WorldWideScience

Sample records for analytic geometries

  1. 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

  2. Overconvergent global analytic geometry

    OpenAIRE

    Paugam, Frédéric

    2014-01-01

    We define a notion of global analytic space with overconvergent structure sheaf. This gives an analog on a general base Banach ring of Grosse-Kloenne's overconvergent p-adic spaces and of Bambozzi's generalized affinoid varieties over R. This also gives an affinoid version of Berkovich's and Poineau's global analytic spaces. This affinoid approach allows the introduction of a notion of strict global analytic space, that has some relations with the ideas of Arakelov geometry, since the base ex...

  3. 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.

  4. Course of analytical geometry

    CERN Document Server

    Sharipov, Ruslan

    2011-01-01

    This book is a regular textbook of analytical geometry covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The stress is made on vector algebra by using skew-angular coordinates and by introducing some notations and prerequisites for understanding tensors. The book is addressed to students specializing in mathematics, physics, engineering, and technologies and to students of other specialities where educational standards require learning this subject.

  5. Global analytic geometry

    OpenAIRE

    Paugam, Frederic

    2008-01-01

    We define a new type of valuation of a ring that combines the notion of Krull valuation with that of multiplicative seminorm. This definition partially restores the broken symmetry between archimedean and non-archimedean valuations. This also allows us to define a notion of global analytic space that reconciles Berkovich's notion of analytic space of a (Banach) ring with Huber's notion of non-archimedean analytic space. After defining natural generalized valuation spectra and computing the sp...

  6. Programming system for analytic geometry

    International Nuclear Information System (INIS)

    After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry

  7. Some links between turtle geometry and analytic geometry

    OpenAIRE

    Rowe, Neil C.

    1984-01-01

    The computer language Logo facilitates the teaching of analytic geometry and calculus from the notion of curvature, through its turtle geometry facility. The author provides some theoretical basis for finding turtle geometry equivalents of familiar curves in analytic geometry, and vice versa, by some simple methods apparently previously unnoticed. In particular, he studied turtle geometry programs where the curvature of a line is a trigonometric function of its orientation. (Author)

  8. Bruhat-Tits buildings and analytic geometry

    OpenAIRE

    Remy, Bertrand; Thuillier, Amaury; Werner, Annette

    2012-01-01

    This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry canbe used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archimedean analytic geometry.

  9. Recent topics in differential and analytic geometry

    CERN Document Server

    Ochiai, T

    2014-01-01

    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

  10. Analytic Coleman-de Luccia Geometries

    Energy Technology Data Exchange (ETDEWEB)

    Dong, Xi; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC; Harlow, Daniel; /Stanford U., ITP /Stanford U., Phys. Dept.

    2012-02-16

    We present the necessary and sufficient conditions for a Euclidean scale factor to be a solution of the Coleman-de Luccia equations for some analytic potential V ({psi}), with a Lorentzian continuation describing the growth of a bubble of lower-energy vacuum surrounded by higher-energy vacuum. We then give a set of explicit examples that satisfy the conditions and thus are closed-form analytic examples of Coleman-de Luccia geometries.

  11. The analytic nodal method in cylindrical geometry

    International Nuclear Information System (INIS)

    Nodal diffusion methods have been used extensively in nuclear reactor calculations, specifically for their performance advantage, but also for their superior accuracy. More specifically, the Analytic Nodal Method (ANM), utilising the transverse integration principle, has been applied to numerous reactor problems with much success. In this work, a nodal diffusion method is developed for cylindrical geometry. Application of this method to three-dimensional (3D) cylindrical geometry has never been satisfactorily addressed and we propose a solution which entails the use of conformal mapping. A set of 1D-equations with an adjusted, geometrically dependent, inhomogeneous source, is obtained. This work describes the development of the method and associated test code, as well as its application to realistic reactor problems. Numerical results are given for the PBMR-400 MW benchmark problem, as well as for a 'cylindrisized' version of the well-known 3D LWR IAEA benchmark. Results highlight the improved accuracy and performance over finite-difference core solutions and investigate the applicability of nodal methods to 3D PBMR type problems. Results indicate that cylindrical nodal methods definitely have a place within PBMR applications, yielding performance advantage factors of 10 and 20 for 2D and 3D calculations, respectively, and advantage factors of the order of 1000 in the case of the LWR problem

  12. Gauge field geometry from complex and harmonic analyticities

    International Nuclear Information System (INIS)

    The concept of preservation of harmonic analyticity is applied to find unconstrained prepotentials of hyper-Kehler geometry. The geometric meaning of prepotentials is revealed with introducing extra central charge coordinates. Finally, we establish the one-to one correspondence between hyper-Kehler geometry and off-shell d=4, N=2 supersymmetric σ-models. Their general Lagrangian is shown to be uniquely composed of hyper-Kehler prepotentials, with the analytic space coordinates replaced by analytic hypermultiplet superfields defined on the same set of harmonic variables

  13. An analytical benchmark of MYRRHA ADS in cylindrical geometry

    International Nuclear Information System (INIS)

    In this study, the steady and transient neutronic behaviour of MYRRHA ADS is investigated. For this purpose, a recently proposed analytical benchmark of the diffusion kinetics as 1D slab model of the MYRRHA ADS concept developed in Belgium has been extended to the cylindrical geometry which represents the system more realistically. Analytical calculations are performed using the Customized Solution Method and numerical Laplace inversion techniques such as Fixed-Talbot and Gaver-Wynn-Rho algorithms. Results are compared with the finite element program FLEXPDE registered and they are found to be in complete agreement. The necessity of modeling the MYRHHA reactor in cylindrical geometry rather than slab geometry to obtain more realistic benchmark results is demonstrated. (orig.)

  14. Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics

    CERN Document Server

    Miron, Radu

    2012-01-01

    The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...

  15. Making and Understanding Analytic Geometry using the software Geogebra

    Directory of Open Access Journals (Sweden)

    Juliana Pereira Berti

    2016-02-01

    Full Text Available Mathematics Education has been undergoing transformations, especially with regard to the new requirements contained in legal documents. The various forms of expression language of mathematics and the use of technological resources are some of the suggestions of the National Curriculum Guidelines for Secondary Education. Thus, analytic geometry as a curricular component of mathematics also goes through these adjustments. In order to create alternatives to work that content and, thinking of the subject-object interaction, it developed a short course that uses the Dynamic Geometry through the GeoGebra software, as facilitator of the knowledge construction process. The methodology has seven activities. Are activities aimed at the line of study, including its equations and the relative position of the lines in the plan; the study of the circumference and the relative position of two circles in the plane; and the geometric interpretation of the ellipse, the parabola and hyperbole. We hope, therefore, provide educators strategies to reflect and rebuild their practices in math classes in high school.

  16. Analytic hyperbolic geometry in N dimensions an introduction

    CERN Document Server

    Ungar, Abraham Albert

    2014-01-01

    The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation la

  17. Analytical numerical methods applied to linear discontinuous angular approximations of the transport equation in slab geometry

    International Nuclear Information System (INIS)

    In this paper we describe two analytical numerical methods applied to one-speed slab-geometry deep penetration transport problems. The linear discontinuous (LDN) equations are used to approximate the monoenergetic Boltzmann equation in slab geometry; they are obtained by considering a linear expansion of the angular flux inside each of the N elements of a uniform angular grid. The two analytical numerical methods are referred to as the spectral Green's function (SGF) nodal method and the Laplace transform (LTLDN) method. The SGF nodal method and the LTLDN method generate numerical solutions to the LDN equations that are completely free of spatial approximations, apart from finite arithmetic considerations. Numerical results to typical model problems and suggestions for future work are also presented. (orig.)

  18. An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

    International Nuclear Information System (INIS)

    Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

  19. An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

    Energy Technology Data Exchange (ETDEWEB)

    Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.br, E-mail: vilhena@pq.cnpq.br [Programa de Pos Graduacao em Matematica Aplicada (DMPA/UFRGS), Universidade Federal do Rio Grande do Sul Porto Alegre, RS (Brazil); Bodmann, Bardo Ernst, E-mail: bardo.bodmann@ufrgs.br [Programa de Pos-Graduacao em Engenharia Mecanica (PROMEC/UFRGS), Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil)

    2011-07-01

    Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

  20. An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

    International Nuclear Information System (INIS)

    In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

  1. Human eye analytical and mesh-geometry models for ophthalmic dosimetry using MCNP6

    International Nuclear Information System (INIS)

    Eye tumors can be treated with brachytherapy using Co-60 plaques, I-125 seeds, among others materials. The human eye has regions particularly vulnerable to ionizing radiation (e.g. crystalline) and dosimetry for this region must be taken carefully. A mathematical model was proposed in the past [1] for the eye anatomy to be used in Monte Carlo simulations to account for dose distribution in ophthalmic brachytherapy. The model includes the description for internal structures of the eye that were not treated in previous works. The aim of this present work was to develop a new eye model based on the Mesh geometries of the MCNP6 code. The methodology utilized the ABAQUS/CAE (Simulia 3DS) software to build the Mesh geometry. For this work, an ophthalmic applicator containing up to 24 model Amersham 6711 I-125 seeds (Oncoseed) was used, positioned in contact with a generic tumor defined analytically inside the eye. The absorbed dose in eye structures like cornea, sclera, choroid, retina, vitreous body, lens, optical nerve and optical nerve wall were calculated using both models: analytical and MESH. (author)

  2. Human eye analytical and mesh-geometry models for ophthalmic dosimetry using MCNP6

    Energy Technology Data Exchange (ETDEWEB)

    Angelocci, Lucas V.; Fonseca, Gabriel P.; Yoriyaz, Helio, E-mail: hyoriyaz@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)

    2015-07-01

    Eye tumors can be treated with brachytherapy using Co-60 plaques, I-125 seeds, among others materials. The human eye has regions particularly vulnerable to ionizing radiation (e.g. crystalline) and dosimetry for this region must be taken carefully. A mathematical model was proposed in the past [1] for the eye anatomy to be used in Monte Carlo simulations to account for dose distribution in ophthalmic brachytherapy. The model includes the description for internal structures of the eye that were not treated in previous works. The aim of this present work was to develop a new eye model based on the Mesh geometries of the MCNP6 code. The methodology utilized the ABAQUS/CAE (Simulia 3DS) software to build the Mesh geometry. For this work, an ophthalmic applicator containing up to 24 model Amersham 6711 I-125 seeds (Oncoseed) was used, positioned in contact with a generic tumor defined analytically inside the eye. The absorbed dose in eye structures like cornea, sclera, choroid, retina, vitreous body, lens, optical nerve and optical nerve wall were calculated using both models: analytical and MESH. (author)

  3. Crossed source-detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results.

    Science.gov (United States)

    Berrocal, Edouard; Churmakov, Dmitry Y; Romanov, Vadim P; Jermy, Mark C; Meglinski, Igor V

    2005-05-01

    Sprays and other industrially relevant turbid media can be quantitatively characterized by light scattering. However, current optical diagnostic techniques generate errors in the intermediate scattering regime where the average number of light scattering is too great for the single scattering to be assumed, but too few for the diffusion approximation to be applied. Within this transitional single-to-multiple scattering regime, we consider a novel crossed source-detector geometry that allows the intensity of single scattering to be measured separately from the higher scattering orders. We verify Monte Carlo calculations that include the imperfections of the experiment against analytical results. We show quantitatively the influence of the detector numerical aperture and the angle between the source and the detector on the relative intensity of the scattering orders in the intermediate single-to-multiple scattering regime. Monte Carlo and analytical calculations of double light-scattering intensity are made with small particles that exhibit isotropic scattering. The agreement between Monte Carlo and analytical techniques validates use of the Monte Carlo approach in the intermediate scattering regime. Monte Carlo calculations are then performed for typical parameters of sprays and aerosols with anisotropic (Mie) scattering in the intermediate single-to-multiple scattering regime. PMID:15881059

  4. 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

  5. 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...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....

  6. Thin double layer approximation to describe streaming current fields in complex geometries: analytical framework and applications to microfluidics.

    Science.gov (United States)

    Brunet, Edouard; Ajdari, Armand

    2006-05-01

    We set up an analytical framework that allows one to describe and compute streaming effects and electro-osmosis on an equal footing. This framework relies on the thin double layer approximation commonly used for description of electroosmotic flows, but rarely used for streaming problems. Using this framework we quantitatively assess the induction of bulk streaming current patterns by topographic or charge heterogeneities on surfaces. This too also permits analytical computation of all linear electrokinetic effects in complex microfluidic geometries, and we discuss a few immediate applications. PMID:16803036

  7. The analytic nodal diffusion solver ANDES in multigroups for 3D rectangular geometry: Development and performance analysis

    OpenAIRE

    Lozano Montero, Juan Andrés; García Herranz, Nuria; Ahnert Iglesias, Carolina; Aragonés Beltrán, José María

    2008-01-01

    In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure i...

  8. Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

  9. A polynomial analytical method for one-group slab-geometry discrete ordinates heterogeneous problems

    International Nuclear Information System (INIS)

    In this work we evaluate polynomial approximations to obtain the transfer functions that appear in SGF auxiliary equations (Green's Functions) for monoenergetic linearly anisotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use Lagrange Polynomials in order to compare the numerical results with the ones generated by the standard SGF method applied to SN problems in heterogeneous domains. This work is a preliminary investigation of a new proposal for handling the transverse leakage terms that appear in the transverse-integrated one-dimensional SN equations when we use the SGF - exponential nodal method (SGF-ExpN) in multidimensional rectangular geometry. (author)

  10. Development of a kinetics code in three-dimensional hexagonal geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    During the last decade, the analytic function expansion nodal (AFEN) method has been developed and successfully applied to the static and kinetic problems in rectangular geometry and also applied to the static problems in hexagonal geometry. Although the results of two-dimensional hexagonal problems were very accurate, the accuracy becomes poor when the current hexagonal-z method is applied to the three-dimensional hexagonal problems. In this thesis, we develop a new method which improves the accuracy in three-dimensional hexagonal geometry and computerize the method into a new kinetics code. At first we add the edge fluxes in the upper and lower planes as additional nodal unknowns in axial direction to improve the accuracy. These nodal unknowns are updated through leakage balance equations by using a simple expansion of nodal fluxes at the vicinity of the edge fluxes. The relation of delayed neutron precursor densities between time steps is obtained analytically by using the transformed fluxes and assuming linear variations of the fission rates within a time step. The code developed for the steady state is verified in the cases of 2-D VVER-1000, 3-D SNR-300, and 3-D VVER-440 benchmark problems. The results of the static problems show higher accuracy than those of the original formulations in hexagonal geometry. Finally, a kinetics code is developed and tested by introducing step changes of nodal cross sections for the VVER-440 benchmark problem. The results appear to be accurate enough for this code to be useful for analyzing realistic three-dimensional hexagonal reactors

  11. Analytical Model for Outdoor Millimeter Wave Channels using Geometry-Based Stochastic Approach

    OpenAIRE

    Muhammad, Nor Aishah; Wang, Peng; Li, Yonghui; Vucetic, Branka

    2016-01-01

    The severe bandwidth shortage in conventional microwave bands has spurred the exploration of the millimeter wave (MMW) spectrum for the next revolution in wireless communications. However, there is still lack of proper channel modeling for the MMW wireless propagation, especially in the case of outdoor environments. In this paper, we develop a geometry-based stochastic channel model to statistically characterize the effect of all the first-order reflection paths between the transmitter and re...

  12. Solution of the multigroup analytic nodal diffusion equations in 3-dimensional cylindrical geometry / Rian Hendrik Prinsloo

    OpenAIRE

    Prinsloo, Rian Hendrik

    2006-01-01

    Nodal diffusion methods have been used extensively in nuclear reactor calculations specifically for their performance advantage, but also their superior accuracy. In this work a nodal diffusion method is developed for three-dimensional cylindrical geometry. Recent developments in the Pebble Bed Modular Reactor (PBMR) project have sparked renewed interest in the application of different modelling methods to its design, and naturally included in this effort is a nodal method for ...

  13. Modeling of cavities using the analytic modal method and an open geometry formalism

    DEFF Research Database (Denmark)

    de Lasson, Jakob Rosenkrantz; Christensen, Thomas; Mørk, Jesper;

    2012-01-01

    We present an eigenmode expansion technique for calculating the properties of a dipole emitter inside a micropillar. We consider a solution domain of infinite extent, implying no outer boundary conditions for the electric field, and expand the field on analytic eigenmodes. In contrast to finite-s...

  14. Spatial stochastic and analytical approaches to describe the complex hydraulic variability inherent channel geometry

    Directory of Open Access Journals (Sweden)

    N. Hadadin

    2011-07-01

    Full Text Available The effects of basin hydrology on channel hydraulic variability for incised streams were investigated using available field data sets and models of watershed hydrology and channel hydraulics for Yazoo River Basin, USA. The study presents the hydraulic relations of bankfull discharge, channel width, mean depth, cross- sectional area, longitudinal slope, unit stream power, and runoff production as a function of drainage area using simple linear regression. The hydraulic geometry relations were developed for sixty one streams, twenty of them are classified as channel evaluation model (CEM Types IV and V and forty one of them are streams of CEM Types II and III. These relationships are invaluable to hydraulic and water resources engineers, hydrologists, and geomorphologists, involved in stream restoration and protection. These relations can be used to assist in field identification of bankfull stage and stream dimension in un-gauged watersheds as well as estimation of the comparative stability of a stream channel.

    Results of this research show good fit of hydraulic geometry relationships in the Yazoo River Basin. The relations indicate that bankfull discharge, channel width, mean depth, cross-sectional area have stronger correlation to changes in drainage area than the longitudinal slope, unit stream power, and runoff production for streams CEM Types II and III. The hydraulic geometry relations show that runoff production, bankfull discharge, cross-sectional area, and unit stream power are much more responsive to changes in drainage area than are channel width, mean depth, and slope for streams of CEM Types IV and V. Also, the relations show that bankfull discharge and cross-sectional area are more responsive to changes in drainage area than are other hydraulic variables for streams of CEM Types II and III. The greater the regression slope, the more responsive to changes in drainage area will be.

