these methods provides the necessary results for the project initial stage of the machine. Later on, more complex tools are employed to refine the design of some machine components. In the Gutierrez report et al., (1989) 34 programs were developed for the preliminary design and diagnosis of rotating equipment; in this article, one of them is presented in which a method for the analysis of mechanical and thermal stresses is applied in discs of uniform or variable thickness that are normally found in turbomachines and rotary equipment. [Espanol] En el diseno preliminar y diagnostico de maquinas rotatorias es muy comun emplear metodos de calculo sencillos para el analisis de esfuerzos mecanicos y termicos, analisis dinamico y termodinamico y de flujo de fluidos en estas maquinas (Gutierrez et al., 1989). El analisis con estos metodos proporcionan los resultados necesarios para la etapa del proyecto inicial de la maquina. Posteriormente, para refinar el diseno de algunos componentes de la maquina, se aplican las herramientas mas complejas. En el informe de Gutierrez et al., (1989) se desarrollan 34 programas para el diseno preliminar y diagnostico de equipo rotatorio; en este articulo, se presenta uno de ellos, en el que se emplea un metodo para el analisis de esfuerzos mecanicos y termicos en discos de espesor constante o variable que se encuentran comunmente en turbomaquinas y en equipos rotatorios.

  13. 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...

  14. 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......, 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...

  15. Linear algebra and projective geometry

    CERN Document Server

    Baer, Reinhold

    2005-01-01

    Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra

  16. Finding Proofs in Tarskian Geometry

    OpenAIRE

    Beeson, Michael; Wos, Larry

    2016-01-01

    We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some \\Otter proofs in Tarskian geometry (solving challenges issued in Wos's 1998...

  17. Phase structures in fuzzy geometries

    CERN Document Server

    Govindarajan, T R; Gupta, K S; Martin, X

    2012-01-01

    We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.

  18. Thermodynamics of Asymptotically Conical Geometries.

    Science.gov (United States)

    Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H

    2015-06-12

    We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.

  19. Planetary Image Geometry Library

    Science.gov (United States)

    Deen, Robert C.; Pariser, Oleg

    2010-01-01

    The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

  20. Development of a computational model applied to a unitary 144 CM{sup 2} proton exchange membrane fuel cell; Desenvolvimento de um modelo numerico computacional aplicado a uma celula a combustivel unitaria de 144 CM{sup 2} tipo PEM

    Energy Technology Data Exchange (ETDEWEB)

    Robalinho, Eric

    2009-07-01

    This work presents the development of a numerical computer model and methodology to study and design polymeric exchange membrane fuel cell - PEM. For the validation of experimental results, a sequence of routines, appropriate to fit the data obtained in the laboratory, was described. At the computational implementation it was created a new strategy of coupling two 3-dimensional models to satisfy the requirements of the comprehensive model of the fuel cell, including its various geometries and materials, as well as the various physical and chemical processes simulated. To effective assessment of the real cell analogy with numerical model, numerical studies were carried out. Comparisons with values obtained in the literature, characterization of variables through laboratory experiments and estimates from models already tested in the literature were also performed. Regarding the experimental part, a prototype of a fuel cell unit of 144 cm{sup 2} of geometric area was designed, produced and operated at laboratory with the purpose of validating the numerical computer model proposed, with positive results. The results of simulations for the 2D and 3D geometries proposed are presented in the form of polarization curves, highlighting the catalytic layer model based on the geometry of agglomerates. Parametric and sensitivity studies are presented to illustrate the change in performance of the fuel cell studied. The final model is robust and useful as a tool for design and optimization of PEM type fuel cells in a wide range of operating conditions. (author)

  1. Development of a computational model applied to a unitary 144 cm{sup 2} proton exchange membrane fuel cell; Desenvolvimento de um modelo numerico computacional aplicado a uma celula a combustivel unitaria de 144 CM{sup 2} tipo PEM

    Energy Technology Data Exchange (ETDEWEB)

    Robalinho, Eric

    2009-07-01

    This work presents the development of a numerical computer model and methodology to study and design polymeric exchange membrane fuel cell - PEM. For the validation of experimental results, a sequence of routines, appropriate to fit the data obtained in the laboratory, was described. At the computational implementation it was created a new strategy of coupling two 3-dimensional models to satisfy the requirements of the comprehensive model of the fuel cell, including its various geometries and materials, as well as the various physical and chemical processes simulated. To effective assessment of the real cell analogy with numerical model, numerical studies were carried out. Comparisons with values obtained in the literature, characterization of variables through laboratory experiments and estimates from models already tested in the literature were also performed. Regarding the experimental part, a prototype of a fuel cell unit of 144 cm of geometric area was designed, produced and operated at laboratory with the purpose of validating the numerical computer model proposed, with positive results. The results of simulations for the 2D and 3D geometries proposed are presented in the form of polarization curves, highlighting the catalytic layer model based on the geometry of agglomerates. Parametric and sensitivity studies are presented to illustrate the change in performance of the fuel cell studied. The final model is robust and useful as a tool for design and optimization of PEM type fuel cells in a wide range of operating conditions. (author)

  2. Digital geometry in image processing

    CERN Document Server

    Mukhopadhyay, Jayanta

    2013-01-01

    Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of

  3. 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

  4. Null twisted geometries

    CERN Document Server

    Speziale, Simone

    2013-01-01

    We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...

  5. Matrix Information Geometry

    CERN Document Server

    Bhatia, Rajendra

    2013-01-01

    This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR).  During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented  are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.  

  6. Functional integration over geometries

    CERN Document Server

    Mottola, E

    1995-01-01

    The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber \\cal G, the functional measure on the coset space {\\cal M}/{\\cal G} is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it i.e.} metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the me...

  7. Coframe geometry and gravity

    CERN Document Server

    Itin, Yakov

    2007-01-01

    The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Ma...

  8. Ostrich eggs geometry

    Directory of Open Access Journals (Sweden)

    Šárka Nedomová

    2013-01-01

    Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.

  9. Geometries from field theories

    Science.gov (United States)

    Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya

    2015-10-01

    We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.

  10. Optimum Stirling engine geometry

    Energy Technology Data Exchange (ETDEWEB)

    Senft, J.R. [University of Wisconsin, River Walls, WI (United States). Mathematics Dept.

    2002-07-01

    This paper combines the author's work on mechanical efficiency of reciprocating engines with the classic Schmidt thermodynamic model for Stirling engines and revisits the problem of identifying optimal engine geometry. All previous optimizations using the Schmidt theory focused on obtaining a maximal specific indicated cyclic work. This does not necessarily produce the highest shaft output. Indeed, some optima based upon indicated work would yield engines that cannot run at all due to excessive intrinsic mechanical losses. The analysis presented in this paper shows how to optimize for shaft or brake work output. Specifically, it presents solutions to the problem of finding the piston-to-displacer swept volume ratio and phase angle which will give the maximum brake output for a given total swept volume, given temperature extremes, a given mean operating pressure, and a given engine mechanism effectiveness. The paper covers the split-cylinder or gamma-type Stirling in detail, serving as a model for similar analysis of the other Stirling engine configurations. (author)

  11. Numerical Analysis of Turbulent Structures with a {kappa}-{epsilon} 3D Model of a Flow over a Cubic Obstacle; Estudio numerico de estructuras turbulentas con un modelo {kappa}-{epsilon} en 3D de un flujo sobre un obstaculo cubico

    Energy Technology Data Exchange (ETDEWEB)

    Millan Barrera, Cecia; Ramirez Leon, Hermilo [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico)

    2001-12-01

    A numerical analysis is applied to a flow in an open channel and deformed by a three dimensional obstacle. The proposed model solves the 3-D Navier-Stokes equations, to which a {kappa}-{epsilon} turbulence model is coupled. The numerical analysis was constructed using a finite difference formulation for time evaluation purposed and staggered cells for space evaluation. The main goal of the present work was to study the turbulent structures and patterns of the flow due to an obstacle at the bottom of the channel plate. Our results are according to those found in the related literature. Flow patterns allow establishing the generation of turbulent structures by means of a comparison between this study and a most recent related work that evaluates the vorticity of the flow. [Spanish] Se reportan los resultados obtenidos, mediante simulaciones numericas, del movimiento del flujo en un canal con superficie libre y un obstaculo en el fondo. El sistema ecuaciones utilizado resuelve las ecuaciones de Navier-Stokes en tres dimensiones, al cual se le acoplo un modelo de turbulencia tipo {kappa}-{epsilon}. La solucion se obtiene numericamente utilizando un esquema en diferencias finitas para la evaluacion temporal de las variables y una celda escalonada para la evaluacion espacial de las mismas. El objetivo del modelo es estudiar los patrones de flujo y las estructuras turbulentas que se generan debido a la presencia del obstaculo. El estudio se realizo para un flujo en tres dimensiones. Los resultados son satisfactorios, ya que muestran concordancia con otros estudios numericos y experimentales encontrados en la literatura.

  12. 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....

  13. Analytic Geometry, A Tentative Guide.

    Science.gov (United States)

    Helwig, G. Alfred; And Others

    This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…

  14. 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...

  15. Index Theorems on Torsional Geometries

    CERN Document Server

    Kimura, Tetsuji

    2007-01-01

    We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.

  16. The Geometry Description Markup Language

    Institute of Scientific and Technical Information of China (English)

    RadovanChytracek

    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.This article 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.

  17. Hamilton geometry: Phase space geometry from modified dispersion relations

    CERN Document Server

    Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian

    2015-01-01

    We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.

  18. Geometry and W-Gravity

    OpenAIRE

    Hull, C. M.

    1993-01-01

    The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Ho...

  19. Linear algebra, geometry and transformation

    CERN Document Server

    Solomon, Bruce

    2014-01-01

    Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg

  20. 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

  1. 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

  2. A new look at geometry

    CERN Document Server

    Adler, Irving

    1967-01-01

    This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa

  3. CATIA-GDML geometry builder

    Science.gov (United States)

    Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.

    2011-12-01

    Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.

  4. Quantum Consequences of Parameterizing Geometry

    Science.gov (United States)

    Wanas, M. I.

    2002-12-01

    The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.

  5. Geometry and W-Gravity

    CERN Document Server

    Hull, C M

    1993-01-01

    The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)

  6. Thermal Phase in Bubbling Geometries

    Institute of Scientific and Technical Information of China (English)

    LIU Chang-Yong

    2008-01-01

    We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.

  7. An improved combinatorial geometry model for arbitrary geometry in DSMC

    Science.gov (United States)

    Kargaran, H.; Minuchehr, A.; Zolfaghari, A.

    2017-03-01

    This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.

  8. Hyperbolic Metamaterials with Complex Geometry

    DEFF Research Database (Denmark)

    Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei

    2016-01-01

    We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...

  9. Instability of supersymmetric microstate geometries

    CERN Document Server

    Eperon, Felicity C; Santos, Jorge E

    2016-01-01

    We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.

  10. Molecular motion in restricted geometries

    Indian Academy of Sciences (India)

    Siddharth Gautam; S Mitra; R Mukhopadhyay

    2008-10-01

    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 scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.

  11. Moment methods in extremal geometry

    NARCIS (Netherlands)

    De Laat, D.

    2016-01-01

    In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state

  12. An introduction to differential geometry

    CERN Document Server

    Willmore, T J

    2012-01-01

    This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

  13. Instability of supersymmetric microstate geometries

    Energy Technology Data Exchange (ETDEWEB)

    Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

    2016-10-07

    We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.

  14. Moment methods in extremal geometry

    NARCIS (Netherlands)

    De Laat, D.

    2016-01-01

    In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state

  15. 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......Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first......, 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...

  16. 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, ...