  15. Analytical modeling of turn-milling process geometry, kinematics and mechanics

    OpenAIRE

    Karagüzel, Umut; Karaguzel, Umut; Uysal, Emre; Budak, Erhan; Bakkal, Mustafa

    2014-01-01

    This paper presents an analytical approach for modeling of turn-milling which is a promising cutting process combining two conventional machining operations; turning and milling. This relatively new technology could be an alternative to turning for improved productivity in many applications but especially in cases involving hard-to-machine material or large work diameter. Intermittent nature of the process reduces forces on the workpiece, cutting temperatures and thus tool wear, and helps bre...

  16. Analytical investigation of the influence of spacer geometry and position on turbulent flow structure and parameters

    Energy Technology Data Exchange (ETDEWEB)

    Stosic, Z.V.; Stevanovic, V.D. [Framatome ANP GmbH - NBTT, Erlangen (Germany)

    2001-07-01

    Nuclear fuel rod bundle thermal-hydraulics strongly depends on the presence of fuel rod spacers. High Reynolds number coolant flows around spacers of different geometry and position are numerically investigated in two-dimensions. Predicted is the influence of the spacer's geometry and its position within a flow channel, on the recirculation zones formation and corresponding reattachment lengths. The numerical procedure is based on the two-equation k-{epsilon} turbulence model and the control volume procedure. Numerical simulation and analyses of high Reynolds fluid flow over the bluff bodies of the nuclear fuel spacer shapes are performed. Two types of flow channels and conditions are considered: spacers mounted on the wall and spacers in a free fluid stream. The major findings are as follows: 1) In fluid flow over the spacer mounted on the wall, the large recirculation zone is formed behind the spacer's fin. The reattachment length and width of this large vortex are increasing with the spacer's fin inclination angle increase. The reattachment length is rapidly increasing for fin inclination angles greater than 45 degrees. The maximum value of the reattachment length is achieved with fin inclination angle of 75 degrees. For angles from 75 to 90 degrees this length is slightly decreasing (the result with the Re=1.6*10{sup 6}). 2) A small vortex is formed in front of the spacer's fin in case of the flow over wall mounted spacer. 3) In case of fluid flow around the spacer in a free stream, the vortexes are formed behind the fin. Vortex shedding is observed, which is contrary to the formation of a stable vortex behind the wall mounted spacers. No small recirculation zone exists in front of the fin, which is opposite to the flow structure in case of wall mounted spacer. (authors)

  17. Jet formation in GRBs: a semi-analytic model of MHD flow in Kerr geometry with realistic plasma injection

    International Nuclear Information System (INIS)

    We construct a semi-analytic model for magnetohydrodynamic (MHD) flows in Kerr geometry that incorporates energy loading via neutrino annihilation on magnetic field lines threading the horizon. We compute the structure of the double-flow established in the magnetisphere for a wide range of energy injection rates and identify the different operation regimes. At low injection rates, the outflow is powered by the spinning black hole via the Blandford-Znajek mechanism, whereas at high injection rates, it is driven by the pressure of the plasma deposited on magnetic field lines. In the intermediate regime, both processes contribute to the outflow formation. The parameter that quantifies the load is the ratio of the net power injected below the stagnation radius and the maximum power that can be extracted magnetically from the black hole.

  18. Development and performance of the analytic nodal diffusion solver 'ANDES' in multi-groups for 3D rectangular geometry

    International Nuclear Information System (INIS)

    The Analytic Coarse-Mesh Finite-Difference method is developed in detail for multi-group and multi-dimensional diffusion calculations, including the general and particular modal solutions in the complex space for any number of groups. For rectangular multidimensional geometries, the Chao's generalized relations with transverse integration provide a high-order approximation of the ACMFD method, where all energy groups are coupled by matrix-vector FD relations and the errors are limited to the ones incurred by the interpolation of the transverse interface currents, in a non-linear iterative scheme. The implementation of the method in a multigroup 3D rectangular geometry nodal solver called ANDES is discussed, pointing out the encapsulation achieved for integration of the solver as an optional module within larger code systems. The performance of the ANDES solver in 3D rectangular (X-Y-Z) geometry and multi-groups is verified by its application to several 2D-3D model and international benchmarks (NEA-OECD), with given diffusion cross section sets in few-groups (2 to 8). The extensive verification, always required for new methods and codes, shows a quite fast convergence of ANDES in both the eigenvalue and transverse leakage iteration loops and with the nodal coarse-mesh size, allowing to reach the conclusion that quite high accuracy is achieved with rather large nodes, one node or four nodes per PWR fuel assembly, as compared with reference solutions obtained with fine-mesh finite-difference diffusion calculations using mesh sizes 64 to 128 times smaller than the ANDES nodes. (authors)

  19. A semi-analytical approach for stiffness modeling of PKM by considering compliance of machine frame with complex geometry

    Institute of Scientific and Technical Information of China (English)

    WANG YouYu; HUANG Tian; ZHAO XueMan; MEI JiangPing; Derek G CHETWYND

    2008-01-01

    Stiffness modeling is one of the most significant issues in the design of parallel kinematic machine (PKM).This paper presents a semi-analytical approach that enables the stiffness of PKM with complex machine frame geometry to be estimated effectively.This approach can be implemented by three steps:(i) decomposition of the entire system into two sub-systems associated with the parallel mechanism and the machine frame respectively;(ii) stiffness modeling of each sub-system using the analytical approach and the finite element analysis;and (iii) generation of the stiffness model of the entire system by means of linear superposition.In the modeling process of each sub-system,the virtual work princi-ple and overall deflection Jacobian are employed with special attention to the bending rigidity of the constrained passive limb and the interface stiffness of the machine frame.The stiffness distribution of a 5-DOF hybrid robot named TriVariant-B is investigated as an example to illustrate the effectivaness of this approach.The contributions of component rigidities to that of the system are evaluated using global indices.It shows that the results achieved by this approach have a good match to those obtained through finite element analysis and experiments.

  20. Determination of neutron buildup factor using analytical solution of one-dimensional neutron diffusion equation in cylindrical geometry

    Energy Technology Data Exchange (ETDEWEB)

    Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

    2011-07-01

    The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)

  1. Analytical solution of the multigroup neutron diffusion kinetic equation in one-dimensional cartesian geometry by the integral transform technique

    International Nuclear Information System (INIS)

    The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)

  2. The analytic function expansion nodal (AFEN) method with half-interface averaged fluxes in mixed geometry nodes for analysis of pebble bed modular reactor (PBMR) cores

    International Nuclear Information System (INIS)

    The analytic function expansion nodal (AFEN) method has been successfully applied to the rectangular and hexagonal geometries in the cartesian coordinates system. In this paper, we extended the AFEN method to the cylindrical geometry in the R-Z coordinates for the analysis of pebble bed modular reactors (PBMRs). To treat the mixed geometry of rectangular and triangular nodes appearing in the lower periphery of the reactors, we used half-interface averaged fluxes as nodal unknowns. Numerical results obtained attest to their accuracy and applicability to practical problems. (author)

  3. Analytical Study of the Effect of the System Geometry on Photon Sensitivity and Depth of Interaction of Positron Emission Mammography

    Directory of Open Access Journals (Sweden)

    Pablo Aguiar

    2012-01-01

    Full Text Available Positron emission mammography (PEM cameras are novel-dedicated PET systems optimized to image the breast. For these cameras it is essential to achieve an optimum trade-off between sensitivity and spatial resolution and therefore the main challenge for the novel cameras is to improve the sensitivity without degrading the spatial resolution. We carry out an analytical study of the effect of the different detector geometries on the photon sensitivity and the angle of incidence of the detected photons which is related to the DOI effect and therefore to the intrinsic spatial resolution. To this end, dual head detectors were compared to box and different polygon-detector configurations. Our results showed that higher sensitivity and uniformity were found for box and polygon-detector configurations compared to dual-head cameras. Thus, the optimal configuration in terms of sensitivity is a PEM scanner based on a polygon of twelve (dodecagon or more detectors. We have shown that this configuration is clearly superior to dual-head detectors and slightly higher than box, octagon, and hexagon detectors. Nevertheless, DOI effects are increased for this configuration compared to dual head and box scanners and therefore an accurate compensation for this effect is required.

  4. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2012-01-01

    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.

  5. The analytic nodal diffusion solver ANDES in multigroups for 3D rectangular geometry: Development and performance analysis

    International Nuclear Information System (INIS)

    In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods - implicit or explicit -, and the error assessment due to transverse integration. A new approach for solving the control rod 'cusping' problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks

  6. An analytical solution for the one-dimensional time dependent SN transport equation for bounded and unbounded domain in cartesian geometry

    International Nuclear Information System (INIS)

    In this work we report an analytical solution for the time dependent SN transport equation in a plane parallel geometry for unbounded domain, we mean for 0 ≤ x ≤ ∞. For such, we apply the Laplace transform technique in the time variable and the LTSN approach in the spatial variable. By this procedure we come out with an analytical solution for the angular flux in integral form applying the boundness of the angular flux at infinity. We present numerical simulations and also validation by the analysis of the asymptotic behavior of the scalar flux in a slab. (author)

  7. Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis.

    OpenAIRE

    Lozano Montero, Juan Andrés; Jiménez Escalante, Javier; García Herranz, Nuria; Aragonés Beltrán, José María

    2010-01-01

    In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal–hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthog...

  8. Relation of visuospatial and analytical skills and span of short-term memory to academic achievement in high school geometry

    OpenAIRE

    Brown, Martha

    1991-01-01

    The purpose of this research was to investigate hypothesized relations of visuospatial and logical reasoning skills, and span of short-term memory to achievement in geometry. In addition, major subfactors of visuospatial ability (visualization, speeded rotations, spatial orientation, and disembedding) were assessed to determine which were significant predictors of geometry achievement. Vernon's (1965) model of intelligence and Baddeley's model of working memory provided the theoretical fra...

  9. Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: Geometry optimization and spin-state energetics of a ruthenium nitrosyl complex

    Energy Technology Data Exchange (ETDEWEB)

    Delcey, Mickaël G. [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Freitag, Leon; González, Leticia, E-mail: leticia.gonzalez@univie.ac.at [Institut für Theoretische Chemie, Universität Wien, Währinger Straße 17, 1090 Vienna (Austria); Pedersen, Thomas Bondo [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway); Aquilante, Francesco [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Dipartimento di Chimica “G. Ciamician,” Università di Bologna, V. F. Selmi 2, 40126 Bologna (Italy); Lindh, Roland, E-mail: roland.lindh@kemi.uu.se [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Uppsala Center for Computational Chemistry - UC3, Uppsala University, Box 518, 751 20 Uppsala (Sweden)

    2014-05-07

    We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S{sub 0} and 0.11 Å for T{sub 1}, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.

  10. Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: Geometry optimization and spin-state energetics of a ruthenium nitrosyl complex

    International Nuclear Information System (INIS)

    We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S0 and 0.11 Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry

  11. Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: geometry optimization and spin-state energetics of a ruthenium nitrosyl complex.

    Science.gov (United States)

    Delcey, Mickaël G; Freitag, Leon; Pedersen, Thomas Bondo; Aquilante, Francesco; Lindh, Roland; González, Leticia

    2014-05-01

    We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S0 and 0.11 Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry. PMID:24811621

  12. Analytic trigonometry

    CERN Document Server

    Bruce, William J; Maxwell, E A; Sneddon, I N

    1963-01-01

    Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions

  13. Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

    International Nuclear Information System (INIS)

    An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label

  14. Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

    International Nuclear Information System (INIS)

    In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal-hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.

  15. Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

    International Nuclear Information System (INIS)

    In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

  16. Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

    International Nuclear Information System (INIS)

    A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the Keff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for Keff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)

  17. Analytical GIAO and hybrid-basis integral derivatives: application to geometry optimization of molecules in strong magnetic fields.

    Science.gov (United States)

    Tellgren, Erik I; Reine, Simen S; Helgaker, Trygve

    2012-07-14

    Analytical integral evaluation is a central task of modern quantum chemistry. Here we present a general method for evaluating differentiated integrals over standard Gaussian and mixed Gaussian/plane-wave hybrid orbitals. The main idea is to have a representation of basis sets that is flexible enough to enable differentiated integrals to be reinterpreted as standard integrals over modified basis functions. As an illustration of the method, we report a very simple implementation of Hartree-Fock level geometrical derivatives in finite magnetic fields for gauge-origin independent atomic orbitals, within the London program. As a quantum-chemical application, we optimize the structure of helium clusters and some well-known covalently bound molecules (water, ammonia and benzene) subject to strong magnetic fields. PMID:22653039

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-07-01

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

  19. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry

    Energy Technology Data Exchange (ETDEWEB)

    Jalili Bahabadi, Mohammad Hasan; Pazirandeh, Ali; Athari, Mitra [Islamic Azad Univ., Tehran (Iran, Islamic Republic of). Dept. of Nuclear Engineering, Science and Research Branch

    2015-12-15

    In this paper, we developed a new approach of analytic function expansion nodal (AFEN) method to solve the multi-group and multi-dimensional neutron diffusion equation in reactor cores with hexagonal fuel assembly. This method represents a multidimensional intra nodal flux distribution in terms of analytic basis functions at any points in the node. New types of boundary conditions have been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. We utilized the coarse group rebalancing (CGR) method to increase the speed of code calculations. The computer code takes a few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (k{sub eff}), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for two well-known benchmark problems. The numerical results demonstrate that the new AFEN method is an accurate method for calculating k{sub eff} and power density distribution in hexagonal-z geometries.

  20. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry

    International Nuclear Information System (INIS)

    In this paper, we developed a new approach of analytic function expansion nodal (AFEN) method to solve the multi-group and multi-dimensional neutron diffusion equation in reactor cores with hexagonal fuel assembly. This method represents a multidimensional intra nodal flux distribution in terms of analytic basis functions at any points in the node. New types of boundary conditions have been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. We utilized the coarse group rebalancing (CGR) method to increase the speed of code calculations. The computer code takes a few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (keff), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for two well-known benchmark problems. The numerical results demonstrate that the new AFEN method is an accurate method for calculating keff and power density distribution in hexagonal-z geometries.

  1. Simplified models of stellar wind anatomy for interpreting high-resolution data. Analytical approach to embedded spiral geometries

    Science.gov (United States)

    Homan, Ward; Decin, Leen; de Koter, Alex; van Marle, Allard Jan; Lombaert, Robin; Vlemmings, Wouter

    2015-07-01

    Context. Recent high-resolution observations have shown that stellar winds harbour complexities that strongly deviate from spherical symmetry, which generally is assumed as standard wind model. One such morphology is the Archimedean spiral, which is generally believed to be formed by binary interactions, as has been directly observed in multiple sources. Aims: We seek to investigate the manifestation in the observables of spiral structures embedded in the spherical outflows of cool stars. We aim to provide an intuitive bedrock with which upcoming ALMA data can be compared and interpreted. Methods: By means of an extended parameter study, we modelled rotational CO emission from the stellar outflow of asymptotic giant branch stars. To this end, we developed a simplified analytical parametrised description of a 3D spiral structure. This model is embedded into a spherical wind and fed into the 3D radiative transfer code LIME, which produces 3D intensity maps throughout velocity space. Subsequently, we investigated the spectral signature of rotational transitions of CO in the models, as well as the spatial aspect of this emission by means of wide-slit position-velocity (PV) diagrams. Additionally, we quantified the potential for misinterpreting the 3D data in a 1D context. Finally, we simulated ALMA observations to explore the effect of interferometric noise and artefacts on the emission signatures. Results: The spectral signatures of the CO rotational transition v = 0J = 3 - 2 are very efficient at concealing the dual nature of the outflow. Only a select few parameter combinations allow for the spectral lines to disclose the presence of the spiral structure. If the spiral cannot be distinguished from the spherical signal, this might result in an incorrect interpretation in a 1D context. Consequently, erroneous mass-loss rates would be calculated. The magnitude of these errors is mainly confined to a factor of a few, but in extreme cases can exceed an order of magnitude

  2. A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

    International Nuclear Information System (INIS)

    A semi-analytical approach is presented to model the effects of complicated boundary conditions and rarefaction on the squeeze-film damping dependent quality factor in a double-gimballed MEMS torsion mirror. To compute squeeze-film damping in a rectangular torsion mirror with simple boundaries, compact models derived by solving the conventional Reynolds equation with zero pressure boundary conditions on the edges of the plate are generally used. These models are not applicable if the air-gap thickness is comparable to the length of the plate. To extend the validity of the existing models in devices with large air-gap thickness and complicated boundaries, we present a procedure that requires the computation of the effective length of the structure and uses this length for the computation of damping in all flow regimes using a modified effective viscosity model. The effective length is computed by comparing the damping obtained from a numerical solution of Navier–Stokes equations with that obtained from a Reynolds-equation-based compact model. To capture the effect of rarefaction in different flow regimes, we use two different approaches: the effective viscosity approach which is valid for continuum, slip, transition and molecular flow regimes, and an approach based on the free molecular model which is valid only in a molecular flow regime. We show that the effective length obtained for complicated structures in the continuum regime may still be used to capture the rarefaction effect in the slip, transition and molecular regimes. On comparing different empirical models based on the effective viscosity approach with experimental results, we find some anomaly in the region between the molecular regime and the intrinsic regime where non-fluid damping dominates. To improve modelling in the rarified regimes, we modify the best model among the existing models by minimizing error obtained with respect to the experimental results. We find that the proposed model captures

  3. Spinning geometry = Twisted geometry

    International Nuclear Information System (INIS)

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

  4. Analytical geometry of three dimensions

    CERN Document Server

    McCrea, William H

    2006-01-01

    Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.

  5. Technical calculus with analytic geometry

    CERN Document Server

    Gersting, Judith L

    2010-01-01

    This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, in

  6. Modern calculus and analytic geometry

    CERN Document Server

    Silverman, Richard A

    2012-01-01

    A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory - many of the answers are fo

  7. An analytical spatial reconstruction algorithm for the SD-SGF-CN hybrid nodal method for one-speed X,Y-geometry SN eigenvalue problems

    International Nuclear Information System (INIS)

    In this paper the X,Y-geometry SD-SGF-CN spectral nodal method, cf. spectral diamond-spectral Green's function-constant nodal, is used to determine the one-speed node-edge average angular fluxes in heterogeneous domains. This hybrid spectral nodal method uses the spectral diamond (SD) auxiliary equation for the multiplying regions and the spectral Green's function (SGF) auxiliary equation for the non-multiplying regions of the domain. Moreover, we consider constant approximations for the transverse-leakage terms in the transverse integrated SN nodal equations. We solve the SD-SGF-CN equations using the one-node block inversion (NBI) iterative scheme, which uses the most recent estimates available for the node-entering fluxes to evaluate the node-exiting fluxes in the directions that constitute the incoming fluxes for the adjacent node. Using these results, we offer an algorithm for analytical reconstruction of the coarse-mesh nodal solution within each spatial node, as localized numerical solutions are not generated by usual accurate nodal methods. Numerical results are presented to illustrate the accuracy of the present algorithm. (author)

  8. 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...

  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. Analytical quadrics

    CERN Document Server

    Spain, Barry; Ulam, S; Stark, M

    1960-01-01

    Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordi

  11. 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

  12. 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

  13. 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.

  14. 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

  15. The Potential of GeoGebra Dynamic Mathematics Software in Teaching Analytic Geometry: The Opinion of Pre-service Mathematics Teachers [Analitik Geometri Öğretiminde GeoGebra Yazılımının Potansiyeli: Öğretmen Adaylarının Görüşleri

    Directory of Open Access Journals (Sweden)

    Serdal Baltacı

    2016-12-01

    Full Text Available The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers at 3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants were at medium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment. [Bu çalışmada, analitik geometri kavramlarının öğretiminde GeoGebra’ nın potansiyeli incelenmiştir. Özel durum çalışması yöntemiyle yürütülen bu araştırmanın katılımcılarını, ilköğretim matematik öğretmenliği 3. sınıfa devam eden 6 öğretmen adayı oluşturmaktadır. Katılımcılar kendini ifade etme becerisi yüksek, mülakata gönüllü ve farklı başarı düzeyinde (yüksek, orta, düşük olan ikişer öğretmen adayından oluşmaktadır. Çalışmada analitik geometri dersleri, araştırmacılar tarafından geliştirilen çalışma yaprakları kullanılarak yürütülmüştür. Araştırmanın verileri derslerin sonunda yapılan yarı yapılandırılmış mülakatlarla toplanmıştır. Araştırmadan elde edilen veriler, içerik analizi yöntemi ile analiz edilmiştir. Araştırma sonuçları öğretmen adaylarının analitik geometri kavramlarını öğrenmede yazılımı kullanmalarının onlara kolaylık sa

  16. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

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

  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. Preschool Geometry

    CERN Document Server

    Levenson, Esther; Tsamir, Pessia

    2011-01-01

    Recently the issue of early childhood mathematics has come to the fore and with it the importance of teaching geometrical concepts and reasoning from a young age. Geometry is a key domain mentioned in many national curricula and may also support the learning of other mathematical topics, such as number and patterns. This book is based on the rich experience (research and practice) of the authors and is devoted entirely to the learning and teaching of geometry in preschool. The first part of the book is dedicated to children's geometrical thinking, building concept images in line with concept d

  19. 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,

  20. Molecular Geometry.

    Science.gov (United States)

    Desseyn, H. O.; And Others

    1985-01-01

    Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…

  1. Geometrie coniugate

    Directory of Open Access Journals (Sweden)

    Leonardo Paris

    2012-06-01

    Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.

  2. 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 ...

  3. 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...

  4. Geometry of numbers

    CERN Document Server

    Gruber, Peter M

    1987-01-01

    This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit

  5. 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

  6. A polynomial analytical method for one-group slab-geometry discrete ordinates heterogeneous problems; Metodo analitico de aproximacao polinomial para problemas de ordenadas discretas em geometria Cartesiana unidimensional

    Energy Technology Data Exchange (ETDEWEB)

    Leal, Andre Luiz do Carmo

    2008-07-01

    In this work we evaluate polynomial approximations to obtain the transfer functions that appear in SGF auxiliary equations (Green's Functions) for monoenergetic linearly anisotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use Lagrange Polynomials in order to compare the numerical results with the ones generated by the standard SGF method applied to SN problems in heterogeneous domains. This work is a preliminary investigation of a new proposal for handling the transverse leakage terms that appear in the transverse-integrated one-dimensional SN equations when we use the SGF - exponential nodal method (SGF-ExpN) in multidimensional rectangular geometry. (author)

  7. Quantum Geometry and Quantum Gravity

    OpenAIRE

    Barbero González, Jesús Fernando

    2008-01-01

    The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues concerning the relationship of the formalism with other more traditional approaches inspired in the treatment of the fundamental interactions in the standard model. Mathematically I will pay special attention to functional analytic issues, the construction of t...

  8. 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.

  9. 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.

  10. 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...

  11. General 2 charge geometries

    CERN Document Server

    Taylor, M

    2006-01-01

    Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.

  12. Veronese geometry and the electroweak vacuum moduli space

    International Nuclear Information System (INIS)

    We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential

  13. Veronese geometry and the electroweak vacuum moduli space

    Energy Technology Data Exchange (ETDEWEB)

    He, Yang-Hui, E-mail: hey@maths.ox.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University, Tianjin 300071 (China); Merton College, University of Oxford, Oxford OX1 4JD (United Kingdom); Jejjala, Vishnu, E-mail: vishnu@neo.phys.wits.ac.za [Centre for Theoretical Physics, NITheP, and School of Physics, University of the Witwatersrand, Johannesburg, WITS 2050 (South Africa); Matti, Cyril, E-mail: Cyril.Matti.1@city.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); Nelson, Brent D., E-mail: b.nelson@neu.edu [Department of Physics, Northeastern University, Boston, MA 02115 (United States); ICTP, Strada Costiera 11, Trieste 34014 (Italy)

    2014-09-07

    We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential.

  14. Writhing Geometry of Open DNA

    CERN Document Server

    Rossetto, V

    2003-01-01

    Motivated by recent experiments on DNA torsion-force-extension characteristics we consider the writhing geometry of open stiff molecules. We exhibit a cyclic motion which allows arbitrarily large twisting of the end of a molecule via an activated process. This process is suppressed for forces larger than femto-Newtons which allows us to show that experiments are sensitive to a generalization of the Calugareanu-White formula for the writhe. Using numerical methods we compare this formulation of the writhe with recent analytic calculations.

  15. Thermodynamic geometry of holographic superconductors

    CERN Document Server

    Basak, Sayan; Nandi, Poulami; Sengupta, Gautam

    2015-01-01

    We obtain the thermodynamic geometry of a (2+1) dimensional strongly coupled quantum field theory at a finite temperature in a holographic set up through the gauge/gravity correspondence. The bulk dual gravitational theory is described by a 3+1 dimensional charged AdS black hole in the presence of a charged massive scalar field. The holographic free energy of the (2+1) dimensional strongly coupled boundary field theory is computed analytically through the bulk boundary correspondence. The thermodynamic metric and the corresponding scalar curvature is then obtained from the holographic free energy. The thermodynamic scalar curvature characterizes the superconducting phase transition of the boundary field theory.

  16. Casimir forces and geometry

    International Nuclear Information System (INIS)

    Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the

  17. 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

  18. 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

  19. Bendix: intuitive helix geometry analysis and abstraction

    OpenAIRE

    Dahl, Anna Caroline E.; Chavent, Matthieu; Sansom, Mark S P

    2012-01-01

    Summary: The flexibility of α-helices is important for membrane protein function and calls for better visualization and analysis. Software is presented that quantifies and projects the helix axis evolution over time, with the choice of uniform or analytic heatmap graphics according to the local geometry. Bendix supports static, molecular dynamics, atomistic and coarse-grained input.

  20. 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...

  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. CMS geometry through 2020

    CERN Document Server

    Osborne, Ianna

    2013-01-01

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

  3. Tame geometry with application in smooth analysis

    CERN Document Server

    Yomdin, Yosef

    2004-01-01

    The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.

  4. Fundamental concepts of geometry

    CERN Document Server

    Meserve, Bruce E

    2014-01-01

    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.

  5. Split Special Lagrangian Geometry

    OpenAIRE

    Harvey, F. Reese; Lawson Jr, H. Blaine

    2010-01-01

    One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced. The natural setting is provided by doing geometry with the complex numbers C replaced by the double numbers D, where i with i^2 = -1 is replaced by tau with tau^2 = 1. A rather surprising amount of complex geometry carries over, almost untouched, and this has been the subject of many papers. We briefly review this ...

  6. 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

  7. Analytical Laboratories

    Data.gov (United States)

    Federal Laboratory Consortium — NETL’s analytical laboratories in Pittsburgh, PA, and Albany, OR, give researchers access to the equipment they need to thoroughly study the properties of materials...

  8. Analytical testing

    Science.gov (United States)

    Flannelly, W. G.; Fabunmi, J. A.; Nagy, E. J.

    1981-01-01

    Analytical methods for combining flight acceleration and strain data with shake test mobility data to predict the effects of structural changes on flight vibrations and strains are presented. This integration of structural dynamic analysis with flight performance is referred to as analytical testing. The objective of this methodology is to analytically estimate the results of flight testing contemplated structural changes with minimum flying and change trials. The category of changes to the aircraft includes mass, stiffness, absorbers, isolators, and active suppressors. Examples of applying the analytical testing methodology using flight test and shake test data measured on an AH-1G helicopter are included. The techniques and procedures for vibration testing and modal analysis are also described.

  9. Geometry of multihadron production

    International Nuclear Information System (INIS)

    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. 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.

  11. Discrete quantum geometries and their effective dimension

    International Nuclear Information System (INIS)

    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.

  12. 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.

  13. Game Analytics

    DEFF Research Database (Denmark)

    Seif El-Nasr, Magy; Drachen, Anders; Canossa, Alessandro

    2013-01-01

    Game Analytics has gained a tremendous amount of attention in game development and game research in recent years. The widespread adoption of data-driven business intelligence practices at operational, tactical and strategic levels in the game industry, combined with the integration of quantitative...... measures in user-oriented game research, has caused a paradigm shift. Historically, game development has not been data-driven, but this is changing as the benefits of adopting and adapting analytics to inform decision making across all levels of the industry are becoming generally known and accepted....

  14. 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

  15. 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.

  16. 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

  17. Viral nematics in confined geometries.

    Science.gov (United States)

    Manyuhina, O V; Lawlor, K B; Marchetti, M C; Bowick, M J

    2015-08-14

    Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. In the case of an annulus, whose topology does not require the presence of topological defects, we find that nematic textures with boundary defects are stable compared to defect-free configurations when the anchoring is weak. Our simple approach, with no fitting parameters, suggests a possible symmetry breaking mechanism responsible for the formation of one-, two- and three-fold textures under annular confinement. PMID:26135676

  18. Thermodynamic geometry of holographic superconductors

    Directory of Open Access Journals (Sweden)

    Sayan Basak

    2016-02-01

    Full Text Available We obtain the thermodynamic geometry of a (2+1 dimensional strongly coupled quantum field theory at a finite temperature in a holographic setup, through the gauge/gravity correspondence. The bulk dual gravitational theory is described by a (3+1 dimensional charged AdS black hole in the presence of a massive charged scalar field. The holographic free energy of the (2+1 dimensional strongly coupled boundary field theory is computed analytically through the bulk boundary correspondence. The thermodynamic metric and the corresponding scalar curvature are then obtained from the holographic free energy. The thermodynamic scalar curvature characterizes the superconducting phase transition of the boundary field theory.

  19. Analytical Searching.

    Science.gov (United States)

    Pappas, Marjorie L.

    1995-01-01

    Discusses analytical searching, a process that enables searchers of electronic resources to develop a planned strategy by combining words or phrases with Boolean operators. Defines simple and complex searching, and describes search strategies developed with Boolean logic and truncation. Provides guidelines for teaching students analytical…

  20. 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...

  1. 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)

  2. Noncommutative Geometry and Physics

    International Nuclear Information System (INIS)

    In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a 'sum over geometries' on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of 'observables' in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries

  3. 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...

  4. Confinement and related transport in Extrap geometry

    International Nuclear Information System (INIS)

    The properties of the plasma equilibrium are investigated for the Extrap magnetic confinement geometry. An analytical solution for the profiles of the plasma parameters are found under the assumption that the energy is lost primarily in the radical direction by heat conduction and convection. An estimate of the radial particle confinement time is given, showing favorable scaling with plasma density and temperature. The conventional assumption of a uniform current density is shown to be unjustified in the case of an inhomogeneus electron temperature. An analytical expression is found for the pinch radius at different mechanisms of the heat transport. (author)

  5. Implosions and hypertoric geometry

    DEFF Research Database (Denmark)

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

    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....

  6. 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.

  7. Quantum Mechanics of Geometry

    OpenAIRE

    Ashtekar, Abhay

    1999-01-01

    Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate students in physics. As an illustrative application, I indicate how some of the detailed features of the micro-structure of geometry can be tested using black hole thermodynamics. Current and future directions of research in this area are discussed.

  8. Compositional Geometry and Programming

    OpenAIRE

    Bantchev, Boyko

    2013-01-01

    Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014 Functional, or compositional, geometry is a method of constructing complex pictures from simpler ones, apllying binding operations. The method is naturally related to functional programming and can be used as a tool for education or self-education in programming. The paper introduces to compositional geometry, bringing attention to its severa...

  9. An invitation to web geometry

    CERN Document Server

    Vitório Pereira, Jorge

    2015-01-01

    This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which  webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern’s bound and Trépreau’s algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.

  10. Induced geometry from disformal transformation

    Energy Technology Data Exchange (ETDEWEB)

    Yuan, Fang-Fang, E-mail: ffyuan@nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China); Huang, Peng, E-mail: huangp46@mail.sysu.edu.cn [School of Astronomy and Space Science, Sun Yat-Sen University, Guangzhou 510275 (China)

    2015-05-11

    In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.

  11. Software Geometry in Simulations

    Science.gov (United States)

    Alion, Tyler; Viren, Brett; Junk, Tom

    2015-04-01

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

  12. Introduction to combinatorial geometry

    International Nuclear Information System (INIS)

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

  13. CMS geometry through 2020

    International Nuclear Information System (INIS)

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

  14. CMS Geometry Through 2020

    Science.gov (United States)

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

    2014-06-01

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

  15. Wobbling geometry in simple triaxial rotor

    CERN Document Server

    Shi, W X

    2014-01-01

    The spectroscopy properties and angular momentum geometry for the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model up to spin $I=40\\hbar$. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions by harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulas. The evolution of the angular momentum geometry as well as the $K$-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increasing of wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nuclei is proposed.

  16. Compaction of granular material inside confined geometries

    Directory of Open Access Journals (Sweden)

    Benjy eMarks

    2015-06-01

    Full Text Available In both nature and the laboratory, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured stress. The micromechanical behaviour is studied for a range of system parameters, and the limitations of existing analytic models are described. In particular, we show the smallest sized systems which can be treated using existing models. Additionally, the effects of increasing piston rate, and variations of the initial packing fraction, are described.

  17. Update on Scroll Compressor Chamber Geometry

    OpenAIRE

    Bell, Ian; Groll, Eckhard; Braun, James; King, Galen

    2010-01-01

    The geometry of the scroll compressor determines the efficiency of the scroll compressor and controls all elements of its operation. It is therefore critical to be able to accurately model the volumes of the compressor over the course of a revolution. This paper proposes a novel quasi-analytic formulation of the suction, compression and discharge chambers based on a change of variables from involute angle to polar integration angle. This solution has been compared against a reference polyg...

  18. Analytical chemistry

    International Nuclear Information System (INIS)

    This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.

  19. Analytical chemistry

    International Nuclear Information System (INIS)

    The division for Analytical Chemistry continued to try and develope an accurate method for the separation of trace amounts from mixtures which, contain various other elements. Ion exchange chromatography is of special importance in this regard. New separation techniques were tried on certain trace amounts in South African standard rock materials and special ceramics. Methods were also tested for the separation of carrier-free radioisotopes from irradiated cyclotron discs

  20. Geometry - Construction - Architecture

    Directory of Open Access Journals (Sweden)

    Riccardo Migliari

    2012-06-01

    Full Text Available Geometry, in Drawing, is suffering from a profound crisis, more than other disciplines of the area, and this crisis has confined it, according a few, within a field of study of top-grade specialization, that only few scholars are interested in. The reason for this crisis can be found in the changes that were induced, during the last thirty years, by the advent of the information technology, but not only there. It can also be found, in my opinion, in the rightful ambition of all of us architects to carry out research, an ambition that the traditional Geometry, both descriptive and more in general graphical, could not satisfy. In fact, that part of descriptive geometry, which deals with the graphical representation on a plane of three-dimensional objects, has been outclassed by 3D modelling, both in simplicity of execution and in quality of the results. Whilst the graphical geometry has been neglected even by the mathematicians, during the axiomatic turning-point of the 1920s, a part from some exceptions - Coxeter - and a few recent reconsiderations. Yet, geometry continues to play a leading role in drawing, in general, and in architecture, in particular, and I refer to the historical studies, to the studies of surfaces, to the relation with art and, last but not least important, to teaching.

  1. 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...

  2. 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...

  3. Quantum Geometry and Interferometry

    CERN Document Server

    Hogan, Craig

    2012-01-01

    All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at the Planck scale. If directions in emergent quantum geometry do not commute, new quantum-geometrical degrees of freedom can produce detectable macroscopic deviations from classicality: spatially coherent, transverse position indeterminacy between any pair of world lines, with a displacement amplitude much larger than the Planck length. Positions of separate bodies are entangled with each other, and undergo quantum-geometrical fluctuations that are not describable as metric fluctuations or gravitational waves. These fluctuations can either be cleanly identified or ruled out using interferometers. A Planck-precision test of the classical coherence of space-time on a laboratory scale is now underway at Fermilab.