  17. Paper Interfaces for Learning Geometry

    OpenAIRE

    Bonnard, Quentin; Verma, Himanshu; Kaplan, Frédéric; Dillenbourg, Pierre

    2012-01-01

    Paper interfaces offer tremendous possibilities for geometry education in primary schools. Existing computer interfaces designed to learn geometry do not consider the integration of conventional school tools, which form the part of the curriculum. Moreover, most of computer tools are designed specifically for individual learning, some propose group activities, but most disregard classroom-level learning, thus impeding their adoption. We present an augmented reality based tabletop system with ...

  18. Courant Algebroids in Parabolic Geometry

    CERN Document Server

    Armstrong, Stuart

    2011-01-01

    To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.

  19. Topology and geometry for physicists

    CERN Document Server

    Nash, Charles

    2011-01-01

    Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

  20. Higgs mass in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)

    2014-09-11

    In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. The Common Geometry Module (CGM).

    Energy Technology Data Exchange (ETDEWEB)

    Tautges, Timothy James

    2004-12-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

  2. Holomorphic Cartan geometries and rational curves

    CERN Document Server

    Biswas, Indranil

    2010-01-01

    We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.

  3. General Construction of Tubular Geometry

    CERN Document Server

    Mukhopadhyay, Partha

    2016-01-01

    We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.

  4. Quantum geometry and gravitational entropy

    Energy Technology Data Exchange (ETDEWEB)

    Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan

    2007-05-29

    Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

  5. Conventionalism and integrable Weyl geometry

    Science.gov (United States)

    Pucheu, M. L.

    2015-03-01

    Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.

  6. Wave propagation on microstate geometries

    CERN Document Server

    Keir, Joseph

    2016-01-01

    Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...

  7. Euclidean geometry and its subgeometries

    CERN Document Server

    Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

    2015-01-01

    In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

  8. Geometry of black hole spacetimes

    CERN Document Server

    Andersson, Lars; Blue, Pieter

    2016-01-01

    These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.

  9. Geometric Transformations in Engineering Geometry

    Directory of Open Access Journals (Sweden)

    I. F. Borovikov

    2015-01-01

    Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

  10. 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

  11. Stochastic geometry and its applications

    CERN Document Server

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

    2013-01-01

    An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

  12. Geometry Design of Wooden Barrels

    Directory of Open Access Journals (Sweden)

    Ivan CISMARU

    2010-12-01

    Full Text Available The aim of this paper is to present a design methodology of the wooden barrel geometry, as an algorithm of successive calculations. Thus, starting from the required elements (volume, length, shape, maximum height of storage space the user will be able to define the geometry which must be obtained by processing. Based on these calculations, one can define the structure, size and shape of the staves in order to establish the processing technology of both components and subassemblies (jacket and bottoms which are to form the final product by their assembling using metal circles.

  13. Geometry, topology, and string theory

    Energy Technology Data Exchange (ETDEWEB)

    Varadarajan, Uday

    2003-07-10

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  14. Spatial geometry and special relativity

    DEFF Research Database (Denmark)

    Kneubil, Fabiana Botelho

    2016-01-01

    In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...

  15. Introduction to topology and geometry

    CERN Document Server

    Stahl, Saul

    2014-01-01

    An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele

  16. Lectures on classical differential geometry

    CERN Document Server

    Struik, Dirk J

    1988-01-01

    Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ

  17. Gauging Geometry: A Didactic Lecture

    CERN Document Server

    Kannenberg, L

    2016-01-01

    Local inertial frame invariance is taken as the fundamental principle of physical geometry, where a local inertial frame is represented by a verbein. Invariance of the vierbein with respect to local Lorentz transformations then expresses local inertial frame invariance. The dynamics of physical geometry develops as a gauge theory of the verbein that is closely analogous to the Yang-Mills field provided the verbein connection and curvature correspond to the geometric potential and field respectively. The resulting theory is shown to be equivalent to Einstein's tensor form of relativistic gravitation.

  18. Algebraic geometry and theta functions

    CERN Document Server

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  19. Comparison theorems in Riemannian geometry

    CERN Document Server

    Cheeger, Jeff

    2008-01-01

    The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

  20. Lectures on Algebraic Geometry I

    CERN Document Server

    Harder, Gunter

    2012-01-01

    This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho

  1. Teaching Activity-Based Taxicab Geometry

    Science.gov (United States)

    Ada, Tuba

    2013-01-01

    This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…

  2. Differential geometry meets the cell.

    Science.gov (United States)

    Marshall, Wallace F

    2013-07-18

    A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.

  3. The geometry of SU(3)

    Energy Technology Data Exchange (ETDEWEB)

    Byrd, M.

    1997-10-01

    The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.

  4. Fractal geometry and stochastics IV

    CERN Document Server

    Bandt, Christoph

    2010-01-01

    Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.

  5. Signature geometry and quantum engineering

    Science.gov (United States)

    Samociuk, Stefan

    2013-09-01

    As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.

  6. Instructional Identities of Geometry Students

    Science.gov (United States)

    Aaron, Wendy Rose; Herbst, Patricio

    2012-01-01

    We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…

  7. Loop groups and noncommutative geometry

    CERN Document Server

    Carpi, Sebastiano

    2015-01-01

    We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group LG. The construction is based on certain supersymmetric conformal field theory models associated with LG.

  8. 3DHZETRN: Inhomogeneous Geometry Issues

    Science.gov (United States)

    Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.

    2017-01-01

    Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

  9. The Basics of Information Geometry

    CERN Document Server

    Caticha, Ariel

    2014-01-01

    To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".

  10. College geometry a unified development

    CERN Document Server

    Kay, David C

    2011-01-01

    ""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273

  11. Foucault pendulum through basic geometry

    Science.gov (United States)

    von Bergmann, Jens; von Bergmann, HsingChi

    2007-10-01

    We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.

  12. Analogical Reasoning in Geometry Education

    Science.gov (United States)

    Magdas, Ioana

    2015-01-01

    The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

  13. Open problems in algebraic geometry

    NARCIS (Netherlands)

    Edixhoven, S.J.; Moonen, B.J.J.; Oort, F.

    2000-01-01

    The open problems presented here were collected on the occasion of a workshop on Arithmetic Geometry at the University ofUtrecht, 26{30 June, 2000. This workshop was organized by the editors of the present article, and was made possible by support of: | NWO, the Netherlands Organization for

  14. Data Imprecision in Computational Geometry

    NARCIS (Netherlands)

    Löffler, M.

    2009-01-01

    The field of computational geometry is concerned with the design and analysis of geometric algorithms. For such algorithms, correctness and efficiency proofs are constructed, or problems are proven to be hard when no correct and efficient algorithms exist. In order to be able to do this, several ass

  15. GEOMETRY AND COMPLEXITY IN ARCHITECTURE

    Directory of Open Access Journals (Sweden)

    RUSU Maria Ana

    2015-06-01

    Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.

  16. Geometri

    DEFF Research Database (Denmark)

    Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...

  17. Geometry of Membrane Sigma Models

    CERN Document Server

    Vysoky, Jan

    2015-01-01

    String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathematical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better ...

  18. Differential geometry and mathematical physics

    CERN Document Server

    Rudolph, Gerd

    Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...

  19. Fractal geometry and computer graphics

    CERN Document Server

    Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

    1992-01-01

    Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

  20. The geometry of surfaces contact

    Directory of Open Access Journals (Sweden)

    Siegl J.

    2007-11-01

    Full Text Available This contribution deals with a geometrical exact description of contact between two given surfaces which are defined by the vector functions. These surfaces are substituted at a contact point by approximate surfaces of the second order in accordance with the Taylor series and consequently there is derived a differential surface of these second order surfaces. Knowledge of principal normal curvatures, their directions and the tensor (Dupin indicatrix of this differential surface are necessary for description of contact of these surfaces. For description of surface geometry the first and the second surface fundamental tensor and a further methods of the differential geometry are used. A geometrical visualisation of obtained results of this analysis is made. Method and results of this study will be applied to contact analysis of tooth screw surfaces of screw machines.

  1. Grassmannian geometry of scattering amplitudes

    CERN Document Server

    Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav

    2016-01-01

    Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...

  2. Foliation theory in algebraic geometry

    CERN Document Server

    McKernan, James; Pereira, Jorge

    2016-01-01

    Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013.  Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...

  3. Euclidean distance geometry an introduction

    CERN Document Server

    Liberti, Leo

    2017-01-01

    This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

  4. Groups and Geometries : Siena Conference

    CERN Document Server

    Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria

    1998-01-01

    On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi­ tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...

  5. Beyond core knowledge: Natural geometry

    Science.gov (United States)

    Spelke, Elizabeth; Lee, Sang Ah; Izard, Véronique

    2010-01-01

    For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. PMID:20625445

  6. Gear geometry of cycloid drives

    Institute of Scientific and Technical Information of China (English)

    CHEN BingKui; FANG TingTing; LI ChaoYang; WANG ShuYan

    2008-01-01

    According to differential geometry and gear geometry,the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion.The correct meshing condition,contact line,contact ratio,calculating method for pin tooth's maximum contact point are developed.Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1,2,3 and -1,respectively.A general method called enveloping method to generate hypocycloid and epicycloid is put forward.The correct mesh-ing condition for cycloid pin wheel gearing is provided,and the contact line and the contact ratio are also discussed.

  7. Geometry of polycrystals and microstructure

    Directory of Open Access Journals (Sweden)

    Ball John M.

    2015-01-01

    Full Text Available We investigate the geometry of polycrystals, showing that for polycrystals formed of convex grains the interior grains are polyhedral, while for polycrystals with general grain geometry the set of triple points is small. Then we investigate possible martensitic morphologies resulting from intergrain contact. For cubic-totetragonal transformations we show that homogeneous zero-energy microstructures matching a pure dilatation on a grain boundary necessarily involve more than four deformation gradients. We discuss the relevance of this result for observations of microstructures involving second and third-order laminates in various materials. Finally we consider the more specialized situation of bicrystals formed from materials having two martensitic energy wells (such as for orthorhombic to monoclinic transformations, but without any restrictions on the possible microstructure, showing how a generalization of the Hadamard jump condition can be applied at the intergrain boundary to show that a pure phase in either grain is impossible at minimum energy.

  8. Gear geometry of cycloid drives

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth’s maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.

  9. 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.

  10. Core foundations of abstract geometry.

    Science.gov (United States)

    Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S

    2013-08-27

    Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.

  11. Topics in modern differential geometry

    CERN Document Server

    Verstraelen, Leopold

    2017-01-01

    A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

  12. Geometry for the accelerating universe

    CERN Document Server

    Punzi, R; Wohlfarth, M N R; Punzi, Raffaele; Schuller, Frederic P.; Wohlfarth, Mattias N.R.

    2006-01-01

    The Lorentzian spacetime metric is replaced by an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the gravitational Einstein-Hilbert action is re-interpreted as dynamics for an area metric. Without the need for dark energy or fine-tuning, area metric cosmology explains the observed small acceleration of the late Universe.

  13. Number theory III Diophantine geometry

    CERN Document Server

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  14. Black Holes as Effective Geometries

    CERN Document Server

    Balasubramanian, Vijay; El-Showk, Sheer; Messamah, Ilies

    2008-01-01

    Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective t...

  15. Introduction to geometry and relativity

    CERN Document Server

    2013-01-01

    This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...

  16. 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

  17. 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.

  18. 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

  19. Towards a Nano Geometry? Geometry and Dynamics on Nano Scale

    CERN Document Server

    Booss-Bavnbek, Bernhelm

    2012-01-01

    This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elaborated - in contrast to the familiar Newtonian mechanics and the more recent, but by now also rather well established quantum field theories. Examples are given originating from the systems biology of insulin secreting pancreatic beta-cells and the mathematical challenges of an envisioned non-invasive control of magnetic nanoparticles.