  4. Strings on Bubbling Geometries

    CERN Document Server

    Lin, Hai; Shock, Jonathan P

    2010-01-01

    We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.

  5. 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...

  6. Riemann-Finsler geometry

    CERN Document Server

    Chern, Shiing-Shen

    2005-01-01

    Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann-Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such as the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar flag curvature or iso

  7. 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

  8. Elementary differential geometry

    CERN Document Server

    O'Neill, Barrett

    2006-01-01

    Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition p

  9. 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.

  10. Listening to Geometry

    Science.gov (United States)

    Cooper, Brett D.; Barger, Rita

    2009-01-01

    The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…

  11. Towards relativistic quantum geometry

    Science.gov (United States)

    Ridao, Luis Santiago; Bellini, Mauricio

    2015-12-01

    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.

  12. Metrics for Probabilistic Geometries

    DEFF Research Database (Denmark)

    Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo; Lawrence, Neil D.

    We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where...

  13. 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...

  14. Fractal geometry of music.

    OpenAIRE

    Hsü, K J; Hsü, A J

    1990-01-01

    Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.

  15. Towards relativistic quantum geometry

    Directory of Open Access Journals (Sweden)

    Luis Santiago Ridao

    2015-12-01

    Full Text Available 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.

  16. 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.

  17. Towards a nano geometry?

    DEFF Research Database (Denmark)

    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 elabo...

  18. Topics in Riemannian geometry

    International Nuclear Information System (INIS)

    The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

  19. Physics and geometry

    International Nuclear Information System (INIS)

    The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

  20. 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.

  1. Analytical techniques

    International Nuclear Information System (INIS)

    The paper concerns the physical principles behind the analytical techniques employing high energy ion microbeams, with special attention to features that affect their use with microbeams. Particle-induced x-ray emission (PIXIE) is discussed with respect to X-ray production, thick-target PIXIE, a microbeam PIXIE system, sensitivity, and microbeam PIXIE applications. An explanation of nuclear reaction analysis (NRA) is given for NRA with charged particle detection, NRA with neutron detection and NRA with gamma detection. The essentials of Rutherford back scattering (RBS) are given, along with the elastic recoil detection analysis, which has very close connections with RBS but was introduced much more recently. Finally a comparison of the microbeam's capability with those of its main competitors is presented. (UK)

  2. Kinetics of binding and geometry of cells on molecular biochips

    OpenAIRE

    Chechetkin, V.R.

    2011-01-01

    We examine how the shape of cells and the geometry of experiment affect the reaction-diffusion kinetics at the binding between target and probe molecules on molecular biochips. In particular, we compare the binding kinetics for the probes immobilized on surface of the semispherical and flat circular cells, the limit of thin slab of analyte solution over probe cell as well as hemispherical gel pads and cells printed in gel slab over a substrate. It is shown that hemispherical geometry provides...

  3. Polarizability of nanowires at surfaces: Exact solution for general geometry

    OpenAIRE

    Jung, Jesper; Pedersen, Thomas G.

    2012-01-01

    The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a cylinder that can be arbitrarily buried in a substrate is derived using bipolar coordinates, cosine-, and sine-transformations. Based on the presented expressions, we analyze the polarizability of several metal nanowire geometries that are important within plasmon...

  4. Novel geometry gradient coils for MRI designed by genetic algorithm

    OpenAIRE

    Williams, Guy Barnett

    2001-01-01

    This thesis concerns the design of gradient coils for magnetic resonance imaging systems. The method of design by genetic algorithm optimisation is applied to novel gradient geometries both by use of conventional computer facilities, and, by parallelisation of the design algorithm, on a supercomputer architecture. Geometries and regions of interests which are inaccessible to analytic solution are considered, and the criteria which are difficult to include in such algorithms, such as the robus...

  5. Puzzle geometry and rigidity

    Science.gov (United States)

    Smania, Daniel

    2007-07-01

    We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admit a topological conjugacy, quasiconformal outside the filled-in Julia set, are indeed quasiconformally conjugate. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen and Koskela and of Kallunki and Koskela, optimized for applications in complex dynamics. We prove, as the first application of this new method, that, for even criticalities distinct from two, the period two cycle of the Fibonacci renormalization operator is hyperbolic with 1 -dimensional unstable manifold.

  6. Quanta of Geometry

    CERN Document Server

    Chamseddine, Ali H; Mukhanov, Viatcheslav

    2014-01-01

    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 manifolds with large quantized volume are then obtained as solutions. When this condition is adopted in the gravitational action it leads to the quantization of the four volume with the cosmological constant obtained as an integration constant. Restricting the condition to a three dimensional hypersurface implies quantization of the three volume and the possible appearance of mimetic dark matter. When restricting to a two dimensional hypersurface, under appropriate bounda...

  7. 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.

  8. Observing in school geometry

    OpenAIRE

    Zupan, Karmen

    2013-01-01

    Observing is an important process in learning geometry. In the first part of the thesis observing is considered from a psychological perspective: the Gestalt theory, its history, the distribution of gestalt qualities, as well as various studies and theories of templates. The observing process is considered also from the didactic point of view by means of the van Hiele’s theory of levels of geometric reasoning. Since colours also influence observing, a list of advices for teachers about using ...

  9. Vehicular intercept geometry

    OpenAIRE

    Tysver, Joseph Bryce

    1982-01-01

    This report presents the potential use of 3-D data at NUWES on trial runs to provide information on the geometry of two vehicles in the vicinity of intercept. Smoothing on data segments provides velocity components as well as smoothed estimates or vehicle locations. Analysis of this smoothed data can be analyzed to establish (1) distance between vehicles (2) vehicular heading directional angles (3) look angle for attack vehicle, (4) attack angle (5) projected intercept point and time, (6) p...

  10. 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....

  11. Noncommutative Geometry Year 2000

    OpenAIRE

    Connes, Alain

    2000-01-01

    We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools of the theory, K-theory, Cyclic cohomology, Morita equivalence, Operator theoretic index theorems, Hopf algebra symmetry are reviewed. They cover the global aspects of noncommutative spaces, such as the transformation $\\theta \\to 1/\\theta$ for the NC torus $...

  12. 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...

  13. 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.

  14. Relativistic quantum equation in nonstationary space-time geometry

    Energy Technology Data Exchange (ETDEWEB)

    Gaffour, L, E-mail: lgaffour.usba@yahoo.fr [Department of Physics, Laboratory of Elaboration and Caracterisation of Materials, Faculty of Sciences, Sidi-Bel-Abbes university, 22000 (Algeria)

    2011-07-08

    An analytical solution for the 1-1 D relativistic quantum equation in dependent space-time geometry is given when the imaginary part of the particle mass is negligible. The solution is accomplished through covariant transformations of wave equation. The solutions have a modal structure and the modes are dynamics. The relativistic redshift turns out to be a manifestation of the space-time geometry motion. As illustrations, two space-time geometry motions corresponding to nonlinear mappings and the linear Lorentz transformations are discussed.

  15. Geometry Optimization Of Marinelli Sample In Environmental Radioactivity Measurement

    International Nuclear Information System (INIS)

    The problem of geometry optimization in environmental radioactivity determination has been studied by many scientists in the world. However, up to now, there have been not any published articles which studied optimum sample geometry in any given volumes. In this work, the simulation program MCNP was used to build the detection efficiency analytical formulas which can be used to calculate optimized geometries of Marinelli beaker in environmental radioactivity measurement. The geometry optimization was carried out with the sample volumes from 10 ml to 450 ml and the gamma-ray energy from 60 keV to 2 MeV. These optimized geometries give the highest detection efficiencies corresponding to given volumes. The goal of our study is to improve the limitation in low-level radioactivity measurement of environmental samples. (author)

  16. Two lectures on D-geometry and noncommutative geometry

    International Nuclear Information System (INIS)

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

  17. Holographic free energy and thermodynamic geometry

    CERN Document Server

    Ghorai, Debabrata

    2016-01-01

    We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

  18. The universal instability in general geometry

    Energy Technology Data Exchange (ETDEWEB)

    Helander, P.; Plunk, G. G. [Max-Planck-Institut für Plasmaphysik, Wendelsteinstr. 1, 17491 Greifswald (Germany)

    2015-09-15

    The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.

  19. The universal instability in general geometry

    International Nuclear Information System (INIS)

    The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability

  20. LEARNING GEOMETRY THROUGH MIMESIS AND DIGITAL CONSTRUCT

    Directory of Open Access Journals (Sweden)

    Maria Mion POP

    2015-12-01

    Full Text Available The theme proposed by us is useful to teachers and students for mathematics in the compulsory school cycle. The issues faced by school teachers/parents are the difficulty with which students read and understand the lessons/examples/synthesis in order to assimilate technical terms. The echoic and iconic memory facilitates the learning of the specific curriculum of linear, spatial and analytical geometry by the students using digital platform designed by us; it facilitates the acquiring of the theoretical elements of applied geometry by encoding-decoding, so that the teacher's role becomes the one of the advisor and not only a person who transmits the information. The utility of the program extends from mainstream schools to special schools.

  1. Geometry of Quantum States

    International Nuclear Information System (INIS)

    A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and

  2. Introductory non-Euclidean geometry

    CERN Document Server

    Manning, Henry Parker

    2013-01-01

    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.

  3. Reflexive functors in Algebraic Geometry

    OpenAIRE

    Sancho, Pedro

    2015-01-01

    Reflexive functors of modules naturally appear in Algebraic Geometry. In this paper we define a wide and elementary family of reflexive functors of modules, closed by tensor products and homomorphisms, in which Algebraic Geometry can be developed.

  4. 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

  5. Geometry and Combinatorics

    DEFF Research Database (Denmark)

    Kokkendorff, Simon Lyngby

    2002-01-01

    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 is then...... applied to show, that hyperbolic spaces are of strictly negative type. We also give an application to maximal distributions of subharmonic kernels. The most important application is probably the discussion of closed geodesics and negative type. Among other things we show, that a compact Riemannian...

  6. 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

  7. 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

  8. Duality and asymptotic geometries

    CERN Document Server

    Boonstra, H J; Skenderis, K

    1997-01-01

    We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \\xx E^l \\xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed.

  9. The geometry of thermodynamics

    CERN Document Server

    Quevedo, Hernando

    2007-01-01

    We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre invariant metric, which is given in terms of the fundamental equation of the corresponding thermodynamic system, and analyze its geometric properties in the case of the van der Waals gas, and black holes. We conclude that the geometry of this particular metric reproduces the thermodynamic behavior of the van der Waals gas, and the Reissner-Nordstr\\"om black hole, but it is not adequate for the thermodynamic description of Kerr black holes.

  10. Developing thinking in geometry

    CERN Document Server

    Johnston-Wilder, Sue

    2005-01-01

    'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice `This creative, innovative and fascinating book/CD package is one you ""MUST BUY"". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics' - Professor Sylvia Johnson, Sheffield Hallam University 'This book exudes activity and interactivity. Moreov

  11. 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

  12. Geometry and Analysis Seminar

    CERN Document Server

    Isaev, Alexander

    2007-01-01

    Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.

  13. 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.

  14. Nonlinear connections and spinor geometry

    Directory of Open Access Journals (Sweden)

    Nadejda A. Vicol

    2004-05-01

    Full Text Available We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.

  15. Stability and mix in spherical geometry

    International Nuclear Information System (INIS)

    We consider a spherical system composed of N concentric fluid shells having perturbations of amplitude ηi at interface i, i=1,2,...,N-1. For arbitrary implosion-explosion histories Ri(t), we present the set of N-1 second-order differential equations describing the time evolution of the ηi which are coupled to the two adjacent ηi±1. We report analytical solutions for the N=2 and N=3 cases. We also present a model to describe the evolution of a turbulent mixing layer in spherical geometry when the interface between two fluids undergoes a constant acceleration or a shock

  16. The Geometry of Walker Manifolds

    CERN Document Server

    Gilkey, Peter

    2009-01-01

    This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in

  17. Geometry methods and packages

    International Nuclear Information System (INIS)

    The authors address the problem of following the trajectory of a particle in simulations. It is necessary to follow the motion of the particle, and to determine its intersection with different geometric surfaces in the problem, in order to relate the stepping of the particle trajectory into real motion through the physical problem at hand. The distance a particle moves before encountering a surface is needed to compare with the actual transport distance that is about to be used in the simulation. Basic mathematical expressions are developed for the intersections of particle trajectories with plane and conic surfaces. The authors show how these are used in the EGS4 code system, which should be typical of the general problem. They also review geometry packages currently being used in electron-photon Monte Carlo programs

  18. Emergent geometry of membranes

    Science.gov (United States)

    de Badyn, Mathias Hudoba; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che

    2015-11-01

    In work [1], a surface embedded in flat ℝ 3 is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ 3. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

  19. Optically defined mechanical geometry

    Science.gov (United States)

    Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.

    2016-05-01

    In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.

  20. Critique of information geometry

    International Nuclear Information System (INIS)

    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

  1. Geometry of Periodic Monopoles

    CERN Document Server

    Maldonado, Rafael

    2013-01-01

    BPS monopoles on $\\mathbb{R}^2\\timesS^1$ correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder $\\mathbb{R}\\times S^1$. The moduli space M of two monopoles with their centre-of-mass fixed is a 4-dimensional manifold with a natural hyperk\\"ahler metric, and its geodesics correspond to slow-motion monopole scattering. The purpose of this paper is to study the geometry of M in terms of the Nahm/Hitchin data, i.e. in terms of structures on $\\mathbb{R}\\times S^1$. In particular, we identify the moduli, derive the asymptotic metric on M, and discuss several geodesic surfaces and geodesics on M. The latter include novel examples of monopole dynamics.

  2. Geometry, Renormalization, And Supersymmetry

    CERN Document Server

    Berg, G M

    2001-01-01

    This thesis is about understanding, applying and improving quantum field theory. We compute renormalization group flows as the evolution of a “coarse-graining” operator without the need for a Euclidean formulation. Renormalization is cast in the form of a Lie algebra of (in general infinite) matrices that generate, by exponentiation, counterterms for diagrams with subdivergences. These results may shed light on noncommutative geometry. We check our results in a scalar three-loop example. Then, we consider the renormalization of a certain supersymmetric gauge theory, the low-energy limit of a string model. We compare results to those computed directly in the string model and find agreement. Finally, we discuss the possibility of detecting quantum-mechanical phases distinguishing the two Pin groups, double covers of the full Lorentz group. Majorana fermions, if detected, would provide an important testing ground; such particles can restrict the choice of Pin group.

  3. Principles of algebraic geometry

    CERN Document Server

    Griffiths, Phillip A

    1994-01-01

    A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top

  4. A new approach to two-charge fuzzball geometries

    Indian Academy of Sciences (India)

    Rui-Yan Yu

    2009-04-01

    A few years ago, Mathur proposed a `fuzzball' conjecture to give a microscopic description of black hole entropy. In the fuzzball scenario, the entropy in a two-charge black hole corresponds to microstates of a two-charge string (brane) system, e.g., a winding fundamental string with momentum modes. The geometry of such a two-charge system is fuzzy near the horizon, and is very difficult to get analytically in general. In this paper, we show a new method to get geometries of two-charge fuzzball. Our method is based on the multipole expansion. We find that the method is powerful enough to get a clean analytic form of metric of the fuzzball with one-momentum mode. It is expected to get multi-mode geometries using this method in the near future.

  5. 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

  6. On ''conformal spinor geometry'': An attempt to ''understand'' internal symmetry

    International Nuclear Information System (INIS)

    The natural homomorphism of pure spinors corresponding to a given Clifford algebra Csub(2n) to polarized isotropic n-planes of complex Euclidean space Esub(2n)sup(c) is taken as a starting point for the construction of a geometry called spinor geometry where pure spinors are the only elements out of which all tensors have to be constructed (analytically as bilinear polynomia of the components of a pure spinor). C4 and C6 spinor geometry are analyzed but it seems that C8 spinor geometry is necessary to construct Minkowski space Msup(3,1). C6 spinor field equations give rise in Minkowski space to a pair of Dirac equations (for conformal semispinors) presenting an SU(2) internal symmetry algebra. Mass is generated by spontaneously breaking the original O(4,2) symmetry of the spinor equation. (author)

  7. Euclidean distance geometry and applications

    OpenAIRE

    Liberti, Leo; Lavor, Carlile; Maculan, Nelson; Mucherino, Antonio

    2012-01-01

    Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.

  8. 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

  9. Universal Hyperbolic Geometry I: Trigonometry

    OpenAIRE

    Wildberger, N J

    2009-01-01

    Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry of Lorentz, Einstein and Minkowski comes from a projective point of view, with trigonometric laws that extend to `points at infinity', here called `null points', and beyond to `ideal points' associated to a hyperboloid of one sheet. The theory works over a general field not of characteristic two, and the main laws ...

  10. Gravity, Geometry and the Quantum

    OpenAIRE

    Ashtekar, Abhay

    2006-01-01

    After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic cosmology. Quantum geometry effects are shown to replace the big bang by a big bounce. Thus, quantum physics does not stop at the big-bang singularity. Rather there is a pre-big-bang branch joined to the current post-big-bang branch by a `quantum bridge'. Furth...

  11. The Geometry of Homological Triangles

    CERN Document Server

    Smarandache, Florentin

    2012-01-01

    This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a "filter" through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles, while the last ones to their applications.

  12. Color From Geometry

    CERN Document Server

    Guijosa, A

    1999-01-01

    This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...

  13. Topics In Quantum Geometry

    CERN Document Server

    Raugas, M V

    2001-01-01

    In this work, we investigate different features of the quantum geometry associated to string theory. In chapter one, we use the language of quiver theory to determine the toric part of the classical moduli space of D-branes on a nonabelian Calabi-Yau threefold singularity and see that it admits topology-changing transitions. In chapter two, we determine the worldvolume field theories of D3-branes transverse to Calabi-Yau cones over singular Fano surfaces, which can be realized as partial resolutions of an orbifold of complex three-space by a discrete group. A mismatch between the isometries of the complex line bundle over the Fano surfaces and the discrete symmetries of the effective superpotential is found. In chapter three, we investigate the quantum volume of D-branes wrapped around cycles of various dimension in Calabi-Yau fourfolds and fivefolds. We consider the cases of the sextic and heptic hypersurface Calabi-Yau manifolds, as well as one example in weighted projective space, and find expressions for...

  14. 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.  

  15. 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)

  16. 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

  17. Quantum roots in geometry : II

    International Nuclear Information System (INIS)

    The present work is a review of a series of papers, published in the last ten. years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, Spin-Torsion Interaction, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, Charge-Torsion Interaction, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-geometry are special cases of PAP-geometry

  18. Virtual Monopole Geometry and Confinement

    CERN Document Server

    La, H S

    1999-01-01

    Generalizing the geometry of the gauge covariant variables in Yang-Mills theory proposed by Johnson and Haagensen, the 4-d geometry associated with a monopole is defined for SU(2). There are three relevant geometries: AdS$_2\\times S^2$, $R^2\\times S^2$ and $H_+\\times S^2$, depending on the asymptotic behavior of the torsion. Using this geometry, the Wilson loop average is computed {\\it à la} Nambu-Goto action. In case of AdS$_2\\times S^2$, it satisfies the area law.

  19. Impact of lattice geometry distortion due to ageing on selected physics parameters of a CANDU reactor

    International Nuclear Information System (INIS)

    In this paper, results related to a limited scope assessment of the geometry-distortion-induced effects on key reactor physics parameters of a CANDU reactor are discussed. These results were generated by simulations using refined analytical methods and detailed modeling of CANDU reactor core with aged lattice cell geometry. (authors)

  20. Casimir effects for classical and quantum liquids in slab geometry: A brief review

    International Nuclear Information System (INIS)

    We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries

  1. Diophantine and tropical geometry, and uniformity of rational points on curves

    OpenAIRE

    Katz, Eric; Rabinoff, Joseph; Zureick-Brown, David

    2016-01-01

    We describe recent work connecting combinatorics and tropical/non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curves and for torsion packets of curves. The method of Chabauty--Coleman lies at the heart of this connection, and we emphasize the clarification that tropical geometry affords throughout the theory of $p$-adic integration, especially to the comparison of analytic continuations of $p$-adic integrals and to the analysis ...

  2. Identification of Plasmonic Modes in Parabolic Cylinder Geometry by Quasi-Separation of Variables

    OpenAIRE

    KURIHARA, Kazuyoshi; Otomo, Akira; Yamamoto, Kazuhiro; TAKAHARA, Junichi; Tani, Masahiko; Kuwashima, Fumiyoshi

    2014-01-01

    This paper describes the plasmonic modes in the parabolic cylinder geometry as a theoretical complement to the previous paper (J Phys A 42:185401) that considered the modes in the circular paraboloidal geometry. In order to identify the plasmonic modes in the parabolic cylinder geometry, analytic solutions for surface plasmon polaritons are examined by solving the wave equation for the magnetic field in parabolic cylindrical coordinates using quasi-separation of variables in combination with ...

  3. Surrogate Modeling for Geometry Optimization

    DEFF Research Database (Denmark)

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

    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....

  4. GPS: Geometry, Probability, and Statistics

    Science.gov (United States)

    Field, Mike

    2012-01-01

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

  5. Limits of downstream hydraulic geometry

    Science.gov (United States)

    Wohl, Ellen

    2004-10-01

    Adjustments to flow width, depth, and velocity in response to changes in discharge are commonly characterized by using downstream hydraulic geometry relationships. The spatial limits of these relationships within a drainage basin have not been systematically quantified. Where the erosional resistance of the channel substrate is sufficiently large, hydraulic driving forces presumably will be unable to adjust channel form. Data sets from 10 mountain rivers in the United States, Panama, Nepal, and New Zealand are used in this study to explore the limits of downstream hydraulic geometry relationships. Where the ratio of stream power to sediment size (Ω/D84) exceeds 10,000 kg/s3, downstream hydraulic geometry is well developed; where the ratio falls below 10,000 kg/s3, downstream hydraulic geometry relationships are poorly developed. These limitations on downstream hydraulic geometry have important implications for channel engineering and simulations of landscape change.

  6. Lobachevsky's Geometry and Research of Geometry of the Universe

    Science.gov (United States)

    Brylevskaya, L. I.

    2008-10-01

    For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.

  7. Analytics for Education

    Science.gov (United States)

    MacNeill, Sheila; Campbell, Lorna M.; Hawksey, Martin

    2014-01-01

    This article presents an overview of the development and use of analytics in the context of education. Using Buckingham Shum's three levels of analytics, the authors present a critical analysis of current developments in the domain of learning analytics, and contrast the potential value of analytics research and development with real world…

  8. Controlling electromagnetic fields at boundaries of arbitrary geometries

    Science.gov (United States)

    Teo, Jonathon Yi Han; Wong, Liang Jie; Molardi, Carlo; Genevet, Patrice

    2016-08-01

    Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realize coatings to achieve exotic effects like optical illusions and anomalous diffraction behavior. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.

  9. Controlling Electromagnetic Fields at Boundaries of Arbitrary Geometries

    CERN Document Server

    Teo, Jonathon Yi Han; Molardi, Carlo; Genevet, Patrice

    2015-01-01

    Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realise coatings to achieve exotic effects like optical illusions and anomalous diffraction behaviour. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.

  10. The geometry description markup language

    International Nuclear Information System (INIS)

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

  11. 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.

  12. Quantum Roots in Geometry: II

    CERN Document Server

    Wanas, M I

    2006-01-01

    The present work is a review of a series of papers, published in the last ten years, comprising an attempt to find a suitable avenue from geometry to quantum. It shows clearly that, any non-symmetric geometry admits some built-in quantum features. These features disappear completely once the geometry becomes symmetric (torsion-less). It is shown that, torsion of space-time plays an important role in both geometry and physics. It interacts with the spin of the moving particle and with its charge. The first interaction, {\\bf{Spin-Torsion Interaction}}, has been used to overcome the discrepancy in the results of the COW-experiment. The second interaction, {\\bf{Charge-Torsion Interaction}}, is similar to the Aharonov-Bohm effect. As a byproduct, a new version of Absolute Parallelism (AP) geometry, the Parameterized Absolute Parallelism (PAP) geometry, has been established and developed. This version can be used to construct field theories that admit some quantum features. Riemannian geometry and conventional AP-g...

  13. Riemannian statistics geometry: A counterpart approach of inference geometry

    CERN Document Server

    Velazquez, L

    2011-01-01

    Riemannian statistics geometry is proposed in this work as a counterpart approach of inference geometry. This geometry framework is inspired on the existence of a notable analogy between the general theorems of inference theory and the the general fluctuation theorems associated with a parametric family of distribution functions $dp(I|\\theta)$, which describes the stochastic behavior of a set of continuous stochastic variables driven by a set of control parameters $\\theta$. In this approach, statistical properties are rephrased as purely geometric notions derived from the Riemannian structure on the manifold $\\mathcal{M}_{\\theta}$ of stochastic variables $I$. Consequently, this theory arises as an alternative framework for applying the powerful methods of differential geometry for the statistical analysis.

  14. Fluctuation geometry: A counterpart approach of inference geometry

    OpenAIRE

    Velazquez, L.

    2011-01-01

    Starting from an axiomatic perspective, \\emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of \\emph{inference theory} and the the \\emph{general fluctuation theorems} associated with a parametric family of distribution functions $dp(I|\\theta)=\\rho(I|\\theta)dI$, which describes the behavior of a set of \\emph{continuous stochastic variables} driven by a set of contr...

  15. 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

  16. 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

  17. 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

  18. A proposal of an open PET geometry

    Energy Technology Data Exchange (ETDEWEB)

    Yamaya, Taiga [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Inaniwa, Taku [Research Center for Charged Particle Therapy, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan); Minohara, Shinichi [Research Center for Charged Particle Therapy, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 263-8555 (Japan); Yoshida, Eiji [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Inadama, Naoko [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Nishikido, Fumihiko [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Shibuya, Kengo [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Lam, Chih Fung [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan); Murayama, Hideo [Molecular Imaging Center, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba, 263-8555 (Japan)

    2008-02-07

    The long patient port of a PET scanner tends to put stress on patients, especially patients with claustrophobia. It also prevents doctors and technicians from taking care of patients during scanning. In this paper, we proposed an 'open PET' geometry, which consists of two axially separated detector rings. A long and continuous field-of-view (FOV) including a 360 deg. opened gap between two detector rings can be imaged enabling a fully 3D image reconstruction of all the possible lines-of-response. The open PET will become practical if iterative image reconstruction methods are applied even though image reconstruction of the open PET is analytically an incomplete problem. First we implemented a 'masked' 3D ordered subset expectation maximization (OS-EM) in which the system matrix was obtained from a long 'gapless' scanner by applying a mask to detectors corresponding to the open space. Next, in order to evaluate imaging performance of the proposed open PET geometry, we simulated a dual HR+ scanner (ring diameter of D = 827 mm, axial length of W = 154 mm x 2) separated by a variable gap. The gap W was the maximum limit to have axially continuous FOV of 3W though the maximum diameter of FOV at the central slice was limited to D/2. Artifacts, observed on both sides of the open space when the gap exceeded W, were effectively reduced by inserting detectors partially into unnecessary open spaces. We also tested the open PET geometry using experimental data obtained by the jPET-D4. The jPET-D4 is a prototype brain scanner, which has 5 rings of 24 detector blocks. We simulated the open jPET-D4 with a gap of 66 mm by eliminating 1 block-ring from experimental data. Although some artifacts were seen at both ends of the opened gap, very similar images were obtained with and without the gap. The proposed open PET geometry is expected to lead to realization of in-beam PET, which is a method for an in situ monitoring of charged particle therapy, by

  19. Highlights of Noncommutative Spectral Geometry

    CERN Document Server

    Sakellariadou, Mairi

    2012-01-01

    A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.

  20. 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.

  1. 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.

  2. 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, ...

  3. Guide to Computational Geometry Processing

    DEFF Research Database (Denmark)

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

    processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction to the......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 be......, 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...

  4. When to carry out analytic continuation?

    CERN Document Server

    Zuo, J M

    1998-01-01

    This paper discusses the analytic continuation in the thermal field theory by using the theory of $\\eta-\\xi$ spacetime. Taking a simple model as example, the $2\\times 2$ matrix real-time propagator is solved from the equation obtained through continuation of the equation for the imaginary-time propagator. The geometry of the $\\eta-\\xi$ spacetime plays important role in the discussion.

  5. 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)

  6. Duality principle and braided geometry

    CERN Document Server

    Majid, S

    1994-01-01

    We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided geometry.

  7. Higgs mass in noncommutative geometry

    International Nuclear Information System (INIS)

    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)

  8. 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.

  9. Geometry of the quantum universe

    International Nuclear Information System (INIS)

    A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell decompositions of spacetime. More specifically, we focus on evidence of fractality and global anisotropy, and on how they depend on the bare coupling constants of the theory.

  10. 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

  11. 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.

  12. Resistive drift wave turbulence in a three-dimensional geometry

    DEFF Research Database (Denmark)

    Korsholm, Søren Bang; Michelsen, Poul; Naulin, V.

    1999-01-01

    The Hasegawa-Wakatani model describing resistive drift waves is investigated analytically and numerically in a three-dimensional periodic geometry. After an initial growth of the energy the drift waves couple nonlinearly to convective cells, which eventually dominate the system completely. An app...... approach to include more physical boundary conditions to the system is presented. This changes the results of the simulations significantly. (C) 1999 American Institute of Physics.......The Hasegawa-Wakatani model describing resistive drift waves is investigated analytically and numerically in a three-dimensional periodic geometry. After an initial growth of the energy the drift waves couple nonlinearly to convective cells, which eventually dominate the system completely. An...

  13. Geometry-independent energy band simulator for radially symmetric diodes

    Science.gov (United States)

    Kirkpatrick, T.; Buonassisi, T.

    2016-07-01

    In this work, a geometrically independent method to calculate the energy band diagram of radially symmetric diodes is reported. For radially symmetric diodes, the calculation of electron (or hole) energies across the junction can be reduced to a singular spatially dependent variable. Because geometry is not incorporated into the calculation a priori, by reducing the physics to a single spatial variable, energy band calculations can be performed in multiple geometries, simultaneously, for direct comparison to each other. The calculation outlined herein is pseudo-analytical and does not utilize finite element and/or control volume methods. It is, therefore, capable of generating spatially analytic equations for analyzing limiting scenarios of the junction, beneficial for yielding insight into the physics and design criteria of depletion for non-planar semiconducting devices.

  14. Optimizing the Superlens: manipulating geometry to enhance the resolution

    OpenAIRE

    Podolskiy, Viktor A.; Kuhta, Nicholas A.; Milton, Graeme W.

    2005-01-01

    We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not optimal from the resolution point-of-view, develop an analytical expression for the resolution limit of a generalized lens, use it to find the optimum lens configuration, and calculate the maximum absorption practical nearfield superlenses may have. We demonst...

  15. Croatian Analytical Terminology

    OpenAIRE

    Kastelan-Macan; M.

    2008-01-01

    Results of analytical research are necessary in all human activities. They are inevitable in making decisions in the environmental chemistry, agriculture, forestry, veterinary medicine, pharmaceutical industry, and biochemistry. Without analytical measurements the quality of materials and products cannot be assessed, so that analytical chemistry is an essential part of technical sciences and disciplines.The language of Croatian science, and analytical chemistry within it, was one of the goals...

  16. 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.

  17. 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...

  18. 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.

  19. 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...

  20. Embedding problems in symplectic geometry

    CERN Document Server

    Schlenk, Felix

    2005-01-01

    Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov''s famous "non-squeezing'''' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'''', and "lifting''''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.

  1. Classification of complex simple Lie algebras via projective geometry geometry

    OpenAIRE

    Landsberg, J. M.; Manivel, Laurent

    1999-01-01

    We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential varieties of homogeneous varieties already constructed. Our algorithms make no reference to root systems. Our proofs use properties of root systems, but not their classification.

  2. 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.

  3. Geometry of the random interlacement

    CERN Document Server

    Procaccia, Eviatar B

    2011-01-01

    We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory proved in \\cite{benjamini2004geometry} to prove the following: Given that two vertices $x,y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $\\lceil d/2 \\rceil$ trajectories. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $\\lceil d/2 \\rceil-1$ trajectories.

  4. 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

  5. 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

  6. On Sasakian-Einstein Geometry

    OpenAIRE

    Boyer, Charles P.; Galicki, Krzysztof

    1998-01-01

    We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are given for the `product' of two Sasakian-Einstein manifolds to be a smooth Sasakian-Einstein manifold. Using spectral sequence arguments we work out the cohomology ring in many cases of interest. This type of geometry has recently become of interest in the p...

  7. 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.

  8. Geometry, topology, and string theory

    International Nuclear Information System (INIS)

    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

  9. 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.

  10. Combinatorial geometry in the plane

    CERN Document Server

    Hadwiger, Hugo; Klee, Victor

    2014-01-01

    Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

  11. 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

  12. Analytical and numerical analyses of hydrologic well-bore experiments

    International Nuclear Information System (INIS)

    An analytical approximate method and a finite-difference numerical model (based on the rate at which a borehole fills with water) were developed to estimate permeability of the Magenta Formation in southeastern New Mexico near the proposed Waste Isolation Pilot Project (WIPP) site. The analytical treatment applies to certain simple geometries with idealized boundary conditions (constant properties, ground water compressibility negligible). Permissible geometries include water-collecting cylinders with large needle-like aspect ratios located beneath the water table. The analytical treatment clearly shows the sensitivity of inferences and conclusions to material properties and geometries. Much of the existing well-bore fill-rate data fall within the range of validity of this simplified analysis. Admission of compressibility effects into the generalized Darcy law, and a nondimensionalization of the equations identify the range of experimental conditions and material properties for which the approximations are invalid. In the numerical capability to complement this analytical treatment, numerous restrictions have been removed so that the code can treat complex geometries for a variety of boundary conditions and variable properties. The compressibility term that is excluded in the analytical treatment is maintained in these numerical solutions. The resulting equations are formally parabolicand can be solved by an implicit integrator with guaranteed stability. The two methods, applied to several different experimental situations, agree with each other. 9 figures, 3 tables

  13. News for analytical chemists

    DEFF Research Database (Denmark)

    Andersen, Jens Enevold Thaulov; Karlberg, Bo

    2009-01-01

    The EuCheMS Division of Analytical Chemistry (DAC) maintains a website with informations on groups of analytical chemistry at European universities (www.dac-euchems. org). Everyone may contribute to the database and contributors are responsible for an annual update of the information. The service...... is offered free of charge. The report on activities of DAC during 2008 was published in journals of analytical chemistry where Manfred Grasserbauer contributed with his personal view on analytical chemistry in the assessment of climate changes and sustainable application of the natural resources to...... committee directed to various topics of analytical chemistry. Although affected by the global financial crisis, the Euroanalysis Conference will be held on 6 to 10 September in Innsbruck, Austria. For next year, the programme for the analytical section of the 3rd European Chemistry Congress is in...

  14. Geometri og Ølkrus

    DEFF Research Database (Denmark)

    Lützen, Jesper

    Der argumenteres for at matematikkens natur har undergået to store revolutioner: en i forbindelse med den antikke græske indførelse af den aksiomatisk-deduktive opbygning af matematikken og en anden i forbindelse med strukturmatematikkens fremkomst omkring 1900. Den ikke-euklidiske geometris rolle...

  15. Exploring Bundling Theory with Geometry

    Science.gov (United States)

    Eckalbar, John C.

    2006-01-01

    The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…

  16. 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

  17. Apollonian circles and hyperbolic geometry

    CERN Document Server

    Klén, Riku

    2010-01-01

    The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric constructions such as the construction of the middle point of a hyperbolic geodesic segment. Apollonian circles have a key role in this study.