  20. A Whirlwind Tour of Computational Geometry.

    Science.gov (United States)

    Graham, Ron; Yao, Frances

    1990-01-01

    Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

  1. Generalised Complex Geometry in Thermodynamical Fluctuation Theory

    Directory of Open Access Journals (Sweden)

    P. Fernández de Córdoba

    2015-08-01

    Full Text Available We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction.

  2. Calculation of economic viability of alternative energy sources considering its environmental costs for small communities of Northeast Brazil; Calculo de viabilidade economica de fontes alternativas de energia considerando seus custos ambientais para pequenas comuidades da regiao nordeste brasileira

    Energy Technology Data Exchange (ETDEWEB)

    Stecher, Luiza Chourkalo

    2014-09-01

    There has been an increasing concern about current environmental issues caused by human activity, as the world searches for development. The production of electricity is an extremely relevant factor in this scenario since it is responsible for a large portion of the emissions that cause the greenhouse effect. Due to this fact, a sustainable development with alternative energy sources, which are attractive for such purpose, must be proposed, especially in places that are not supplied by the conventional electricity grid such as many communities in the Northeast Brazil. This work aims to calculate the environmental cost for the alternative sources of energy - solar, wind and biomass - during electricity generation, and to estimate the economic feasibility of those sources in small communities of Northeast Brazil, considering the avoided costs. The externalities must be properly identified and valued so the costs or benefits can be internalized and reflect accurately the economic feasibility or infeasibility of those sources. For this, the method of avoided costs was adopted for the calculation of externalities. This variable was included in the equation developed for all considered alternative energy sources. The calculations of economic feasibility were performed taking the new configurations in consideration, and the new equation was reprogrammed in the Programa de Calculo de Custos de Energias Alternativas, Solar, Eolica e Biomassa (PEASEB). The results demonstrated that the solar photovoltaic energy in isolated systems is the most feasible and broadly applicable source for small communities of Northeast Brazil. (author)

  3. Geometry in the Early Years: A Commentary

    Science.gov (United States)

    Dindyal, Jaguthsing

    2015-01-01

    The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

  4. Students' Misconceptions and Errors in Transformation Geometry

    Science.gov (United States)

    Ada, Tuba; Kurtulus, Aytac

    2010-01-01

    This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…

  5. Global continuation for distance geometry problems

    Energy Technology Data Exchange (ETDEWEB)

    More, J.J.; Wu, Zhijun

    1995-03-01

    Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. The authors formulate the distance geometry problem as a global minimization problem with special structure, and show the global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.

  6. Geometry in the Early Years: A Commentary

    Science.gov (United States)

    Dindyal, Jaguthsing

    2015-01-01

    The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

  7. Number Theory, Analysis and Geometry

    CERN Document Server

    Goldfeld, Dorian; Jones, Peter

    2012-01-01

    Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th

  8. Integral geometry and representation theory

    CERN Document Server

    Gel'fand, I M; Vilenkin, N Ya

    1966-01-01

    Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp

  9. Porous media geometry and transports

    CERN Document Server

    Adler, Pierre

    1992-01-01

    The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr

  10. Stochastic geometry for image analysis

    CERN Document Server

    Descombes, Xavier

    2013-01-01

    This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are  described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed.  Numerous applications, covering remote sensing images, biological and medical imaging, are detailed.  This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.

  11. Adding momentum to supersymmetric geometries

    Energy Technology Data Exchange (ETDEWEB)

    Lunin, Oleg, E-mail: olunin@albany.edu [Department of Physics, University at Albany (SUNY), Albany, NY 12222 (United States); Mathur, Samir D., E-mail: mathur.16@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States); Turton, David, E-mail: turton.7@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)

    2013-03-11

    We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a traveling wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T{sup 4}. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.

  12. Adding momentum to supersymmetric geometries

    CERN Document Server

    Lunin, Oleg; Turton, David

    2012-01-01

    We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.

  13. Projective geometry and projective metrics

    CERN Document Server

    Busemann, Herbert

    2005-01-01

    The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio

  14. Generalised geometry for string corrections

    CERN Document Server

    Coimbra, André; Triendl, Hagen; Waldram, Daniel

    2014-01-01

    We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz--Bismut theorem. As examples of this construction we discuss the corrections linear in $\\alpha'$ in heterotic strings and the absence of such corrections for type II theories.

  15. Loop quantum geometry: a primer

    Energy Technology Data Exchange (ETDEWEB)

    Corichi, Alejandro [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico)

    2005-01-15

    This is the written version of a lecture given at the 'VI Mexican School of Gravitation and Mathematical Physics' (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate students and non-experts interested in learning the basics of the subject.

  16. Exceptional geometry and Borcherds superalgebras

    CERN Document Server

    Palmkvist, Jakob

    2015-01-01

    We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to e_{n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n less than 8. The closure of the transformations then follows from the Jacobi identity and the grading of e_{n+1} with respect to e_n.

  17. Bondi accretion in trumpet geometries

    Science.gov (United States)

    Miller, August J.; Baumgarte, Thomas W.

    2017-02-01

    The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.

  18. Complexity and Shock Wave Geometries

    CERN Document Server

    Stanford, Douglas

    2014-01-01

    In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by $G_N l_{AdS}$. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.

  19. Loop Quantum Geometry: A primer

    OpenAIRE

    Corichi, Alejandro

    2005-01-01

    This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate students and non-expert...

  20. Isosurfaces geometry, topology, and algorithms

    CERN Document Server

    Wenger, Rephael

    2013-01-01

    Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolutio

  1. Quanta of geometry and unification

    Science.gov (United States)

    Chamseddine, Ali H.

    2016-11-01

    This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

  2. Quanta of Geometry and Unification

    CERN Document Server

    Chamseddine, Ali H

    2016-01-01

    This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

  3. Foundations of arithmetic differential geometry

    CERN Document Server

    Buium, Alexandru

    2017-01-01

    The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

  4. Quanta of Geometry: Noncommutative Aspects

    Science.gov (United States)

    Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

  5. Warped Geometry of Brane Worlds

    CERN Document Server

    Felder, G; Kofman, L A; Felder, Gary; Frolov, Andrei; Kofman, Lev

    2002-01-01

    We study the dynamical equations for a warp factor and a bulk scalar in 5d brane world scenarios. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce two novel methods for studying the warped geometry. First, we construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the tw...

  6. Weyl gravity and Cartan geometry

    Science.gov (United States)

    Attard, J.; François, J.; Lazzarini, S.

    2016-04-01

    We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].

  7. Geometry and the Quantum: Basics

    CERN Document Server

    Chamseddine, Ali H; Mukhanov, Viatcheslav

    2014-01-01

    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these represen...

  8. Fuzzy Logic for Incidence Geometry.

    Science.gov (United States)

    Tserkovny, Alex

    The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.

  9. Toric Geometry and String Theory

    CERN Document Server

    Bouchard, Vincent

    2006-01-01

    In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities. These objects torically encode the local geometry of a degeneration of an elliptic fibration. We classify all tops and give a prescription for assigning an affine, possibly twisted Kac-Moody algebra to any such top. Tops related to twisted Kac-Moody algebras can be used to construct string compactifications with reduced rank of the gauge group. Secondly, we compute all loop closed and open topological string amplitudes on orientifolds of toric Calabi-Yau threefolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex. In particular, we count Klein bottles and projective planes with any number of handles in some Calabi-Yau orientifolds. We determine the BPS structure of the amplitudes, and illustrate ou...

  10. Ring polymers in confined geometries

    CERN Document Server

    Usatenko, Z; Kuterba, P

    2016-01-01

    The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size were performed. Taking into account the correspondence between the field theoretical $\\phi^4$ $O(n)$-vector model in the limit $n\\to 0$ and the behavior of long-flexible polymer chains in a good solvent the correspondent depletion interaction potentials, depletion forces and the forces which exert phantom ideal ring and ring polymer chains with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions d=3 up to one-loop order. Additionally, the investigation of a dilute solution of phantom ideal ring polymers in a slit geometry of two inert walls and mixed walls with one repulsive and other one inert wall were performed and correspondent depletion interaction potentials and the depletion forces were cal...

  11. Fuzzy Logic for Incidence Geometry

    Science.gov (United States)

    2016-01-01

    The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133

  12. Weyl gravity and Cartan geometry

    CERN Document Server

    Attard, Jeremy; Lazzarini, Serge

    2015-01-01

    We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned by two theories: the first one will be the associated Yang-Mills-like Lagrangian, while the second, inspired by~\\cite{Wheeler2014}, will be a slightly more general one which will relax the conformal Cartan geometry. The corresponding gauge symmetry is treated within the BRST language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the `normal conformal Cartan connection'. Finally, we provide in a Lagrangian framework a justification of the identification, in dimension $4$, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in ...

  13. Differential geometry based multiscale models.

    Science.gov (United States)

    Wei, Guo-Wei

    2010-08-01

    Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are

  14. Theory and control calculations. Application to BWR and PWR; Teoria y calculo de elementos de control, Aplicacion a PWR y BWR

    Energy Technology Data Exchange (ETDEWEB)

    Velarde, G.; Guerra, J.

    1972-07-01

    A theoretical method to extend the applicability of P{sub 1} approximation to strong absorbers is given. Tables of effective diffusion parameters for slab and cylindrical geometry as well as a summary of expressions for obtaining the extrapolation length in cases of interest, are included. (Author) 21 refs.

  15. On Geometry and Matrix Models

    CERN Document Server

    Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun

    2002-01-01

    We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

  16. On geometry and matrix models

    Science.gov (United States)

    Dijkgraaf, Robbert; Vafa, Cumrun

    2002-11-01

    We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large- N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large- N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

  17. On geometry and matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun

    2002-11-11

    We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

  18. The noncommutative geometry of Zitterbewegung

    CERN Document Server

    Eckstein, Michał; Miller, Tomasz

    2016-01-01

    Based on the mathematics of noncommutative geometry, we model a 'classical' Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung - the 'trembling motion' of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's 'internal space'. Furthermore, we show that the latter does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Higgs-like field. We discuss a table-top experiment in the domain of quantum simulation to test the predictions of the model and outline the consequences of our model for quantum gauge theories.

  19. Holographic thermalization in noncommutative geometry

    CERN Document Server

    Zeng, Xiao-Xiong; Liu, Wen-Biao

    2014-01-01

    Gravitational collapse of a dust shell in noncommutative geometry is probed by the renormalized geodesic length and minimal area surface, which are dual to the two-point correlation function and expectation value of Wilson loop in the dual conformal field theory. For the spacetime without a horizon, we find the shell will not collapse all the time but will stop in a stable state. For the spacetime with a horizon, we investigate how the noncommutative parameter affects the thermalization process in detail. From the numeric results, we find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. From the fitted functions of the thermalization curve, we find for both thermalization probes, there is a phase transition point during the thermalization process, which divides the thermalization into an acceleration phase and a deceleration phase. During the acceleration phase, the acceleration is found to ...

  20. Geometry of Spinning Ellis Wormholes

    CERN Document Server

    Chew, Xiao Yan; Kunz, Jutta

    2016-01-01

    We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for non-symmetric wormholes. We present mass formulae for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limiting configurations corresponding to an extremal Kerr black hole. Moreover, we analyze the geodesics of these wormholes, and show that they possess bound orbits.

  1. Interactive graphics for geometry modeling

    Science.gov (United States)

    Wozny, M. J.

    1984-01-01

    An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.