  18. Informational geometry of social choice

    OpenAIRE

    Saari, Donald G.

    1997-01-01

    Elementary geometry is used to understand, extend and resolve basic informational difficulties in choice theory. This includes axiomatic conclusions such as Arrow's Theorem, Chichilnisky's dictator, and the Gibbard-Satterthwaite result. In this manner new results about positional voting methods are outlined, and difficulties with axiomatic approach are discussed. A topological result about "dictatorial" behavior is offered.

  19. Global texture in Lyra geometry

    OpenAIRE

    Rahaman, Farook

    2006-01-01

    In this paper, we consider global texture with time dependent displacement vector based on Lyra geometry in normal gauge i.e. displacement vector \\phi_i^* = (\\beta_0(t),0,0,0). We investigate gravitational field of global texture configuration by solving Einstein equations as well as that for the scalar field due to texture.

  20. 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…

  1. 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.

  2. Stochastic Modelling of River Geometry

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.

    1996-01-01

    Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for...... river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

  3. The geometry of SU(3)

    International Nuclear Information System (INIS)

    The group SU(3) is parameterized in terms of generalized open-quotes Euler anglesclose 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. Can (noncommutative) geometry accommodate leptoquarks?

    OpenAIRE

    Paschke, Mario; Scheck, Florian; Sitarz, Andrzej

    1997-01-01

    We investigate the geometric interpretation of the Standard Model based on noncommutative geometry. Neglecting the $S_0$-reality symmetry one may introduce leptoquarks into the model. We give a detailed discussion of the consequences (both for the Connes-Lott and the spectral action) and compare the results with physical bounds. Our result is that in either case one contradicts the experimental results.

  5. Can (noncommutative) geometry accommodate leptoquarks?

    CERN Document Server

    Paschke, M; Sitarz, A; Paschke, Mario; Scheck, Florian; Sitarz, Andrzej

    1999-01-01

    We investigate the geometric interpretation of the Standard Model based on noncommutative geometry. Neglecting the $S_0$-reality symmetry one may introduce leptoquarks into the model. We give a detailed discussion of the consequences (both for the Connes-Lott and the spectral action) and compare the results with physical bounds. Our result is that in either case one contradicts the experimental results.

  6. The Geometry of Noncommutative Symmetries

    International Nuclear Information System (INIS)

    We discuss the notion of noncommutative symmetries based on Hopf algebras in the geometric models constructed within the framework of non-commutative geometry. We introduce and discuss several notions of non-commutative symmetries and outline the construction specific examples, for instance, finite algebras and the application of symmetries in the derivation of the Dirac operator for the noncommutative torus. (author)

  7. ANALYTICAL WEIGHT ESTIMATION OF UNCONVENTIONAL LANDING GEAR DESIGNS

    OpenAIRE

    Parés Prat, Andreu; Borhani Coca, Dario; Munjulury, Raghu Chaitanya; Berry, Patrick

    2015-01-01

    Landing gear weight calculations can be carried out using statistical or analytical methods. Statistical methods were used in the past and offered quick group weights, however, they are not capable of computing with accuracy the weight of unconventional landing gears which have special geometries and performances. In this work, landing gear weight is computed using analytical methods. The procedure established by Kraus and Wille is acquired as a baseline so as to create a program able to deal...

  8. News for analytical chemists

    DEFF Research Database (Denmark)

    Andersen, Jens Enevold Thaulov; Karlberg, Bo

    The EuCheMS Division of Analytical Chemistry (DAC) maintains a website with informations on groups of analytical chemistry at European universities (www.dac-euchems. org). Everyone may contribute to the database and contributors are responsible for an annual update of the information. The service...... is offered free of charge. The report on activities of DAC during 2008 was published in journals of analytical chemistry where Manfred Grasserbauer contributed with his personal view on analytical chemistry in the assessment of climate changes and sustainable application of the natural resources to...

  9. Local shear in general magnetic stellarator geometry

    International Nuclear Information System (INIS)

    There has been relatively little work on microturbulence in stellarators. Bhattacharjee et al. gave a purely numerical illustration of linear instability for the simplest cold ion electrostatic drift wave using a general magnetic geometry ballooning mode representation. This approach was recently extended by N. Dominguez et al. with emphasis on analytic formulas derived from a single stellarator harmonic and a treatment of dissipative helical well trapped electron modes. Neither paper treats the puzzling question: How are high-m modes radially localized in stellarators with weak or no global shear? Since diffusion is likely proportional to the square of radial mode widths, this is as important as determining the growth rate. This paper argues that modes are localized by local shear not global shear. Local shear arises from the fact that the helical ripple from the external coils providing the stellarator transform increase with radius. The authors note that local curvature from the helical ripple can localize the modes along the field lines. Thus they argue that stellarators with no global shear and favorable average curvature (W7-AS) should have the same basic transport as torsatrons (Heliotron and ATF) with global shear and average unfavorable curvature. In detail they derive a complete along the field line nonlinear ballooning mode formalism in magnetic coordinates for general stellarator geometry. They apply this to the case of a single helical harmonic. For illustration, they derive a formula for diffusion from collisionless helically trapped electrons modes proportional to the square of the local shear. The model diffusion matches the universal gyroBohm LHD stellarator scaling

  10. The spin connection of twisted geometry

    OpenAIRE

    Haggard, Hal M.; Rovelli, Carlo; Vidotto, Francesca; Wieland, Wolfgang

    2012-01-01

    Twisted geometry is a piecewise-flat geometry less rigid than Regge geometry. In Loop Gravity, it provides the classical limit for each step of the truncation utilized in the definition of the quantum theory. We define the torsionless spin-connection of a twisted geometry. The difficulty given by the discontinuity of the triad is addressed by interpolating between triads. The curvature of the resulting spin connection reduces to the Regge curvature in the case of a Regge geometry.

  11. Learning Analytics Considered Harmful

    Science.gov (United States)

    Dringus, Laurie P.

    2012-01-01

    This essay is written to present a prospective stance on how learning analytics, as a core evaluative approach, must help instructors uncover the important trends and evidence of quality learner data in the online course. A critique is presented of strategic and tactical issues of learning analytics. The approach to the critique is taken through…

  12. Analytical mass spectrometry. Abstracts

    Energy Technology Data Exchange (ETDEWEB)

    1990-12-31

    This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)

  13. Analytical mass spectrometry

    Energy Technology Data Exchange (ETDEWEB)

    1990-01-01

    This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)

  14. The Analytical Hierarchy Process

    DEFF Research Database (Denmark)

    Barfod, Michael Bruhn

    2007-01-01

    The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use.......The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use....

  15. Teaching the Analytical Life

    Science.gov (United States)

    Jackson, Brian

    2010-01-01

    Using a survey of 138 writing programs, I argue that we must be more explicit about what we think students should get out of analysis to make it more likely that students will transfer their analytical skills to different settings. To ensure our students take analytical skills with them at the end of the semester, we must simplify the task we…

  16. Analytic Moufang-transformations

    International Nuclear Information System (INIS)

    The paper is aimed to be an introduction to the concept of an analytic birepresentation of an analytic Moufang loop. To describe the deviation of (S,T) from associativity, the associators (S,T) are defined and certain constraints for them, called the minimality conditions of (S,T) are established

  17. European Analytical Column

    DEFF Research Database (Denmark)

    Karlberg, B.; Grasserbauer, M.; Andersen, Jens Enevold Thaulov

    2009-01-01

    The European Analytical Column has once more invited a guest columnist to give his views on various matters related to analytical chemistry in Europe. This year, we have invited Professor Manfred Grasserbauer of the Vienna University of Technology to present some of the current challenges for...

  18. Some Heterodox Analytic Philosophy

    Directory of Open Access Journals (Sweden)

    Guillermo E. Rosado Haddock

    2013-04-01

    Full Text Available Analytic philosophy has been the most influential philosophical movement in 20th century philosophy. It has surely contributed like no other movement to the elucidation and demarcation of philosophical problems. Nonetheless, the empiricist and sometimes even nominalist convictions of orthodox analytic philosophers have served them to inadequately render even philosophers they consider their own and to propound very questionable conceptions.

  19. Guiding center orbit studies in a Tokamak Edge geometry employing boozer and Cartesian coordinate

    International Nuclear Information System (INIS)

    Guiding center Monte-Carlo codes (GCMC) in both open and closed field line regions in the tokamak edge geometry are developed for the future applications in examining the integration of core and edge turbulence transport simulations. Introducing a simple analytical model for the edge geometry, the orbital studies are presented. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  20. Casimir effects for classical and quantum liquids in slab geometry: A brief review

    Energy Technology Data Exchange (ETDEWEB)

    Biswas, Shyamal, E-mail: sbsp@uohyd.ac.in [School of Physics, University of Hyderabad, C.R. Rao Road, Gachibowli, Hyderabad-500046 (India)

    2015-05-15

    We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.

  1. Mode-mixity in Beam-like Geometries: Linear Elastic Cases and Local Partitioning

    OpenAIRE

    Blackman, B. R. K.; Conroy, Mark; Ivankovic, Alojz; et al.

    2012-01-01

    This work is conducted as a part of a wider international activity on mixed mode fractures in beam-like geometries under the coordination of European Structural Integrity Society, Technical Committee 4. In its initial phase, it considers asymmetric double cantilever beam geometry made of a linear elastic material with varying lower arm thickness and constant bending moment applied to the upper arm of the beam. A number of relevant analytical solutions are reviewed including classical Hutchins...

  2. Quo vadis, analytical chemistry?

    Science.gov (United States)

    Valcárcel, Miguel

    2016-01-01

    This paper presents an open, personal, fresh approach to the future of Analytical Chemistry in the context of the deep changes Science and Technology are anticipated to experience. Its main aim is to challenge young analytical chemists because the future of our scientific discipline is in their hands. A description of not completely accurate overall conceptions of our discipline, both past and present, to be avoided is followed by a flexible, integral definition of Analytical Chemistry and its cornerstones (viz., aims and objectives, quality trade-offs, the third basic analytical reference, the information hierarchy, social responsibility, independent research, transfer of knowledge and technology, interfaces to other scientific-technical disciplines, and well-oriented education). Obsolete paradigms, and more accurate general and specific that can be expected to provide the framework for our discipline in the coming years are described. Finally, the three possible responses of analytical chemists to the proposed changes in our discipline are discussed. PMID:26631024

  3. Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries

    CERN Document Server

    Kim, Chanju; Kwon, O-Kab

    2016-01-01

    We calculate the holographic entanglement entropy (HEE) of the $\\mathbb{Z}_k$ orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level $k$. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and $k$ up to $\\mu_0^2$-order where $\\mu_0$ is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the $F$-theorem. Except the multiplication factor and to all orders in $\\mu_0$, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with $\\mathbb{Z}_k$ orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to $...

  4. Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries

    Directory of Open Access Journals (Sweden)

    Chanju Kim

    2016-08-01

    Full Text Available We calculate the holographic entanglement entropy (HEE of the Zk orbifold of Lin–Lunin–Maldacena (LLM geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern–Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to μ02-order where μ0 is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in μ0, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with Zk orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to μ04-order for the symmetric droplet case.

  5. Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries

    Science.gov (United States)

    Kim, Chanju; Kim, Kyung Kiu; Kwon, O.-Kab

    2016-08-01

    We calculate the holographic entanglement entropy (HEE) of the Zk orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to μ02 -order where μ0 is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in μ0, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with Zk orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to μ04 -order for the symmetric droplet case.

  6. 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.

  7. 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...

  8. Geometry-Invariant Resonant Cavities

    CERN Document Server

    Liberal, Iñigo; Engheta, Nader

    2015-01-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional cavities are a function of its geometry, and, thus, the size and shape of a resonant cavity is selected in order to operate at a specific frequency. Here, we demonstrate theoretically the existence of geometry-invariant resonant cavities, i.e., resonators whose eigenfrequency is invariant with respect to geometrical deformations. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, which enable decoupling of the time and spatial field variations. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

  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. 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...

  11. Geometry of strings and fields

    CERN Document Server

    2013-01-01

    Ever since the birth of string theory, interaction with geometry has been one of the primary driving forces that has led to progress in superstring theory. On one hand, string theory has generated many new geometrical concepts; and on the other hand new ideas from geometry have often found their first applications in string theory. These topics include vertex algebras, conformal field theory, mirror symmetry, topological field theory and string theory, exact solutions of supersymmetric gauge theory and noncommutative field theory. Recent exciting developments include the matrix model approach to N=1 gauge theory, open string mirror symmetry, the derived category approach to D-branes on Calabi-Yau manifolds, geometric transitions, proof of the N=2 Seiberg-Witten solution by instanton methods, wall crossing formulas, the relation between Langlands program and supersymmetric gauge theories, indications of integrable structures in super Yang-Mills theory and AdS string theory. The program will be devoted to geome...

  12. 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 ...

  13. 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...

  14. 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...

  15. Geometry of area without length

    Science.gov (United States)

    Ho, Pei-Ming; Inami, Takeo

    2016-01-01

    To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.

  16. Geometry of Area Without Length

    CERN Document Server

    Ho, Pei-Ming

    2015-01-01

    To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of metric to area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill-defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.

  17. Algebraic geometry a concise dictionary

    CERN Document Server

    Rubei, Elena

    2014-01-01

    Algebraic geometry has a complicated, difficultlanguage. This bookcontains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of relatedsubjects are included. It helps beginners that know some, but not all,basic facts of algebraic geometryto follow seminars and to read papers. The dictionaryform makes it easy and quick to consult.

  18. Differential Geometry Based Multiscale Models

    OpenAIRE

    Wei, Guo-Wei

    2010-01-01

    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 descript...

  19. Entanglement renormalization and integral geometry

    OpenAIRE

    Huang, Xing; Lin, Feng-Li

    2015-01-01

    We revisit the applications of integral geometry in AdS$_3$ and argue that the metric of the kinematic space can be realized as the entanglement contour, which is defined as the additive entanglement density. From the renormalization of the entanglement contour, we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz. Furthermore, a renormalization group equation of the long-distance entanglement contour is then derived....

  20. Wormhole geometries in modified gravity

    OpenAIRE

    Lobo, Francisco S. N.

    2011-01-01

    A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In the context of modified gravity, it has also been shown that the normal matter can be imposed to satisfy the null energy condition, and it is the higher order curvature terms, interpreted as a gravitati...

  1. Riemannian thermo-statistics geometry

    OpenAIRE

    Velazquez, L.

    2010-01-01

    It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret entropy $\\mathcal{S}_{g}(I|\\theta)$ and all its associated thermo-statistical quantities as purely geometric notions derived from the Riemannian structure on the manifold of macroscopic observables $\\mathcal{M}_{\\theta}$ (existence of a distance $ds^{2}=g_{ij}...

  2. Un peu de geometrie tropicale

    CERN Document Server

    Brugalle, Erwan

    2009-01-01

    This basic introduction to tropical geometry is hopefully accessible to a first years student in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking. I tried as much as possible to illustrate each new definition with concrete examples and nice pictures. As the title suggests, this text is in French. A Portuguese (Brazil) version, as well as correction of exercises, can be found at http://people.math.jussieu.fr/~brugalle/largerpubli.html

  3. Is geometry bosonic or fermionic?

    CERN Document Server

    Hughes, Taylor L

    2011-01-01

    It is generally assumed that the gravitational field is bosonic. Here we show that a simple propagating torsional theory can give rise to localized geometric structures that can consistently be quantized as fermions under exchange. To demonstrate this, we show that the model can be formally mapped onto the Skyrme model of baryons, and we use well-known results from Skyrme theory. This begs the question: {\\it Is geometry bosonic or fermionic (or both)?}

  4. String Theory and Noncommutative Geometry

    OpenAIRE

    Seiberg, Nathan; Witten, Edward

    1999-01-01

    We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This ...

  5. Holographic thermalization in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Xiao-Xiong, E-mail: xxzengphysics@163.com [School of Science, Chongqing Jiaotong University, Chongqing 400074 (China); Liu, Xian-Ming, E-mail: liuxianming1980@163.com [Department of Physics, Hubei University for Nationalities, Enshi 445000, Hubei (China); Liu, Wen-Biao, E-mail: wbliu@bnu.edu.cn [Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing 100875 (China)

    2015-05-11

    Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that the larger the noncommutative parameter is, the longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.

  6. Spacetime geometry from graviton condensation

    OpenAIRE

    Zielinski, Sophia

    2016-01-01

    In this thesis we introduce a novel approach viewing spacetime geometry as an emergent phenomenon based on the condensation of a large number of quanta on a distinguished flat background. We advertise this idea with regard to investigations of spacetime singularities within a quantum field theoretical framework and semiclassical considerations of black holes. Given that in any physical theory apart from General Relativity the metric background is determined in advance, singu...

  7. 09111 Abstracts Collection -- Computational Geometry

    OpenAIRE

    Agarwal, Pankaj Kumar; Alt, Helmut; Teillaud, Monique

    2009-01-01

    From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general...

  8. 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 ...

  9. Orbit propagation in Minkowskian geometry

    Science.gov (United States)

    Roa, Javier; Peláez, Jesús

    2015-09-01

    The geometry of hyperbolic orbits suggests that Minkowskian geometry, and not Euclidean, may provide the most adequate description of the motion. This idea is explored in order to derive a new regularized formulation for propagating arbitrarily perturbed hyperbolic orbits. The mathematical foundations underlying Minkowski space-time are exploited to describe hyperbolic orbits. Hypercomplex numbers are introduced to define the rotations, vectors, and metrics in the problem: the evolution of the eccentricity vector is described on the Minkowski plane in terms of hyperbolic numbers, and the orbital plane is described on the inertial reference using quaternions. A set of eight orbital elements is introduced, namely a time-element, the components of the eccentricity vector in , the semimajor axis, and the components of the quaternion defining the orbital plane. The resulting formulation provides a deep insight into the geometry of hyperbolic orbits. The performance of the formulation in long-term propagations is studied. The orbits of four hyperbolic comets are integrated and the accuracy of the solution is compared to other regularized formulations. The resulting formulation improves the stability of the integration process and it is not affected by the perihelion passage. It provides a level of accuracy that may not be reached by the compared formulations, at the cost of increasing the computational time.