  2. Dialogues about geometry and light

    CERN Document Server

    Bermudez, David; Leonhardt, Ulf

    2015-01-01

    Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.

  3. Hofstadter's Butterfly in Quantum Geometry

    CERN Document Server

    Hatsuda, Yasuyuki; Tachikawa, Yuji

    2016-01-01

    We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kahler modulus of the Calabi-Yau, can be found explicitly when the quantum parameter $q=e^{i\\hbar}$ is a root of unity, that its branch cuts are given by Hofstadter's butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging $\\hbar$ and $4\\pi^2/\\hbar$, plays an important role.

  4. Hopf algebras in noncommutative geometry

    CERN Document Server

    Varilly, J C

    2001-01-01

    We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of noncommutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups.

  5. The Distance Geometry of Music

    CERN Document Server

    Demaine, Erik D; Meijer, Henk; Rappaport, David; Taslakian, Perouz; Toussaint, Godfried T; Winograd, Terry; Wood, David R

    2007-01-01

    We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\\emph{ostinatos}) from traditional world music. We prove that these \\emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \\emph{evenness}. We also show that essentially all Euclidean rhythms are \\emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful prop...

  6. Walking droplets in confined geometries

    Science.gov (United States)

    Filoux, Boris; Mathieu, Olivier; Vandewalle, Nicolas

    2014-11-01

    When gently placing a droplet onto a vertically vibrated bath, coalescence may be avoided: the drop bounces permanently. Upon increasing forcing acceleration, a drop interacts with the wave it generates, and becomes a ``walker'' with a well defined velocity. In this work, we investigate the confinement of a walker in a mono-dimensional geometry. The system consists of linear submarine channels used as waveguides for a walker. By studying the dynamics of walkers in those channels, we discover some 1D-2D transition. We also propose a model based on an analogy with ``Quantum Wires.'' Finally, we consider the situation of a walker in a circular submarine channel, and examine the behavior of several walking droplets in this system. We show the quantization of the drop distances, and correlate it to their bouncing modes.

  7. Applied geometry and discrete mathematics

    CERN Document Server

    Sturm; Gritzmann, Peter; Sturmfels, Bernd

    1991-01-01

    This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...

  8. Amoeboid motion in confined geometry

    CERN Document Server

    Wu, Hao; Hu, Wei-Fan; Farutin, Alexander; Rafaï, Salima; Lai, Ming-Chih; Peyla, Philippe; Misbah, Chaouqi

    2015-01-01

    Cells of the immune system, as well as cancer cells, migrating in confined environment of tissues undergo frequent shape changes (described as amoeboid motion) that enable them to move forward through these porous media without the assistance of adhesion sites. In other words, they perform amoeboid swimming (AS) while using extracellular matrices and cells of tissues as support. We introduce a simple model of AS in a confined geometry solved by means of 2D numerical simulations. We find that confinement promotes AS, unless being so strong that it restricts shape change amplitude. A straight AS trajectory in the channel is found to be unstable, and ample lateral excursions of the swimmer prevail. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. This is a spontaneous symmetry-breaking bifurcation. We find that there exists an optimal confinement for migration. We provide numerical results as...

  9. Integrable systems, geometry, and topology

    CERN Document Server

    Terng, Chuu-Lian

    2006-01-01

    The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...

  10. Some Progress in Conformal Geometry

    Directory of Open Access Journals (Sweden)

    Sun-Yung A. Chang

    2007-12-01

    Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.

  11. Hessian geometry and entanglement thermodynamics

    CERN Document Server

    Matsueda, Hiroaki

    2015-01-01

    We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of ...

  12. Geometry of discrete quantum computing

    Science.gov (United States)

    Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung

    2013-05-01

    Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.

  13. 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 ...

  14. 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.

  15. 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.

  16. 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. ...

  17. A Relationship between Geometry and Algebra

    CERN Document Server

    Bejarano, Jose Ricardo Arteaga

    2011-01-01

    The three key documents for study geometry are: 1) "The Elements" of Euclid, 2) the lecture by B. Riemann at G\\"ottingen in 1854 entitled "\\"Uber die Hypothesen welche der Geometrie zu Grunde liegen" (On the hypotheses which underlie geometry) and 3) the "Erlangen Program", a document written by F. Klein (1872) on his income as professor at the Faculty of Philosophy and the Senate of the Erlangen University. The latter document F. Klein introduces the concept of group as a tool to study geometry. The concept of a group of transformations of space was known at the time. The purpose of this informative paper is to show a relationship between geometry and algebra through an example, the projective plane. Erlangen program until today continues being a guideline of how to study geometry.

  18. Riemannian geometry of fluctuation theory: An introduction

    Science.gov (United States)

    Velazquez, Luisberis

    2016-05-01

    Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.

  19. Recent developments and some open problems in Finsler geometry

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open problems in Finsler geometry.

  20. Good Codes From Generalised Algebraic Geometry Codes

    CERN Document Server

    Jibril, Mubarak; Ahmed, Mohammed Zaki; Tjhai, Cen

    2010-01-01

    Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used. In this paper we present 41 new codes over GF(16) which improve on the best known codes of the same length and rate. The construction method uses places of small degree with a technique originally published over 10 years ago for the construction of generalised algebraic geometry codes.

  1. Classical geometry Euclidean, transformational, inversive, and projective

    CERN Document Server

    Leonard, I E; Liu, A C F; Tokarsky, G W

    2014-01-01

    Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

  2. Generalized Kahler Geometry from supersymmetric sigma models

    CERN Document Server

    Bredthauer, A; Persson, J; Zabzine, M; Bredthauer, Andreas; Lindstrom, Ulf; Persson, Jonas; Zabzine, Maxim

    2006-01-01

    We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.

  3. 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.

  4. Geometry of solar coronal rays

    Science.gov (United States)

    Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.

    2016-02-01

    Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field

  5. 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.)

  6. 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

  7. (AJST) EFFECTS OF PARTICLE GEOMETRY AND CHEMICAL ...

    African Journals Online (AJOL)

    Department of Agricultural & Environmental Engineering, ... Effects of Particle Geometry and Chemical Accelerator on Strength ..... American Society of Agricultural Engineers, ASAE EP ... the Engineering Materials Development Institute,.

  8. Combinatorics, geometry, and mathematical physics

    Energy Technology Data Exchange (ETDEWEB)

    Chen, W.Y.C.; Louck, J.D.

    1998-11-01

    This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.

  9. Eye movements and information geometry.

    Science.gov (United States)

    Lenz, Reiner

    2016-08-01

    The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database.

  10. Latent geometry of bipartite networks

    Science.gov (United States)

    Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri

    2017-03-01

    Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

  11. The Geometry of Bourges Cathedral

    Directory of Open Access Journals (Sweden)

    Robert Bork

    2014-09-01

    Full Text Available This article presents a geometrical analysis of Bourges Cathedral, based on the application of computer-aided design (CAD techniques to the results of a recent and highly precise laser survey. This analysis reveals that the cathedral's original designer developed a tightly interlocking and strikingly unified design, in which the five-fold subdivision of the chevet ground plan set proportions that would be vertically extruded into an elevation that can be inscribed both within a square and within a series of progessively smaller equilaterial triangles. These results contribute to an ongoing debate about the use of ‘ad quadratum’ and ‘ad triangulum’ geometries in Gothic architecture, and they provide new evidence for the geometrical coherence of Gothic cathedral design. In methodological terms, meanwhile, this discussion demonstrates the potential of CAD-based geometrical analysis for the study of precisely surveyed medieval buildings. The sequence of images being analysed can be viewed as supplementary material at: http://dx.doi.org/10.5334/ah.bz.s1

  12. Fractal Geometry and Stochastics V

    CERN Document Server

    Falconer, Kenneth; Zähle, Martina

    2015-01-01

    This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Te...

  13. The geometry of population genetics

    CERN Document Server

    Akin, Ethan

    1979-01-01

    The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono­ graph I hope to show that his ideas illuminate many aspects of pop­ ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...

  14. Quantum groups: Geometry and applications

    Energy Technology Data Exchange (ETDEWEB)

    Chu, C.S. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group

    1996-05-13

    The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.

  15. Algebra-Geometry of Piecewise Algebraic Varieties

    Institute of Scientific and Technical Information of China (English)

    Chun Gang ZHU; Ren Hong WANG

    2012-01-01

    Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.

  16. Description of SSG Geometry - phase 1

    DEFF Research Database (Denmark)

    Margheritini, Lucia; Kofoed, Jens Peter

    The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work.......The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work....

  17. Trigonometry and Analytic Geometry: Curriculum Guide.

    Science.gov (United States)

    Harlandale Independent School District, San Antonio, TX. Career Education Center.

    The guide (one-quarter trigonometry course; two-quarter analytic geometry course) provides both subject matter and career preparation assistance for advanced mathematics teachers. It is arranged in vertical columns relating curriculum concepts in trigonometry and analytic geometry to curriculum performance objectives, career concepts and teaching…

  18. Visual and Analytic Strategies in Geometry

    Science.gov (United States)

    Kospentaris, George; Vosniadou, Stella; Kazic, Smaragda; Thanou, Emilian

    2016-01-01

    We argue that there is an increasing reliance on analytic strategies compared to visuospatial strategies, which is related to geometry expertise and not on individual differences in cognitive style. A Visual/Analytic Strategy Test (VAST) was developed to investigate the use of visuo-spatial and analytic strategies in geometry in 30 mathematics…

  19. Computing Bisectors in a Dynamic Geometry Environment

    Science.gov (United States)

    Botana, Francisco

    2013-01-01

    In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…

  20. Improving African American Achievement in Geometry Honors

    Science.gov (United States)

    Mims, Adrian B.

    2010-01-01

    This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…

  1. Geometry of all supersymmetric type I backgrounds

    NARCIS (Netherlands)

    Gran, Ulf; Papadopoulos, George; Sloane, Peter; Roest, Diederik

    2007-01-01

    We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9, 1), while th

  2. A Multivariate Model of Achievement in Geometry

    Science.gov (United States)

    Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha

    2014-01-01

    Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

  3. Making Euclidean Geometry Compulsory: Are We Prepared?

    Science.gov (United States)

    Van Putten, Sonja; Howie, Sarah; Stols, Gerrit

    2010-01-01

    This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…

  4. Symposium on Differential Geometry and Differential Equations

    CERN Document Server

    Berger, Marcel; Bryant, Robert

    1987-01-01

    The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.

  5. Two-spinor geometry and gauge freedom

    CERN Document Server

    Canarutto, Daniel

    2014-01-01

    Gauge freedom in quantum particle physics is shown to arise in a natural way from the geometry of two-spinors (Weyl spinors). Various related mathematical notions are reviewed, and a special ansatz of the kind "the system defines the geometry" is discussed in connection with the stated results.

  6. Recent Advances in Computational Conformal Geometry

    OpenAIRE

    Gu, Xianfeng David; Luo, Feng; Yau, Shing-Tung

    2009-01-01

    Computational conformal geometry focuses on developing the computational methodologies on discrete surfaces to discover conformal geometric invariants. In this work, we briefly summarize the recent developments for methods and related applications in computational conformal geometry. There are two major approaches, holomorphic differentials and curvature flow. Holomorphic differential method is a linear method, which is more efficient and robust to triangulations with lower qua...

  7. Poisson Geometry from a Dirac perspective

    OpenAIRE

    Meinrenken, Eckhard

    2016-01-01

    We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.

  8. Information Geometry and Evolutionary Game Theory

    CERN Document Server

    Harper, Marc

    2009-01-01

    The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.

  9. 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.

  10. A Multivariate Model of Achievement in Geometry

    Science.gov (United States)

    Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha

    2014-01-01

    Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

  11. 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.

  12. Applications Of Nonclassical Geometry To String Theory

    CERN Document Server

    Zunger, Y

    2003-01-01

    String theory is built on a foundation of geometry. This thesis examines several applications of geometry beyond the classical Riemannian geometry of curved surfaces. The first part considers the use of extended spaces with internal dimensions to each point (“twistors”) to probe systems with a great deal of symmetry but complicated dynamics. These systems are of critical interest in understanding holographic phenomena in string theory and the origins of entropy. We develop a twistor formulation of coset spaces and use this to write simplified actions for particles and strings on anti-de Sitter space, which are easier to quantize than the ordinary (highly nonlinear) actions. In the second part, we consider two aspects of noncommutative geometry, a generalization of ordinary geometry where points are “fuzzed out” and functions of space become noncommuting operators. We first examine strings with one endpoint on a D-brane in a background magnetic field. (Strings with both ...

  13. Geometry of Cauchy-Riemann submanifolds

    CERN Document Server

    Shahid, Mohammad; Al-Solamy, Falleh

    2016-01-01

    This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

  14. Transformations of units and world's geometry

    CERN Document Server

    Quirós, I

    2000-01-01

    The issue of the transformations of units is treated, mainly, in a geometrical context. Spacetime singularities are shown to be a consequence of a wrong choice of the geometrical formulation of the laws of gravitation. This result is discussed, in particular, for Friedmann-Robertson-Walker cosmology. It is also shown that Weyl geometry is a consistent framework for the formulation of the gravitational laws since the basic laws on which this geometry rests are invariant under the one-parameter Abelian group of units transformations studied in the paper. Riemann geometry does not fulfill this requirement. Arguments are given that point at Weyl geometry as a geometry implicitly containing the quantum effects of matter. The notion of geometrical relativity is presented. This notion may represent a natural extension of general relativity to include invariance under the group of units transformations.

  15. Discrete quantum geometries and their effective dimension

    CERN Document Server

    Thürigen, 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 ef...

  16. Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry

    Science.gov (United States)

    Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare

    2013-01-01

    A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…

  17. 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…

  18. 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…

  19. Geometry-Related Children's Literature Improves the Geometry Achievement and Attitudes of Second-Grade Students

    Science.gov (United States)

    McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis

    2017-01-01

    Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

  20. Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry

    Science.gov (United States)

    Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare

    2013-01-01

    A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…

  1. 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…

  2. Geometry-Related Children's Literature Improves the Geometry Achievement and Attitudes of Second-Grade Students

    Science.gov (United States)

    McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis

    2017-01-01

    Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

  3. Operating Cell Temperature Determination in Flat-Plate Photovoltaic Modules; Calculo de la Temperature de Operacion de Celulas Solares en un Panel Fotovoltaico Plano

    Energy Technology Data Exchange (ETDEWEB)

    Chenlo, F.

    2002-07-01

    Two procedures (simplified and complete) to determine the operating cell temperature in photovoltaic modules operating in real conditions assuming isothermal stationary modules are presented in this work. Some examples are included that show the dependence of this temperature on several environment (sky, ground and ambient temperatures, solar irradiance, wind speed, etc.) and structural (module geometry and size, encapsulating materials, antirreflexive optical coatings, etc) factors and also on electrical module performance. In a further step temperature profiles for non-isothermal modules are analysed besides transitory effects due to variable irradiance and wind gusts. (Author)

  4. basement reservoir geometry and properties

    Science.gov (United States)

    Walter, bastien; Geraud, yves; Diraison, marc

    2017-04-01

    Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre

  5. Primes, Geometry and Condensed Matter

    Directory of Open Access Journals (Sweden)

    Al Rabeh R. H.

    2009-07-01

    Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of

  6. Primes, Geometry and Condensed Matter

    Directory of Open Access Journals (Sweden)

    Al Rabeh R. H.

    2009-07-01

    Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that

  7. Mathematical and numerical modeling of the turbulent dispersion of reactive pollutant plumes; Modelacion matematica y numerica de la dispersion turbulenta de plumas de contaminantes reactivos

    Energy Technology Data Exchange (ETDEWEB)

    Rodas Grapain, Arturo

    1999-07-01

    One of the main problems involved in air quality models to calculate the pollutant concentration in a single point in the space and time, is the complexity of the numerical method. Even though the numerical methods are based on sophisticated and elaborated mathematics. They present two important and inevitable drawbacks: the stability of the numerical method. This means that its capacity to obtain reliable convergency in relation to the calculated values and real values is limited. The time and memory consumption. The high machine memory used to perform the numerical procedures and the time needed to prepare such procedures. Another problem is the mathematical basis of the structure of the air quality model. Commonly, simple models can perform quick estimations; however they are not exact contrary to the complex and elaborated models. In order to employ these complex models a high speed computer (workstations or Cray computer) is required. For this reason, this work presents a model approach with a relatively simple theoretical structure. The structure of this model named MOTTQUIP (modelo de transporte turbulento y quimica de plumas) can provide good results in point concentration operations. These results are compared with those obtained by two moderately complex mathematical models (Georgopoulos-Seinfeld and Lipphardt reactive plume models). The model developed in this work, shows a special feature where the solution of the differential equations are not involved explicitly. Therefore, it does not present the typical difficult in solving this kind of equations with the traditional numerical methods. [Spanish] Uno de los principales problemas que se presentan en los modelos de calidad del aire para el calculo de la concentracion de un cierto contaminante, para un punto dado en el espacio y en el tiempo, es la complejidad del metodo numerico involucrado para este fin, debido a que dichos metodos de calculo estan basados en matematicas sofisticadas y muy

  8. Moving KML geometry elements within Google Earth

    Science.gov (United States)

    Zhu, Liang-feng; Wang, Xi-feng; Pan, Xin

    2014-11-01

    During the process of modeling and visualizing geospatial information on the Google Earth virtual globe, there is an increasing demand to carry out such operations as moving geospatial objects defined by KML geometry elements horizontally or vertically. Due to the absence of the functionality and user interface for performing the moving transformation, it is either hard or impossible to interactively move multiple geospatial objects only using the existing Google Earth desktop application, especially when the data sets are in large volume. In this paper, we present a general framework and associated implementation methods for moving multiple KML geometry elements within Google Earth. In our proposed framework, we first load KML objects into the Google Earth plug-in, and then extract KML geometry elements from the imported KML objects. Subsequently, we interactively control the movement distance along a specified orientation by employing a custom user interface, calculate the transformed geographic location for each KML geometry element, and adjust geographic coordinates of the points in each KML objects. And finally, transformed KML geometry elements can be displayed in Google Earth for 3D visualization and spatial analysis. A key advantage of the proposed framework is that it provides a simple, uniform and efficient user interface for moving multiple KML geometry elements within Google Earth. More importantly, the proposed framework and associated implementations can be conveniently integrated into other customizable Google Earth applications to support interactively visualizing and analyzing geospatial objects defined by KML geometry elements.

  9. Discrete quantum geometries and their effective dimension

    Energy Technology Data Exchange (ETDEWEB)

    Thuerigen, Johannes

    2015-07-02

    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.

  10. Differential geometry and topology of curves

    CERN Document Server

    Animov, Yu

    2001-01-01

    Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

  11. A Gyrovector Space Approach to Hyperbolic Geometry

    CERN Document Server

    Ungar, Abraham

    2009-01-01

    The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T

  12. A proposal of foundation of spacetime geometry

    CERN Document Server

    Tresguerres, Romualdo

    2014-01-01

    A common approach to metric-affine, local Poincar\\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to alternative concepts of spacetime. In particular, the construction of the Minkowski metric, and its required invariance, allows either to reorganize the original affine bundle as a metric-affine geometry with explicit Lorentz symmetry, or to restrict it to a Poincar\\'e geometry, both of them constituting the background of a wide class of gauge theories of gravity.

  13. Digital and discrete geometry theory and algorithms

    CERN Document Server

    Chen, Li

    2014-01-01

    This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

  14. Information geometry near randomness and near independence

    CERN Document Server

    Arwini, Khadiga A

    2008-01-01

    This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.

  15. Wormhole inspired by non-commutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Rahaman, Farook, E-mail: rahaman@iucaa.ernet.in [Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal (India); Karmakar, Sreya, E-mail: sreya.karmakar@gmail.com [Department of Physics, Calcutta Institute of Engineering and Management, Kolkata 700040, West Bengal (India); Karar, Indrani, E-mail: indrani.karar08@gmail.com [Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bengal (India); Ray, Saibal, E-mail: saibal@iucaa.ernet.in [Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700010, West Bengal (India)

    2015-06-30

    In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.

  16. Wormhole inspired by non-commutative geometry

    Directory of Open Access Journals (Sweden)

    Farook Rahaman

    2015-06-01

    Full Text Available In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV. A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.

  17. On Discrete Differential Geometry in Twistor Space

    OpenAIRE

    2011-01-01

    In this paper we introduce a discrete integrable system generalizing the discrete (real) cross-ratio system in $S^4$ to complex values of a generalized cross-ratio by considering $S^4$ as a real section of the complex Pl\\"ucker quadric, realized as the space of two-spheres in $S^4.$ We develop the geometry of the Pl\\"ucker quadric by examining the novel contact properties of two-spheres in $S^4,$ generalizing classical Lie geometry in $S^3.$ Discrete differential geometry aims to develop disc...

  18. Fractal geometry mathematical foundations and applications

    CERN Document Server

    Falconer, Kenneth

    2013-01-01

    The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

  19. Fault geometry and earthquake mechanics

    Directory of Open Access Journals (Sweden)

    D. J. Andrews

    1994-06-01

    Full Text Available Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1 regeneration of stress irregularities in an earthquake; 2 the concentration of stress drop in an earthquake into asperities; 3 starting and stopping of earthquake slip at fault junctions, and 4 self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the

  20. Spherical, hyperbolic and other projective geometries: convexity, duality, transitions

    OpenAIRE

    Fillastre, François; Seppi, Andrea

    2016-01-01

    Since the end of the 19th century, and after the works of F. Klein and H. Poincar\\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a "limit" of both geometries. Then all the geometries that can be obtained in this way. Some of these geometries had a rich development, most remarkably hyperbolic geometry and the Lorentzian geometries of Minkowski, de Sitter and anti-de Sitter spaces, ...

  1. Kerr geometry in f(T) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)

    2015-02-01

    Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)

  2. Geometry and scaling of cosmic voids

    CERN Document Server

    Gaite, Jose

    2008-01-01

    CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objective is to understand the geometry of cosmic voids in relation to a fractal structure of matter. We intend to distinguish monofractal voids from multifractal voids, regarding their scaling properties. We plan to analyse voids in the distributions of mass concentrations (halos) in a multifractal and their relation to galaxy voids. METHODS: We make a statistical analysis of point distributions based on the void probability function and correlation functions. We assume that voids are spherical and devise a simple spherical void finder. For continuous mass distributions, we employ the methods of fractal geometry. We confirm the analytical predictions with numerical simula...

  3. Evolutionary Algorithm Geometry Optimization of Optical Antennas

    Directory of Open Access Journals (Sweden)

    Ramón Díaz de León-Zapata

    2016-01-01

    Full Text Available Printed circuit antennas have been used for the detection of electromagnetic radiation at a wide range of frequencies that go from radio frequencies (RF up to optical frequencies. The design of printed antennas at optical frequencies has been done by using design rules derived from the radio frequency domain which do not take into account the dispersion of material parameters at optical frequencies. This can make traditional RF antenna design not suitable for optical antenna design. This work presents the results of using a genetic algorithm (GA for obtaining an optimized geometry (unconventional geometries that may be used as optical regime antennas to capture electromagnetic waves. The radiation patterns and optical properties of the GA generated geometries were compared with the conventional dipole geometry. The characterizations were conducted via finite element method (FEM computational simulations.