  10. 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...

  11. 105-KE Basin isolation barrier leak rate test analytical development

    International Nuclear Information System (INIS)

    This report provides analytical developments in support of the proposed leak rate test of the 105-KE Basin. The analytical basis upon which the K-basin leak test results will be used ti determine the basin leakage rates is developed in this report. The leakage of the K-Basin isolation barriers under accident conditions will be determined from the test results. There are two fundamental flow regimes that may exist in the postulated K-Basin leakage, viscous laminar and turbulent flow. An analytical development is presented for each flow regime. The basic geometry and nomenclature of the postulated leak paths are denoted

  12. Analytic vortex dynamics in an annular Bose-Einstein condensate

    Science.gov (United States)

    Toikka, L. A.; Suominen, K.-A.

    2016-05-01

    We consider analytically the dynamics of an arbitrary number and configuration of vortices in an annular Bose-Einstein condensate obtaining expressions for the free energy and vortex precession rates to logarithmic accuracy. We also obtain lower bounds for the lifetime of a single vortex in the annulus. Our results enable a closed-form analytic treatment of vortex-vortex interactions in the annulus that is exact in the incompressible limit. The incompressible hydrodynamics that is developed here paves the way for more general analytical treatments of vortex dynamics in non-simply-connected geometries.

  13. Geometry estimation of planar swarm patterns

    International Nuclear Information System (INIS)

    Phenomena of coupled individuals or particles aggregating to form cohesive patterns are ubiquitous in nature and human society. Estimation of the pattern geometry is of interest in many cases. This Letter considers a planar swarm system consisting of finite particles with long-range attractive and short-range repulsive interactions. An analytical approach is presented to evaluate the relative distance of neighboring particles and the diameter of the swarm pattern. The method is based on a scale transformation on minimum interaction potential condition of the steady state of the system, and can give conditions determining distance between neighboring particles in the steady state pattern as well as the size of it, under certain distribution assumptions. Numerical simulations are also carried out to show effectiveness of the approach. -- Highlights: → We study swarm of particles with long-range attraction and short-range repulsion. → The distance between nearest neighbors and swarm diameter are evaluated. → Scale transformation on minimum potential energy is used. → Gaussian distribution and cubic distribution are assumed. → Satisfactory estimation results for wide range of interaction parameters.

  14. Vesicle Geometries Enabled by Dynamically Trapped States.

    Science.gov (United States)

    Su, Jiaye; Yao, Zhenwei; Olvera de la Cruz, Monica

    2016-02-23

    Understanding and controlling vesicle shapes is a fundamental challenge in biophysics and materials design. In this paper, we design dynamic protocols for enlarging the shape space of both fluid and crystalline vesicles beyond the equilibrium zone. By removing water from within the vesicle at different rates, we numerically produced a series of dynamically trapped stable vesicle shapes for both fluid and crystalline vesicles in a highly controllable fashion. In crystalline vesicles that are continuously dehydrated, simulations show the initial appearance of small flat areas over the surface of the vesicles that ultimately merge to form fewer flat faces. In this way, the vesicles transform from a fullerene-like shape into various faceted polyhedrons. We perform analytical elasticity analysis to show that these salient features are attributable to the crystalline nature of the vesicle. The potential to use dynamic protocols, such as those used in this study, to engineer vesicle shape transformations is helpful for exploiting the richness of vesicle geometries for desired applications. PMID:26795199

  15. Cerebral blood flow simulations in realistic geometries

    Directory of Open Access Journals (Sweden)

    Szopos Marcela

    2012-04-01

    Full Text Available The aim of this work is to perform the computation of the blood flow in all the cerebral network, obtained from medical images as angiographies. We use free finite elements codes as FreeFEM++. We first test the code on analytical solutions in simplified geometries. Then, we study the influence of boundary conditions on the flow and we finally perform first computations on realistic meshes. L’objectif est ici de simuler l’écoulement sanguin dans tout le réseau cérébral (artériel et veineux obtenu à partir d’angiographies cérébrales 3D à l’aide de logiciels d’éléments finis libres, comme FreeFEM++. Nous menons d’abord une étude détaillée des résultats sur des solutions analytiques et l’influence des conditions limites à imposer dans des géométries simplifiées avant de travailler sur les maillages réalistes.

  16. 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

  17. 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.

  18. Analytical laboratory in NUCEF

    International Nuclear Information System (INIS)

    An analytical laboratory was completed in NUCEF (the Nuclear Fuel Cycle Safety Engineering Research Facility) of JAERI. NUCEF has two critical facilities (STACY and TRACY) and a fuel treatment system for criticality safety research. In addition, the facility has BECKY (Back-end Cycle Key Elements Research Facility) for the research on advanced reprocessing technology, TRU waste management and so on. This present report describes the design conditions and structure of the analytical laboratory as well as the specification of each analytical equipment. (J.P.N.)

  19. Google analytics integrations

    CERN Document Server

    Waisberg, Daniel

    2015-01-01

    A roadmap for turning Google Analytics into a centralized marketing analysis platform With Google Analytics Integrations, expert author Daniel Waisberg shows you how to gain a more meaningful, complete view of customers that can drive growth opportunities. This in-depth guide shows not only how to use Google Analytics, but also how to turn this powerful data collection and analysis tool into a central marketing analysis platform for your company. Taking a hands-on approach, this resource explores the integration and analysis of a host of common data sources, including Google AdWords, AdSens

  20. Criteria For Superfluid Instabilities of Geometries with Hyperscaling Violation

    CERN Document Server

    Cremonini, Sera

    2016-01-01

    We examine the onset of superfluid instabilities for geometries that exhibit hyperscaling violation and Lifshitz-like scaling at infrared and intermediate energy scales, and approach AdS in the ultraviolet. In particular, we are interested in the role of a non-trivial coupling between the neutral scalar supporting the scaling regime, and the (charged) complex scalar which condenses. The analysis focuses exclusively on unstable modes arising from the hyperscaling-violating portion of the geometry. Working at zero temperature, we identify simple analytical criteria for the presence of scalar instabilities, and discuss under which conditions a minimal charge will be needed to trigger a transition. Finite temperature examples are constructed numerically for a few illustrative cases.

  1. Structural and Trajectory Control of Variable Geometry Planetary Entry Systems

    Science.gov (United States)

    Quadrelli, Marco; Kwok, Kawai; Pellegrino, Sergio

    2009-01-01

    The results presented in this paper apply to a generic vehicle entering a planetary atmosphere which makes use of a variable geometry change to modulate the heat, drag, and acceleration loads. Two structural concepts for implementing the cone angle variation, namely a segmented shell and a corrugated shell, are presented. A structural analysis of these proposed structural configuration shows that the stress levels are tolerable during entry. The analytic expressions of the longitudinal aerodynamic coefficients are also derived, and guidance laws that track reference heat flux, drag, and aerodynamic acceleration loads are also proposed. These guidance laws have been tested in an integrated simulation environment, and the results indicate that use of variable geometry is feasible to track specific profiles of dynamic load conditions during reentry.

  2. Structural and Control Concepts for Variable Geometry Planetary Entry Systems

    Science.gov (United States)

    Quadrelli, Marco; Boussalis, Dhemetrios; Davis, Gregory; Kwok, Kawai; Pellegrino, Sergio

    2009-01-01

    The results presented in this paper apply to a generic vehicle entering a planetary atmosphere which makes use of a variable geometry change to modulate the heat, drag, and acceleration loads. Two structural concepts for implementing the cone angle variation, namely a segmented shell and a corrugated shell, are presented. A structural analysis of these proposed structural configuration shows that the stress levels are tolerable during entry. The analytic expressions of the longitudinal aerodynamic coefficients are also derived, and guidance laws that track reference heat flux, drag, and aerodynamic acceleration loads are also proposed. These guidance laws have been tested in an integrated simulation environment, and the results indicate that use of variable geometry is feasible to track specific profiles of dynamic load conditions during reentry.

  3. Geometry-dependent viscosity reduction in sheared active fluids

    CERN Document Server

    Słomka, Jonasz

    2016-01-01

    We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.

  4. Location Discovery Based on Fuzzy Geometry in Passive Sensor Networks

    Directory of Open Access Journals (Sweden)

    Rui Wang

    2011-01-01

    Full Text Available Location discovery with uncertainty using passive sensor networks in the nation's power grid is known to be challenging, due to the massive scale and inherent complexity. For bearings-only target localization in passive sensor networks, the approach of fuzzy geometry is introduced to investigate the fuzzy measurability for a moving target in R2 space. The fuzzy analytical bias expressions and the geometrical constraints are derived for bearings-only target localization. The interplay between fuzzy geometry of target localization and the fuzzy estimation bias for the case of fuzzy linear observer trajectory is analyzed in detail in sensor networks, which can realize the 3-dimensional localization including fuzzy estimate position and velocity of the target by measuring the fuzzy azimuth angles at intervals of fixed time. Simulation results show that the resulting estimate position outperforms the traditional least squares approach for localization with uncertainty.

  5. Theory of diffusion-influenced reactions in complex geometries

    CERN Document Server

    Galanti, Marta; Piazza, Francesco

    2015-01-01

    Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical form...

  6. The Effect of Geometry Instruction with Dynamic Geometry Software; GeoGebra on Van Hiele Geometry Understanding Levels of Students

    Science.gov (United States)

    Kutluca, Tamer

    2013-01-01

    The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…

  7. Analytical strategies for phosphoproteomics

    DEFF Research Database (Denmark)

    Thingholm, Tine E; Jensen, Ole N; Larsen, Martin R

    2009-01-01

    highly sensitive and specific strategies. Today, most phosphoproteomic studies are conducted by mass spectrometric strategies in combination with phospho-specific enrichment methods. This review presents an overview of different analytical strategies for the characterization of phosphoproteins. Emphasis...

  8. Enzymes in Analytical Chemistry.

    Science.gov (United States)

    Fishman, Myer M.

    1980-01-01

    Presents tabular information concerning recent research in the field of enzymes in analytic chemistry, with methods, substrate or reaction catalyzed, assay, comments and references listed. The table refers to 128 references. Also listed are 13 general citations. (CS)

  9. 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)

  10. Trends in analytical CRM

    OpenAIRE

    Havelková, Martina

    2014-01-01

    This thesis describes major trends in the field of analytical CRM. The goal is to identify those trends and compare them with current situation on the CRM market. The thesis is devided among several parts. In the opening part is described Customer Relationship Management and architecture of CRM system. The next part discribes analytical CRM and its standard ways of using. The main part of the thesis is identification of trends. Idetificated trends are characterized and compared with situation...

  11. Realtime Web Analytics

    OpenAIRE

    Cardoso, João

    2011-01-01

    Tracking what is happening on a website in realtime is invaluable. The objective of this thesis was to start and launch the first version of Snowfinch, an open source realtime web analytics application. The thesis report contains up-to-date fundamentals of web analytics; reasoning behind the most important and difficult technical decisions in the project; product development methodologies; and an overview of the resulting application. Understanding visitors is the key to a site’s succ...

  12. Encyclopedia of analytical surfaces

    CERN Document Server

    Krivoshapko, S N

    2015-01-01

    This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions  and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.

  13. Learning analytics in education

    OpenAIRE

    Štrukelj, Tajda

    2015-01-01

    Learning analytics is a young field in computer supported learning, which could have a great impact on education in the future. It is a set of analytical tools which measure, collect, analyze and report about students' data for the purpose of understanding and optimizing students' learning and environments in which this learning occurs. Today, more and more learning related activities are placed on the web. Teachers are creating virtual learning environments (VLE), in which a great set of...

  14. Competing on analytics

    OpenAIRE

    Nagin, Gleb

    2011-01-01

    Business analytics refers to the skills, technologies, applications and practisies for continuous iterative exploration and investigation of past business performance to gain insight and drive business planning. Business analytics focuses on developing new insights and understanding of business performance based on data and statistical methods. Business intelligence traditionally focuses on using a consistent set of metrics to both measure past performance and guide business planning, which i...

  15. Intelligent Visual Analytics Queries

    OpenAIRE

    Hao, Ming C.; Dayal, Umeshwar; Keim, Daniel A.; Morent, Dominik; Schneidewind, Jörn

    2007-01-01

    Visualizations of large multi-dimensional data sets, occurring in scientific and commercial applications, often reveal interesting local patterns. Analysts want to identify the causes and impacts of these interesting areas, and they also want to search for similar patterns occurring elsewhere in the data set. In this paper we introduce the Intelligent Visual Analytics Query (IVQuery) concept that combines visual interaction with automated analytical methods to support analysts in discovering ...

  16. Moduli spaces in algebraic geometry

    International Nuclear Information System (INIS)

    This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves

  17. Loop Quantum Geometry: A primer

    CERN Document Server

    Corichi, A

    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-experts interested in learning the basics of the subject.

  18. Adaptative Learning Environment for Geometry

    OpenAIRE

    Santos, Vanda; Quaresma, Pedro

    2010-01-01

    The integration of G EO GCLC, and via this one, the integration of GCLC, in an e-Learning environment course gives to the student in geometry a direct access to a DGS, creating in this way a workbench where the student can explore the constructions already built-in, to transform them, and even to create new ones keeping all the constructions in a personal folder. In this way we provide a strong contribution to the "learning by experience" component of an eLearning course. The GCLC tool integr...

  19. An invitation to noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2008-01-01

    This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke

  20. Bondi Accretion in Trumpet Geometries

    CERN Document Server

    Miller, August J

    2016-01-01

    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.

  1. Geometry of Discrete Quantum Computing

    OpenAIRE

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

    2012-01-01

    Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} 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 ...

  2. 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

  3. 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

  4. 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...

  5. 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.

  6. 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

  7. Arithmetic geometry and number theory

    CERN Document Server

    Weng, Lin

    2006-01-01

    Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of specia

  8. 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

  9. 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.

  10. Optimizing the Superlens: manipulating geometry to enhance the resolution

    CERN Document Server

    Podolskiy, V A; Milton, G W; Podolskiy, Viktor A.; Kuhta, Nicholas A.; Milton, Graeme W.

    2005-01-01

    We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not optimal from the resolution point-of-view, develop an analytical expression for the resolution limit of a generalized lens, use it to find the optimum lens configuration, and calculate the maximum absorption practical nearfield superlenses may have. We demonstrate that in contrast to the conventional superlens picture, planar imaging is typically accompanied by excitation of surface waves at both interfaces of the lens.

  11. The advanced geometry of plane curves and their applications

    CERN Document Server

    Zwikker, C

    2005-01-01

    ""Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating."" - British Journal of Applied PhysicsThis study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves.Informativ

  12. The Casimir effect in the sphere-plane geometry

    CERN Document Server

    Canaguier-Durand, Antoine; Neto, Paulo A Maia; Lambrecht, Astrid; Reynaud, Serge

    2012-01-01

    We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.

  13. Worldline Numerics for Energy-Momentum Tensors in Casimir Geometries

    CERN Document Server

    Schafer, Marco; Gies, Holger

    2015-01-01

    We develop the worldline formalism for computations of composite operators such as the fluctuation induced energy-momentum tensor. As an example, we use a fluctuating real scalar field subject to Dirichlet boundary conditions. The resulting worldline representation can be evaluated by worldline Monte-Carlo methods in continuous spacetime. We benchmark this worldline numerical algorithm with the aid of analytically accessible single-plate and parallel-plate Casimir configurations, providing a detailed analysis of statistical and systematic errors. The method generalizes straightforwardly to arbitrary Casimir geometries and general background potentials.

  14. Worldline numerics for energy-momentum tensors in Casimir geometries

    Science.gov (United States)

    Schäfer, Marco; Huet, Idrish; Gies, Holger

    2016-04-01

    We develop the worldline formalism for computations of composite operators such as the fluctuation induced energy-momentum tensor. As an example, we use a fluctuating real scalar field subject to Dirichlet boundary conditions. The resulting worldline representation can be evaluated by worldline Monte-Carlo methods in continuous spacetime. We benchmark this worldline numerical algorithm with the aid of analytically accessible single-plate and parallel-plate Casimir configurations, providing a detailed analysis of statistical and systematic errors. The method generalizes straightforwardly to arbitrary Casimir geometries and general background potentials.

  15. Thermal Casimir Effect in the Plane-Sphere Geometry

    International Nuclear Information System (INIS)

    The thermal Casimir force between two metallic plates is known to depend on the description of material properties. For large separations the dissipative Drude model leads to a force a factor of 2 smaller than the lossless plasma model. Here we show that the plane-sphere geometry, in which current experiments are performed, decreases this ratio to a factor of 3/2, as revealed by exact numerical and large-distance analytical calculations. For perfect reflectors, we find a repulsive contribution of thermal photons to the force and negative entropy values at intermediate distances.

  16. ELECTRON CYCLOTRON CURRENT DRIVE EFFICIENCY IN GENERAL TOKAMAK GEOMETRY

    International Nuclear Information System (INIS)

    Green's-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The high-velocity collision model is used to model Coulomb collisions and a simplified quasi-linear rf diffusion operator describes wave-particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the non-inductive current drive of electron cyclotron waves

  17. Effects of Magnet Size and Geometry on Magnetic Levitation Force

    Institute of Scientific and Technical Information of China (English)

    M. K. Alqadi; H. M. Al-khateeb; F. Y. Alzoubi; N. Y. Ayoub

    2007-01-01

    We obtain analytical relations for the levitation force as a function of dimensions of the superconductor-magnet system. The force has been calculated on the basis of the dipole-dipole interaction model.The effect of thickness of the superconductor on the levitation force is investigated. The results show that the influence of geometry and thickness of the magnet becomes significantly large at small levitation distances. Furthermore, approximating the permanent magnet as a point dipole results in an inaccurate estimation of the levitation force.

  18. 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.