  4. ARC Code TI: Geometry Manipulation Protocol (GMP)

    Data.gov (United States)

    National Aeronautics and Space Administration — The Geometry Manipulation Protocol (GMP) is a library which serializes datatypes between XML and ANSI C data structures to support CFD applications. This library...

  5. Homological mirror symmetry and tropical geometry

    CERN Document Server

    Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia

    2014-01-01

    The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...

  6. Attitudes of High School Students towards Geometry

    Directory of Open Access Journals (Sweden)

    Esat Avcı

    2014-12-01

    Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words:    Attitudes towards geometry, high school geometry lesson, attitude scale

  7. The Geometry of Soft Materials: A Primer

    OpenAIRE

    2002-01-01

    We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

  8. Playing with geometry in preschool education

    Directory of Open Access Journals (Sweden)

    Filipa Balinha

    2016-12-01

    Full Text Available This article describes the exploration of geometry tasks with a group of children attending pre-school education in Braga. Four tasks were presented in the context of geometry to a group of 20 children aged 3 to 4 years. The tasks included the approach to geometric figures, the topological relations, maps reading and spatial orientation. As it is described in this article, it became clear that with practice, at this age, you can work geometry and mathematics as long the tasks are presented in the form of games or challenges. It is important that the tasks are designed for pre-school education attending the curriculum documents. In this way, we can connect the several areas of knowledgeand build interesting and challenging tasks to help children grow and learn while playing.Keywords: Mathematics; Kindergarten; Geometry; Preschool

  9. Noncommutative geometry, Lorentzian structures and causality

    CERN Document Server

    Franco, Nicolas

    2014-01-01

    The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \\`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.

  10. Emergence of wave equations from quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Majid, Shahn [School of Mathematical Sciences, Queen Mary University of London, 327 Mile End Rd, London E1 4NS (United Kingdom)

    2012-09-24

    We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.

  11. 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.

  12. 10th China-Japan Geometry Conference

    CERN Document Server

    Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping

    2016-01-01

    Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...

  13. Gravitational lensing of wormholes in noncommutative geometry

    CERN Document Server

    Kuhfittig, Peter K F

    2015-01-01

    It has been shown that a noncommutative-geometry background may be able to support traversable wormholes. This paper discusses the possible detection of such wormholes in the outer regions of galactic halos by means of gravitational lensing. The procedure allows a comparison to other models such as the NFW model and f(R) modified gravity and is likely to favor a model based on noncommutative geometry.

  14. Geometry and quantization of moduli spaces

    CERN Document Server

    Andersen, Jørgen; Riera, Ignasi

    2016-01-01

    This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

  15. Geometry of quantum computation with qutrits.

    Science.gov (United States)

    Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming

    2013-01-01

    Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.

  16. Quantum fluctuations of geometry in hot Universe

    CERN Document Server

    Bialynicki-Birula, Iwo

    2015-01-01

    The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The field configurations are described by the linearized Riemann-Weyl tensor. The probability distribution has a foam-like structure; prevailing configurations are those with the large changes of geometry at nearby points. Striking differences are found between the fluctuations of the electromagnetic field and the gravitational field.

  17. Mechanical Theorem Proving in Tarski's geometry.

    OpenAIRE

    Narboux, Julien

    2006-01-01

    International audience; This paper describes the mechanization of the proofs of the first height chapters of Schwabäuser, Szmielew and Tarski's book: Metamathematische Methoden in der Geometrie. The goal of this development is to provide foundations for other formalizations of geometry and implementations of decision procedures. We compare the mechanized proofs with the informal proofs. We also compare this piece of formalization with the previous work done about Hilbert's Gründlagen der Geom...

  18. Phase distribution in complex geometry conduits

    Energy Technology Data Exchange (ETDEWEB)

    Lahey, R.T. Jr.; Lopez de Bertodano, M.; Jones, O.C. Jr.

    1992-12-31

    Some of the most important and challenging problems in two-phase flow today have to do with the understanding and prediction of multidimensional phenomena, in particular, lateral phase distribution in both simple and complex geometry conduits. A prior review paper summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paper is to update that review, with particular emphasis on complex geometry conduit predictive capabilities.

  19. From information geometry to quantum theory

    Energy Technology Data Exchange (ETDEWEB)

    Goyal, Philip [Perimeter Institute, Waterloo (Canada)], E-mail: pgoyal@perimeterinstitute.ca

    2010-02-15

    In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, measurement simulability, and global gauge invariance. When these features are appropriately formalized within an information geometric framework, and combined with a novel information-theoretic principle, the central features of the finite-dimensional quantum formalism can be reconstructed.

  20. Classical Geometry and Target Space Duality

    OpenAIRE

    1995-01-01

    This is the written version of lectures presented at Cargese 95. A new formulation for a ``restricted'' type of target space duality in classical two dimensional nonlinear sigma models is presented. The main idea is summarized by the analogy: euclidean geometry is to riemannian geometry as toroidal target space duality is to ``restricted'' target space duality. The target space is not required to possess symmetry. These lectures only discuss the local theory. The restricted target space duali...

  1. An Elementary Account of Amari's Expected Geometry

    OpenAIRE

    1999-01-01

    Differential geometry has found fruitful application in statistical inference.\\ud In particular, Amari’s (1990) expected geometry is used in higher order\\ud asymptotic analysis, and in the study of sufficiency and ancillarity. However,\\ud we can see three drawbacks to the use of a differential geometric approach in\\ud econometrics and statistics more generally. Firstly, the mathematics is unfamiliar\\ud and the terms involved can be difficult for the econometrician to fully\\ud appreciate. Seco...

  2. Ordinary differential equations in affine geometry

    Directory of Open Access Journals (Sweden)

    Salvador Gigena

    1996-05-01

    Full Text Available The method of qualitative analysis is used, as applied to a class of fourth order, nonlinear ordinary differential equations, in order to classify, both locally and globally, two classes of hypersurfaces of decomposable type in affine geometry: those with constant unimodular affine mean curvature L , and those with constant Riemannian scalar curvature R. This allows to provide a large number of new examples of hypersurfaces in affine geometry.

  3. Ordinary differential equations in affine geometry

    OpenAIRE

    Salvador Gigena

    1996-01-01

    The method of qualitative analysis is used, as applied to a class of fourth order, nonlinear ordinary differential equations, in order to classify, both locally and globally, two classes of hypersurfaces of decomposable type in affine geometry: those with constant unimodular affine mean curvature L , and those with constant Riemannian scalar curvature R. This allows to provide a large number of new examples of hypersurfaces in affine geometry.

  4. Kaluza-Klein Aspects of Noncommutative Geometry

    CERN Document Server

    Madore, J

    2015-01-01

    Using some elementary methods from noncommutative geometry a structure is given to a point of space-time which is different from and simpler than that which would come from extra dimensions. The structure is described by a supplementary factor in the algebra which in noncommutative geometry replaces the algebra of functions. Using different examples of algebras it is shown that the extra structure can be used to describe spin or isospin.

  5. Herbrand's theorem and non-Euclidean geometry

    OpenAIRE

    Beeson, Michael; Boutry, Pierre; Narboux, Julien

    2014-01-01

    International audience; We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.

  6. Perspectives in Analysis, Geometry, and Topology

    CERN Document Server

    Itenberg, I V; Passare, Mikael

    2012-01-01

    The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

  7. 误诊为急性结石性胆囊炎31例病例分析%The analysis of misdiagnosed as acute calculos cholecystitis in 31 cases.

    Institute of Scientific and Technical Information of China (English)

    陈永友

    2012-01-01

    Objective To analyze and explore the causes of misdiagnosed as acute calculos cholecystitis. Methods Thirty - one cases misdiagnosed as acute calculous cholecystitis in our hospital from July 2000 to May 2012 were retrospectively analyzed and summarized. Results Thirty - one patients with cholecystolithiasis were misdiagnosed as acute calculous cholecystitis, The final diagnosis of misdiagnosis cases: 6 cases of acute myocardial infarction , 5 cases of herpes zoster, 4 cases of carcinoma of gallbladder, 3 cases of high - position appendicitis, 2 cases of pancreatitis, 2 cases of pneumonia, 2 cases of colon tumor, 2 cases of upper digestive tract perforation, 2 cases of renal calculus, 1 case of dissection of aorta, 1 case of pleuritis, 1 case of ascariasis of biliary tract. Conclusion Dont detailed inquest the case history, examine the body carelessly, lack of relevant knowledge and experience, ignoring the other disease diagnosis while gallstones found were the main causes of misdiagnosis.%目的 分析、总结其他疾病误诊为急性结石性胆囊炎的原因,积累经验.方法 对2000年7月至2012 年5月收治的31例临床误诊为急性结石性胆囊炎病例进行回顾性分析、总结.结果 31例患者均因原有胆囊结石而误诊为急性结石性胆囊炎.误诊疾病的最终诊断为:急性心肌梗死6例(19.35%),带状疱疹5例(16.13%),胆囊癌4例(12.9%),高位阑尾炎3例(9.68%),胰腺炎2例(6.45%),肺炎2例(6.45%),结肠肿瘤2例(6.45%),上消化道穿孔2例(6.45%),右肾结石2例(6.45%),主动脉夹层1例(3.22%),胸膜炎1例(3.22%),胆道蛔虫1例(3.22%).结论询问病史不详细、查体不仔细、缺少对相关疾病鉴别诊断的知识和经验、发现胆囊结石而忽略其它疾病诊断是造成误诊的主要原因.

  8. Validation of Hiriart equation to compute steam production by the lip pressure method; Validacion de la ecuacion de Hiriart para calculo de gasto de vapor por el metodo de presion de labio

    Energy Technology Data Exchange (ETDEWEB)

    Flores Armenta, Magaly [Gerencia de Proyectos Geotermoelectricos de la Comision Federal de Electricidad, Morelia (Mexico)

    1996-09-01

    Mainly in new geothermal wells, it is necessary to evaluate the production in a very fast, simple and not expensive way, to know the convenience to install surface equipment, such as silencers and separators, to drive the steam to the commercial gathering system. In practice, one of the most known methods is the lip pressure one, which requires a simple set of installations. The objective of this paper is to validate the steam flow rate calculated by the lip pressure method, with respect to the ASME method. The ASME method is known for its accuracy, and is done by measuring the steam and liquid after a high pressure separator, by an orifice plate of known diameter and a triangular weir. Results of the validation show up the feasibility of application of the lip pressure method by using a simple adjustment equation. Percentage of mistake results less than 1%, without any notable influence of the production enthalpy. That equation to be applied in a general case, is as follows: Q{nu} =(20642)(F*P*D{sup 2}/{radical}h-2000). For the particular case of the Los Azufres geothermal field, the equation is: Q{nu}= 810*P*D{sup 2} [Espanol] En los pozos geotermicos, principalmente en los nuevos, es necesario evaluar su produccion de manera rapida, sencilla y economica, para determinar la conveniencia de instalar equipo superficial, como separadores, silenciadores, etc., que permita la integracion del vapor al sistema comercial de generacion electrica. Para fines practicos uno de los metodos mas conocidos es el de presion de labio, que solo requiere un arreglo sencillo de instalaciones superficiales. En este documento se validan y ajustan los calculos de produccion de vapor por ese metodo de presion de labio, con respecto a las mediciones exactas efectuadas con el metodo ASME. Este ultimo es reconocido internacionalmente por su precision, y se lleva a cabo separando la mezcla obtenida en superficie en un recipiente a presion para medir el vapor a traves de una placa de orificio

  9. Geometry-induced protein pattern formation.

    Science.gov (United States)

    Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin

    2016-01-19

    Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.

  10. What is inverse-geometry CT?

    Science.gov (United States)

    Schmidt, Taly Gilat

    2011-01-01

    Inverse-geometry computed tomography (IGCT) systems are being developed to provide improved volumetric imaging. In conventional multislice CT systems, x-rays are emitted from a small area and irradiate a large-area detector. In an IGCT system, x-ray sources are distributed over a large area, with each beam irradiating a small-area detector. Therefore, in the inverse geometry, a series of narrow x-ray beams are switched on and off while the gantry rotates. In conventional CT geometry, cone-beam and scatter artifacts increase with the imaged volume thickness. An inverse geometry may be less susceptible to scatter effects, because only a fraction of the field of view is irradiated at one time. The distributed source in the inverse geometry potentially improves sampling, leading to reduced cone-beam artifacts. In the inverse geometry, the tube current may be adjusted separately for each source location, which potentially reduces dose. Multiple IGCT prototypes have been constructed and tested on phantoms. A gantry-based IGCT system with one-second gantry rotation was developed, and images of phantoms and small animals were successfully acquired. Clinical feasibility with acceptable noise levels and scan times has not yet been shown. Overall, results from prototype systems suggest that the inverse geometry will enable imaging of a thick volume (∼16 cm) while potentially reducing cone-beam artifacts, scatter effects, and radiation dose. The magnitude of these benefits will depend on the specific IGCT implementation and need to be quantified relative to comparable multislice scanners. Copyright © 2011 Society of Cardiovascular Computed Tomography. Published by Elsevier Inc. All rights reserved.

  11. 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

  12. 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...

  13. Quantum Computing in Non Euclidean Geometry

    CERN Document Server

    Resconi, Germano

    2009-01-01

    The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics a...

  14. Calculation of shielding of X rays in radiotherapy facilities with computer aid; Calculo de blindagem para instalacoes de radioterapia por raios X com auxilio de computador

    Energy Technology Data Exchange (ETDEWEB)

    Pedrosa, Paulo Sergio; Farias, Marcos Santana [Instituto de Engenharia Nuclear (IEN), Rio de Janeiro, RJ (Brazil)]. E-mail: pedrosa@ien.gov.br; msantana@ien.gov.br; Gavazza, Sergio [Instituto Militar de Engenharia (IME), Rio de Janeiro, RJ (Brazil). Dept. das Ciencias Fundamentais, Radiacao e Meio Ambiente]. E-mail: gavazza@ugf.br

    2005-07-01

    This work presents a methodology for calculation of shielding of X rays in radiotherapy facilities with computer aid. A friendly program, called RadTeraX, was developed in programming language Delphi that, through manual data input of a basic project of architecture and of some parameters, interprets the geometry and calculates the shielding of the walls, ground and roof of a radiotherapy installation for X rays. As a final product, this program supplies a graphic screen in the computer with all the input data and the calculation of the shielding, besides the respective calculation memory. Still today, in Brazil, the calculation of the shielding for radiotherapy facilities with X rays has been made based on recommendations of NCRP-49, that establishes a necessary calculation methodology to the elaboration of a shielding project. However, in high energies, where it is necessary the construction of a maze, NCRP-49 is insufficient, so that in this field, studies were made originating an article that proposes a solution for the problem and this solution was implemented in the program. The program can be applied in the practical execution of shielding projects for radiotherapy facilities and in didactic way in comparison with NCRP-49 and has been registered under number 00059420 at INPI - Instituto Nacional da Propriedade Industrial (National Institute of Industrial Property). (author)

  15. Laws of granular solids: geometry and topology.

    Science.gov (United States)

    DeGiuli, Eric; McElwaine, Jim

    2011-10-01

    In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions.

  16. Interfacial geometry dictates cancer cell tumorigenicity

    Science.gov (United States)

    Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.

    2016-08-01

    Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.

  17. Lobachevsky geometry and modern nonlinear problems

    CERN Document Server

    Popov, Andrey

    2014-01-01

    This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.

  18. First-order Dyson coordinates and geometry.

    Science.gov (United States)

    Hermes, Matthew R; Hirata, So

    2013-08-15

    The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.

  19. Dynamical Riemannian Geometry and Plant Growth

    CERN Document Server

    Pulwicki, Julia

    2010-01-01

    A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry, (b) a transport velocity of the material and (c) a material density. While the model was developed primarily to determine the effects of geometry (i.e. curvature and scale changes) in two-dimensional systems such as leaves and petals, it can be applied to any dimension. Results for one dimensional systems are presented and compared to measurements of growth made on blades of grass and corn roots. It is found that the model is able to reproduce many features associated with botanical growth.

  20. Conference on Strings, Duality, and Geometry

    CERN Document Server

    Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV

    2002-01-01

    This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...

  1. The Background Geometry of DLCQ Supergravity

    CERN Document Server

    Hyun, S

    1998-01-01

    By following Seiberg's prescriptions on DLCQ of M theory, we give the background geometries of DLCQ supergravity associated with $N$ sector of DLCQ of M theory on $T^p$. Most of these are the product of anti-de Sitter spacetimes and spheres, which have been found as the spontaneous compactifications of eleven dimensional supergravity long time ago and also are revisited recently by Maldacena by considering the near horizon geometry of various D-branes in appropriate limit. Those geometries are maximally symmetric and have full 32 supersymmetries of eleven dimensional supergravity, which agrees with the number of supersymmetries of DLCQ M theory. This tells us that in the large $N$ limit of DLCQ M theory, we get M/string theory on these nontrivial background.

  2. Strontium clusters: electronic and geometry shell effects

    DEFF Research Database (Denmark)

    Lyalin, Andrey G.; Solov'yov, Ilia; Greiner, Walter

    2008-01-01

    is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. It is shown that the excessive charge essentially affects the optimized geometry......The optimized structure and electronic properties of neutral, singly and doubly charged strontium clusters have been investigated using it ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly and doubly...... charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, and spectra of the density of electronic states (DOS). It is demonstrated that the size-evolution of structural and electronic properties of strontium clusters...

  3. Geometry and dynamics of integrable systems

    CERN Document Server

    Matveev, Vladimir

    2016-01-01

    Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...

  4. The geometry of soil crack networks

    CERN Document Server

    Chertkov, V Y

    2014-01-01

    The subject of this work is the modification and specification of an approach to detail the estimation of soil crack network characteristics. The modification aims at accounting for the corrected soil crack volume based on the corrected shrinkage geometry factor compared to known estimates of crack volume and shrinkage geometry factor. The mode of the correction relies on recent results of the soil reference shrinkage curve. The main exposition follows the preliminary brief review of available approaches to dealing with the geometry of soil crack networks and gives a preliminary brief summary of the approach to be modified and specified. To validate and illustrate the modified approach the latter is used in the analysis of available data on soil cracking in a lysimeter.

  5. From groups to geometry and back

    CERN Document Server

    Climenhaga, Vaughn

    2017-01-01

    Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...

  6. ON THE THEORIES OF HYDRAULIC GEOMETRY

    Institute of Scientific and Technical Information of China (English)

    Vijay P. SINGH

    2003-01-01

    Hydraulic geometry is of fundamental importance in planning, design, and management of river engineering and training works. Although some concepts of hydraulic geometry were proposed toward the end of the nineteenth century, the real impetus toward formulating a theory of hydraulic geometry was provided by the work of Leopold and Maddock (1953). A number of theories have since been proposed.Some of the theories are interrelated but others are based on quite different principles. All theories,however, assume that the river flow is steady and uniform and the river tends to attain a state of equilibrium or quasi-equilibrium. The differences are due to the differences in hydraulic mechanisms that the theories employ to explain the attainment of equilibrium by the river.

  7. Geometry of curves and surfaces with Maple

    CERN Document Server

    Rovenski, Vladimir

    2000-01-01

    This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource...

  8. International conference on Algebraic and Complex Geometry

    CERN Document Server

    Kloosterman, Remke; Schütt, Matthias; Springer Proceedings in Mathematics & Statistics : Volume 71

    2014-01-01

    Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the ...

  9. Lectures on formal and rigid geometry

    CERN Document Server

    Bosch, Siegfried

    2014-01-01

    A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.

  10. Emergent hyperbolic geometry of growing simplicial complexes

    CERN Document Server

    Bianconi, Ginestra

    2016-01-01

    A large variety of interacting complex systems, including brain functional networks, protein interactions and collaboration networks is characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such they are ideal structures to investigate the hidden geometry of complex networks and explore whether this geometry is hyperbolic. Here we show an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display all the universal properties of real complex networks. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by dramatic changes in the n...

  11. Detector Geometry Simulation Using GEANT4

    Directory of Open Access Journals (Sweden)

    Daisy Kalra

    2015-08-01

    Full Text Available Neutrino oscillation is an important phenomenon to explain the massive nature of neutrinos. This quantum mechanical phenomenon can be understood as mixing in quark sector just like the one we have in lepton sector. Observed deficit of solar neutrino flux is explained through neutrino oscillations and this study is the only way to investigate for small difference of neutrino masses thus gives signatures for the physics beyond Standard Model. Experimental results by Superkamiokande put a huge interest of experimentalists in neutrino field. In the present article after discussing the theoretical background of neutrinos and their status in standard model, latest important long baseline neutrino oscillations experiments as NOvA and LBNE has been discussed. Straw Tube Detector, an important part of LBNE-near detector, has been reviewed the geometry of which is studied through a software Geometry and Tracking (Geant4. Using Geant4, an important aspect of detector geometry and simulation has been studied.

  12. Geometry of manifolds with area metric

    CERN Document Server

    Schuller, F P

    2005-01-01

    We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, showing that a general area metric is generated by a finite collection of metrics rather than by a single one. Employing curvature invariants for area metric manifolds we devise an entirely new class of gravity theories with inherently stringy character, and discuss gauge matter actions.

  13. Geometric Monte Carlo and Black Janus Geometries

    CERN Document Server

    Bak, Dongsu; Kim, Kyung Kiu; Min, Hyunsoo; Song, Jeong-Pil

    2016-01-01

    We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

  14. 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…

  15. Three Approaches in Computational Geometry and Topology : Persistent Homology, Discrete Differential Geometry and Discrete Morse Theory

    OpenAIRE

    Botnan, Magnus Bakke

    2011-01-01

    We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.

  16. The organization of room geometry and object layout geometry in human memory.

    Science.gov (United States)

    Sluzenski, Julia; McNamara, Timothy P

    2011-08-01

    Research with humans and with nonhuman species has suggested a special role of room geometry in spatial memory functioning. In two experiments, participants learned the configuration of a room with four corners, along with the configuration of four objects within the room, while standing in a fixed position at the room's periphery. The configurations were either rectangular (Experiment 1) or irregular (Experiment 2). Room geometry was not recalled better than object layout geometry, and memories for both configurations were orientation dependent. These results suggest that room geometry and object layout geometry are represented similarly in human memory, at least in situations that promote long-term learning of object locations. There were also some differences between corners and objects in orientation dependence, suggesting that the two sources of information are represented in similar but separate spatial reference systems. [corrected

  17. Planar Ion Trap Geometry for Microfabrication

    CERN Document Server

    Madsen, M J; Stick, D; Rabchuk, J A; Monroe, C

    2004-01-01

    We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This ion trap geometry may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers. PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+Cm

  18. Thin shells joining local cosmic string geometries

    Energy Technology Data Exchange (ETDEWEB)

    Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)

    2016-10-15

    In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)

  19. Riemannian geometry in an orthogonal frame

    CERN Document Server

    Cartan, Elie Joseph

    2001-01-01

    Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n

  20. Thin shells joining local cosmic string geometries

    CERN Document Server

    Eiroa, Ernesto F; Simeone, Claudio

    2016-01-01

    In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a standard thin shell and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.

  1. Recent topics in differential and analytic geometry

    CERN Document Server

    Ochiai, T

    1990-01-01

    Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters con

  2. The geometry of ordinary variational equations

    CERN Document Server

    Krupková, Olga

    1997-01-01

    The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.

  3. Exploring Concepts of Geometry not Euclidean

    Directory of Open Access Journals (Sweden)

    Luiz Ambrozi

    2016-02-01

    Full Text Available With this article we intend to propose different situations of teaching and learning, how they can be applied in schools, mediated by the use of concrete materials and Geogebra software, emphasizing the use of technology in the classroom, that this proposal has the role of assisting in the conceptualization and identification of elements of non-Euclidean geometry. In addition, this short course is designed to be a time of current and continuing education for teachers, with activities to be developed with dynamic geometry and based on the theory of Conceptual Fields of Vergnaud.

  4. Algebra and geometry of Hamilton's quaternions

    CERN Document Server

    Krishnaswami, Govind S

    2016-01-01

    Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.

  5. Two Approaches to Non-Commutative Geometry

    CERN Document Server

    Kisil, V V

    1997-01-01

    Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)--to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. Keywords: Heisenberg group, Weyl commutation relation, Manin plain, quantum groups, SL(2, R), Hardy space, Bergman space, Segal-Bargmann space, Szeg"o projection, Bergman projection, Clifford analysis, Moebius transformations, functional calculus, Weyl calculus (quantization), Berezin quantization, Wick ordering, quantum mechanics.

  6. Quasi-crystalline geometry for architectural structures

    DEFF Research Database (Denmark)

    Weizierl, Barbara; Wester, Ture

    2001-01-01

    Artikel på CD-Rom 8 sider. The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells....... The purpose of the paper is to investigate some possibilities for the application of Quasi-Crystal geometry for structures in architecture. The basis for the investigations is A: to use the Golden Cubes (the two different hexahedra consisting of rhombic facets where the length of the diagonals has the Golden...

  7. Thermal geometry from CFT at finite temperature

    Directory of Open Access Journals (Sweden)

    Wen-Cong Gan

    2016-09-01

    Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  8. Method for Determining Optimum Injector Inlet Geometry

    Science.gov (United States)

    Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)

    2015-01-01

    A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.

  9. Effect of geometry on hydrodynamic film thickness

    Science.gov (United States)

    Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.

    1978-01-01

    The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

  10. Computational fluid dynamics using CATIA created geometry

    Science.gov (United States)

    Gengler, Jeanne E.

    1989-07-01

    A method has been developed to link the geometry definition residing on a CAD/CAM system with a computational fluid dynamics (CFD) tool needed to evaluate aerodynamic designs and requiring the memory capacity of a supercomputer. Requirements for surfaces suitable for CFD analysis are discussed. Techniques for developing surfaces and verifying their smoothness are compared, showing the capability of the CAD/CAM system. The utilization of a CAD/CAM system to create a computational mesh is explained, and the mesh interaction with the geometry and input file preparation for the CFD analysis is discussed.

  11. Differential Geometry of Microlinear Frolicher Spaces I

    CERN Document Server

    Nishimura, Hirokazu

    2010-01-01

    The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, to appear in International Journal of Pure and Applied Mathematics] we have emancipated microlinearity from within well-adapted models to Frolicher spaces. Therein we have shown that Frolicher spaces which are microlinear as well as Weil exponentiable form a cartesian closed category. To make sure that such Frolicher spaces are the central object of infinite-dimensional differential geometry, we develop the theory of vector fields on them in this paper. The central result is that all vector fields on such a Frolicher space form a Lie algebra.

  12. Architectural Geometry and Fabrication-Aware Design

    KAUST Repository

    Pottmann, Helmut

    2013-04-27

    Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction remains a challenge. This is the source of numerous research problems many of which fall into the area of Geometric Computing and form part of a recently emerging research area, called "Architectural Geometry". The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important aspects of function and fabrication. © 2013 Kim Williams Books, Turin.

  13. Information geometry and the renormalization group.

    Science.gov (United States)

    Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata

    2015-11-01

    Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.

  14. Holographic geometries for condensed matter applications

    CERN Document Server

    Keranen, V

    2013-01-01

    Holographic modeling of strongly correlated many-body systems motivates the study of novel spacetime geometries where the scaling behavior of quantum critical systems is encoded into spacetime symmetries. Einstein-Dilaton-Maxwell theory has planar black brane solutions that exhibit Lifshitz scaling and in some cases hyperscaling violation. Entanglement entropy and Wilson loops in the dual field theory are studied by inserting simple geometric probes involving minimal surfaces into the black brane geometry. Coupling to background matter fields leads to interesting low-energy behavior in holographic models, such as U(1) symmetry breaking and emergent Lifshitz scaling.

  15. The VSEPR model of molecular geometry

    CERN Document Server

    Gillespie, Ronald J

    2012-01-01

    Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference was written by Istvan Hartiggai and the developer of VSEPR theory, Ronald J. Gillespie. In addition to its value as a text for courses in molecular geometry and chemistry, it constitutes a classic reference for professionals.Starting with coverage of the broader aspects of VSEPR, this volume narrows its focus to a succinct survey of the methods of structural determination. Additional topics include the appli

  16. Noncommutative geometry and Cayley-Smooth orders

    CERN Document Server

    Le Bruyn, Lieven

    2007-01-01

    Preface Introduction Noncommutative algebra Noncommutative geometryNoncommutative desingularizationsCayley-Hamilton Algebras Conjugacy classes of matrices Simultaneous conjugacy classesMatrix invariants and necklaces The trace algebraThe symmetric group Necklace relations Trace relations Cayley-Hamilton algebrasReconstructing Algebras Representation schemes Some algebraic geometry The Hilbert criterium Semisimple modules Some invariant theory Geometric reconstruction The Gerstenhaber-Hesselink theoremThe real moment mapÉtale Technology Étale topologyCentral simple algebrasSpectral sequencesTse

  17. MRI quantification of human spine cartilage endplate geometry: Comparison with age, degeneration, level, and disc geometry.

    Science.gov (United States)

    DeLucca, John F; Peloquin, John M; Smith, Lachlan J; Wright, Alexander C; Vresilovic, Edward J; Elliott, Dawn M

    2016-08-01

    Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3-1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1410-1417, 2016.

  18. Project-Based Learning to Explore Taxicab Geometry

    Science.gov (United States)

    Ada, Tuba; Kurtulus, Aytac

    2012-01-01

    In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…

  19. Alignment of Elementary Geometry Curriculum with Current Standards.

    Science.gov (United States)

    Pickreign, Jamar; Capps, Lelon R.

    2000-01-01

    Examines geometry language used in K-6 textbooks and compares the findings to language used in modern mathematics standards documents. Finds a substantial misalignment between the geometry presented in textbooks, the geometry teaching expectations of mathematics education professionals, and the geometry being assessed in student performance…

  20. Project-Based Learning to Explore Taxicab Geometry

    Science.gov (United States)

    Ada, Tuba; Kurtulus, Aytac

    2012-01-01

    In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…

  1. Magnetic resonance spectra and statistical geometry

    Science.gov (United States)

    Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate...

  2. Ordering in mechanical geometry theorem proving

    Institute of Scientific and Technical Information of China (English)

    李洪波¥

    1997-01-01

    Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.

  3. Methods of algebraic geometry in control theory

    CERN Document Server

    Falb, Peter

    1999-01-01

    "Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is qui...

  4. The Sticky Geometry of the Cosmic Web

    NARCIS (Netherlands)

    Hidding, Johan; Weygaert, Rien van de; Vegter, Gert; Jones, Bernard J.T.; Teillaud, Monique

    2012-01-01

    In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mech

  5. Some Penrose transforms in complex differential geometry

    Institute of Scientific and Technical Information of China (English)

    ANCO; Stephen; BLAND; John; EASTWOOD; Michael

    2006-01-01

    In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The otherconcerns obstructions to the embedding of CR structures on the three-sphere.

  6. Applications of Differential Geometry to Cartography

    Science.gov (United States)

    Benitez, Julio; Thome, Nestor

    2004-01-01

    This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

  7. The Geometry of the Universe: Part 1

    Science.gov (United States)

    Francis, Stephanie

    2009-01-01

    This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…

  8. Connecting Functions in Geometry and Algebra

    Science.gov (United States)

    Steketee, Scott; Scher, Daniel

    2016-01-01

    One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

  9. Rigid geometry of curves and their Jacobians

    CERN Document Server

    Lütkebohmert, Werner

    2016-01-01

    This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.

  10. Properties and geometry of radio pulsar emission

    NARCIS (Netherlands)

    Smits, Johannes Martinus

    2006-01-01

    This thesis consists of a number of studies on the radio emission of pulsars. The central topics are polarisation and multi frequency observations, which both lead to important information on the geometry of the emission. The first chapter introduces different aspects of pulsars that are related to

  11. Exact Random Walk Distributions using Noncommutative Geometry

    CERN Document Server

    Bellissard, J; Barelli, A; Claro, F; Bellissard, Jean; Camacho, Carlos J; Barelli, Armelle; Claro, Francisco

    1997-01-01

    Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large $ N $, taking into account finite size contributions.

  12. Determination of grain boundary geometry using TEM

    NARCIS (Netherlands)

    Jang, H.; Farkas, D.; Hosson, J.T.M. De

    1992-01-01

    An experimental method to obtain the grain boundary geometry using the transmission electron microscope is presented. The method allows Σ determination including grain boundary plane orientation. In order to determine the specialness of the grain boundary, three different criteria for maximum allowa

  13. Stages As Models of Scene Geometry

    NARCIS (Netherlands)

    Nedović, V.; Smeulders, A.W.M.; Redert, A.; Geusebroek, J.M.

    2010-01-01

    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,

  14. Geometry of the quantum projective plane

    CERN Document Server

    D'Andrea, Francesco

    2009-01-01

    We review some of the geometry of the quantum projective plane with emphasis on the construction of a differential calculus and of the Dirac operator (of a spin^c-structure). We also report on anti-self-dual connections on line bundles, the spectrum of the associated Laplacians, and the definition of classical and quantum characteristic classes.

  15. User Interface Design For Dynamic Geometry Software

    Directory of Open Access Journals (Sweden)

    Ulrich Kortenkamp

    2010-06-01

    Full Text Available In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.

  16. Geometry and the Design of Product Packaging

    Science.gov (United States)

    Cherico, Cindy M.

    2011-01-01

    The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

  17. Variable geometry two mode levitation trap

    Science.gov (United States)

    Babič, D.; Čadež, A.

    1999-11-01

    Construction and operation of the electrodynamic levitation trap which can be operated in a passive and an active mode is described. This combination together with variable electrode geometry simplifies the trap's design and simultaneously gives more flexibility with respect to different kinds of measurements. Sample measurements of mechanocaloric effect caused by nonuniform heating of a single levitated particle are presented and discussed.

  18. Geometry task sheets : grades pk-2

    CERN Document Server

    Rosenberg, Mary

    2009-01-01

    For grades PK-2, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.

  19. Geometry task sheets : grades 3-5

    CERN Document Server

    Rosenberg, Mary

    2009-01-01

    For grades 3-5, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.

  20. User Interface Design for Dynamic Geometry Software

    Science.gov (United States)

    Kortenkamp, Ulrich; Dohrmann, Christian

    2010-01-01

    In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.