  19. General Relativity and Weyl Geometry

    CERN Document Server

    Romero, C; Pucheu, M L

    2012-01-01

    We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same gravitational phenomena. We show that in an arbitrary Weyl frame general relativity, which takes the form of a scalar-tensor gravitational theory, is invariant with respect to Weyl tranformations. A kew point in the development of the formalism is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke gravitational theory. In this scenario, the gravitational field is not described by the metric tensor only, but by a combination of both the metric and a geometrical scalar field. We illustrate this point by, firstly, discussing the Newtonian limit in an arbitrary frame, and, secondly, by examining how distinct geometrical and physica...

  20. Finiteness Problems in Diophantine Geometry

    CERN Document Server

    Zarhin, Yuri G

    2009-01-01

    This survey contains an exposition of ideas and results related to Faltings' proof of the conjectures of Shafarevich, Tate and Mordell. This paper originally appeared in 1986 as an Appendix to the Russian translation of Serge Lang, "Fundamentals of Diophantine Geometry" (Springer Verlag, 1983) published by "Mir", Moscow (MR0854670, 88a:11054). A history of the publication of the Appendix is briefly described by Lang in Section 4 of his paper "Mordell's review, Siegel's letter to Mordell, Diophantine geometry, and 20th century mathematics" that was published (in 1995) simultaneously in Notices of the AMS and Gazette des Math\\'ematiciens (SMF) (MR1316025, 96g:11002a; MR1316133, 96g:11002b) http://smf.emath.fr/Publications/Gazette/1995/63/smf_gazette_63_17-36.pdf . Later an expanded version of the Appendix was translated into English by Neal Koblitz and published in 1989 by the American Mathematical Society as part of the collection "Eight papers translated from the Russian", AMS Translations, Series 2, Vol. 143...

  1. Differential geometry of group lattices

    International Nuclear Information System (INIS)

    In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained

  2. 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...

  3. 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].

  4. 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 ...

  5. Tits Geometry and Positive Curvature

    CERN Document Server

    Fang, Fuquan; Thorbergsson, Gudlaugur

    2012-01-01

    There is a well known link between (maximal) irreducible polar representations and isotropy representations of irreducible symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns - Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and compact topological spherical irreducible buildings of rank at least three. We discover and exploit a rich structure of a (connected) chamber system of finite (Coxeter) type M associated with any polar action of cohomogeneity at least two on any simply connected (closed) positively curved manifold. Although this chamber system is typically not a (Tits) geometry of type M, we prove that in all cases but one that its universal (Tits) cover indeed is a building. We construct a topology on this universal cover making it into a compact topological building in the sense of Burns and Spatzier. Our work shows that the exception indeed provides a new example (also discovered by Lytchak) of a C3 geometry whose unive...

  6. Extrinsic curvature in thermodynamic geometry

    CERN Document Server

    Mansoori, Seyed Ali Hosseini; Sharifian, Elham

    2016-01-01

    We investigate the intrinsic and extrinsic curvatures of certain hypersurfaces in the thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner-Nordstr\\"{o}m-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant $Q$ hypersurface has the same sign as the heat capacity around the phase transition points. For a Kerr-Newmann-AdS (KN-AdS) black hole, the extrinsic curvature of $Q \\to 0$ hypersurface (Kerr black hole) or $J \\to 0$ hypersurface (RN black black hole) has the same sign as the heat capacity around the phase transition points. The extrinsic curvature also diverges at the phase transition points. The intrinsic curvature of the hypersurfaces diverges at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN and Kerr ones \\cite{ref1}. This approach can be easily ...

  7. Croatian Analytical Terminology

    Directory of Open Access Journals (Sweden)

    Kastelan-Macan; M.

    2008-04-01

    Full Text Available Results of analytical research are necessary in all human activities. They are inevitable in making decisions in the environmental chemistry, agriculture, forestry, veterinary medicine, pharmaceutical industry, and biochemistry. Without analytical measurements the quality of materials and products cannot be assessed, so that analytical chemistry is an essential part of technical sciences and disciplines.The language of Croatian science, and analytical chemistry within it, was one of the goals of our predecessors. Due to the political situation, they did not succeed entirely, but for the scientists in independent Croatia this is a duty, because language is one of the most important features of the Croatian identity. The awareness of the need to introduce Croatian terminology was systematically developed in the second half of the 19th century, along with the founding of scientific societies and the wish of scientists to write their scientific works in Croatian, so that the results of their research may be applied in economy. Many authors of textbooks from the 19th and the first half of the 20th century contributed to Croatian analytical terminology (F. Rački, B. Šulek, P. Žulić, G. Pexidr, J. Domac, G. Janeček , F. Bubanović, V. Njegovan and others. M. DeŢelić published the first systematic chemical terminology in 1940, adjusted to the IUPAC recommendations. In the second half of 20th century textbooks in classic analytical chemistry were written by V. Marjanović-Krajovan, M. Gyiketta-Ogrizek, S. Žilić and others. I. Filipović wrote the General and Inorganic Chemistry textbook and the Laboratory Handbook (in collaboration with P. Sabioncello and contributed greatly to establishing the terminology in instrumental analytical methods.The source of Croatian nomenclature in modern analytical chemistry today are translated textbooks by Skoog, West and Holler, as well as by Günnzler i Gremlich, and original textbooks by S. Turina, Z.

  8. The geometry of singularities and the black hole information paradox

    CERN Document Server

    Stoica, Ovidiu Cristinel

    2015-01-01

    The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have {\

  9. Simulating arbitrary-geometry ultrasound transducers using triangles

    DEFF Research Database (Denmark)

    Jensen, Jørgen Arendt

    1996-01-01

    -echo field. The spatial impulse response has only been determined analytically for a few geometries and using apodization over the transducer surface generally makes it impossible to find the response analytically. A popular approach to find the general field is thus to split the aperture into small...... number of transducers can be defined and their properties manipulated. The program can calculate all types of ultrasound fields, and can also be used for simulating B-mode and color flow images. Both the focusing and apodization can be set to be dynamic with respect to time, and it is thus possible to......-field response of a rectangle, as the triangle equations are far more complicated. This approach is therefore best suited for accurate modeling of fields, whereas the rectangle program is better suited to make fast simulated images, since contributions from many scatterers are summed here and the error is...

  10. Analytic theory of curvature effects for wave problems with general boundary conditions

    DEFF Research Database (Denmark)

    Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan

    2010-01-01

    A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found, the...

  11. An analytical formula for the vacuum polarization of rotating black holes

    CERN Document Server

    Cvetic, Mirjam; Satz, Alejandro

    2015-01-01

    We give an analytical formula for the vacuum polarization of a massless minimally coupled scalar field at the horizon of a rotating black hole with subtracted geometry. This is the first example of an exact, analytical result for a four-dimensional rotating black hole.

  12. Plasmonically amplified bioassay - Total internal reflection fluorescence vs. epifluorescence geometry.

    Science.gov (United States)

    Hageneder, Simone; Bauch, Martin; Dostalek, Jakub

    2016-08-15

    This paper investigates plasmonic amplification in two commonly used optical configurations for fluorescence readout of bioassays - epifluorescence (EPF) and total internal reflection fluorescence (TIRF). The plasmonic amplification in the EPF configuration was implemented by using crossed gold diffraction grating and Kretschmann geometry of attenuated total reflection method (ATR) was employed in the TIRF configuration. Identical assay, surface architecture for analyte capture, and optics for the excitation, collection and detection of emitted fluorescence light intensity were used in both TIRF and EPF configurations. Simulations predict that the crossed gold diffraction grating (EPF) can amplify the fluorescence signal by a factor of 10(2) by the combination of surface plasmon-enhanced excitation and directional surface plasmon-coupled emission in the red part of spectrum. This factor is about order of magnitude higher than that predicted for the Kretschmann geometry (TIRF) which only took advantage of the surface plasmon-enhanced excitation. When applied for the readout of sandwich interleukin 6 (IL-6) immunoassay, the plasmonically amplified EPF geometry designed for Alexa Fluor 647 labels offered 4-times higher fluorescence signal intensity compared to TIRF. Interestingly, both geometries allowed reaching the same detection limit of 0.4pM despite of the difference in the fluorescence signal enhancement. This is attributed to inherently lower background of fluorescence signal for TIRF geometry compared to that for EPF which compensates for the weaker fluorescence signal enhancement. The analysis of the inflammation biomarker IL-6 in serum at medically relevant concentrations and the utilization of plasmonic amplification for the fluorescence measurement of kinetics of surface affinity reactions are demonstrated for both EPF and TIRF readout. PMID:27260457

  13. SIXTUS-2. A two dimensional multigroup diffusion theory code in hexagonal geometry. Pt. 1

    International Nuclear Information System (INIS)

    A new algorithm for solving the 2-dimensional multigroup diffusion equations in hexagonal geometry is described. It is based on three novel ideas: analytic intranodal solutions, use of the group irreducible representations and an explicit scheme for solving the response matrix equations. The resulting computer code SIXTUS-2 has been found to be very accurate and effective. (Auth.)

  14. Advances in analytical chemistry

    Science.gov (United States)

    Arendale, W. F.; Congo, Richard T.; Nielsen, Bruce J.

    1991-01-01

    Implementation of computer programs based on multivariate statistical algorithms makes possible obtaining reliable information from long data vectors that contain large amounts of extraneous information, for example, noise and/or analytes that we do not wish to control. Three examples are described. Each of these applications requires the use of techniques characteristic of modern analytical chemistry. The first example, using a quantitative or analytical model, describes the determination of the acid dissociation constant for 2,2'-pyridyl thiophene using archived data. The second example describes an investigation to determine the active biocidal species of iodine in aqueous solutions. The third example is taken from a research program directed toward advanced fiber-optic chemical sensors. The second and third examples require heuristic or empirical models.

  15. Twisted analytic torsion

    Institute of Scientific and Technical Information of China (English)

    MATHAI; Varghese

    2010-01-01

    We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.

  16. Relativistic Geometry and Quantum Electrodynamics

    CERN Document Server

    González-Martin, G R

    2000-01-01

    Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field operator. Because of the inherent geometric algebraic structure these operators obey the standard commutation rules of QED. If we work with excitations, we need to use statistical theory when considering the evolution of microscopic subsystems. The use of classical statistics, in particular techniques of irreversible thermodynamics, determine that the probability of absorption or emission of a geometric excitation is a function of the classical energy density. Emission and absorption of geometric excitations imply discrete changes of certain physical variables, but with a probability determined by its wave energy density. Hence, this geometric theory, without contradicting the fundamental aspects of quantum physics, provides a geometric foundation for the theory.

  17. Model building in noncommutative geometry

    International Nuclear Information System (INIS)

    Noncommutative geometry (NCG) based on spectral triples allows to unify classical Yang-Mills-Higgs (YMH) theories and General Relativity in a single geometrical framework. The relevant spectral triples contain a finite part which encodes the particle content of the YMH models and is subject to strong geometrical restrictions. These restrictions permit a classification of certain (irreducible) spectral triples and lead to a prominent position of the Standard Model (SM) as a ''minimal'' finite spectral triple. I will give a short introduction to the basic ideas of NCG and present a ''bottom-up'' approach to model building in the framework of NCG. This noncommutative model building kit has led to phenomenologically interesting models beyond the SM. These models extend the fermionic and the gauge sector of the SM as well as the scalar sector.

  18. 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.

  19. 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.

  20. Introduction to global variational geometry

    CERN Document Server

    Krupka, Demeter

    2015-01-01

    The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...

  1. Clustering Implies Geometry in Networks.

    Science.gov (United States)

    Krioukov, Dmitri

    2016-05-20

    Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity. PMID:27258887

  2. Trapped surfaces in Lyra's geometry

    CERN Document Server

    Ziaie, Amir Hadi; Sepangi, Hamid Reza

    2013-01-01

    Motivated by the geometrical interpretation of Brans-Dicke scalar field which may also act as a torsion potential in Lyra geometry, we study the effects of space-time torsion on the dynamics of a collapsing massive star. Taking the matter content as spherically symmetric, homogeneous perfect fluid with the equation of state $p=w\\rho$, we show that as long as regularity of the initial data and weak energy condition are satisfied, the space-time torsion may delay the formation of an apparent horizon. It is found that the rate of temporal change of the torsion scalar potential plays the role of a frictional term which makes the collapse to proceed at a slower rate. As a result, a class of collapse models are found for which the apparent horizon fails to appear until the singularity is formed.

  3. 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 ...

  4. 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.

  5. Clustering Implies Geometry in Networks

    Science.gov (United States)

    Krioukov, Dmitri

    2016-05-01

    Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity.

  6. Spinors in Physics and Geometry

    Science.gov (United States)

    Trautman, A.; Furlan, G.

    1988-11-01

    The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants

  7. 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.

  8. Evolving Geometries in General Relativity

    CERN Document Server

    Taliotis, Anastasios

    2010-01-01

    The problem of collisions of shockwaves in gravity is well known and has been studied extensively in the literature. Recently, the interest in this area has been revived trough the anti-de-Sitter space/Conformal Field Theory correspondence (AdS/CFT) with the difference that in this case the background geometry is Anti de Sitter in five dimensions. In a recent project that we have completed in the context of AdS/CFT, we have gained insight in the problem of shockwaves and our goal in this work is to apply the technique we have developed there in the case of ordinary gravity. In the current project, each of the shockwaves correspond to a point-like Stress-Energy tensor that moves with the speed of light while the collision is asymmetric and involves an impact parameter (b). Our method is to expand the metric $(g_{\\mu \

  9. Seesaw mechanism in warped geometry

    International Nuclear Information System (INIS)

    We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to MP1.exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)

  10. 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...

  11. Hopf algebras in noncommutative geometry

    International Nuclear Information System (INIS)

    We give an introductory survey to the use of Hopf algebras in several problems of non- commutative 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 non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

  12. Geometry of discrete quantum computing

    International Nuclear Information System (INIS)

    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 Fp2 (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 CP2n-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 DCP2n-1, the discrete analogue of the complex projective space, which has p2n-1(p-1) Πk=1n-1( p2k+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 Fp2 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. (paper)

  13. Verification of a magnetic island in gyro-kinetics by comparison with analytic theory

    International Nuclear Information System (INIS)

    A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steady state for which the analytic theory is formulated

  14. Flurry Analytics pelikehityksen apuna

    OpenAIRE

    Kuusisto, Rami

    2015-01-01

    Flurry Analytics on Yahoo Mobile Developer Suiten osa, joka keskittyy analytiikkaan. Opinnäytetyössä kerrotaan Flurry Analytics SDK:n implementoimisesta sovellukseen, Flurry Analyticsin tarjoaman web-portaalin käytöstä, sekä siitä, miten näitä ominaisuuksia käytettiin toteutettaessa pelin Cabals: Legends analytiikkatoteutusta. Työssä tarkastellaan myös miten jo kehitettyä analytiikkatoteutusta voitaisiin käyttää pohjana vielä pidemmälle viedylle analytiikkatoteutukselle ja kuinka pystyttäisii...

  15. An analytic thomism?

    Directory of Open Access Journals (Sweden)

    Daniel Alejandro Pérez Chamorro.

    2012-12-01

    Full Text Available For 50 years the philosophers of the Anglo-Saxon analytic tradition (E. Anscombre, P. Geach, A. Kenny, P. Foot have tried to follow the Thomas Aquinas School which they use as a source to surpass the Cartesian Epistemology and to develop the virtue ethics. Recently, J. Haldane has inaugurated a program of “analytical thomism” which main result until the present has been his “theory of identity mind/world”. Nevertheless, none of Thomás’ admirers has still found the means of assimilating his metaphysics of being.

  16. Strictly convergent analytic structures

    OpenAIRE

    Cluckers, Raf; Lipshitz, Leonard

    2013-01-01

    We give conclusive answers to some questions about definability in analytic languages that arose shortly after the work by Denef and van den Dries, [DD], on $p$-adic subanalytic sets, and we continue the study of non-archimedean fields with analytic structure of [LR3], [CLR1] and [CL1]. We show that the language $L_K$ consisting of the language of valued fields together with all strictly convergent power series over a complete, rank one valued field $K$ can be expanded, in a definitial way, t...

  17. Foundations of predictive analytics

    CERN Document Server

    Wu, James

    2012-01-01

    Drawing on the authors' two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish--Fisher expansion and o

  18. Social network data analytics

    CERN Document Server

    Aggarwal, Charu C

    2011-01-01

    Social network analysis applications have experienced tremendous advances within the last few years due in part to increasing trends towards users interacting with each other on the internet. Social networks are organized as graphs, and the data on social networks takes on the form of massive streams, which are mined for a variety of purposes. Social Network Data Analytics covers an important niche in the social network analytics field. This edited volume, contributed by prominent researchers in this field, presents a wide selection of topics on social network data mining such as Structural Pr

  19. Geometry of thin liquid sheet flows

    Science.gov (United States)

    Chubb, Donald L.; Calfo, Frederick D.; Mcconley, Marc W.; Mcmaster, Matthew S.; Afjeh, Abdollah A.

    1994-01-01

    Incompresible, thin sheet flows have been of research interest for many years. Those studies were mainly concerned with the stability of the flow in a surrounding gas. Squire was the first to carry out a linear, invicid stability analysis of sheet flow in air and compare the results with experiment. Dombrowski and Fraser did an experimental study of the disintegration of sheet flows using several viscous liquids. They also detected the formulation of holes in their sheet flows. Hagerty and Shea carried out an inviscid stability analysis and calculated growth rates with experimental values. They compared their calculated growth rates with experimental values. Taylor studied extensively the stability of thin liquid sheets both theoretically and experimentally. He showed that thin sheets in a vacuum are stable. Brown experimentally investigated thin liquid sheet flows as a method of application of thin films. Clark and Dumbrowski carried out second-order stability analysis for invicid sheet flows. Lin introduced viscosity into the linear stability analysis of thin sheet flows in a vacuum. Mansour and Chigier conducted an experimental study of the breakup of a sheet flow surrounded by high-speed air. Lin et al. did a linear stability analysis that included viscosity and a surrounding gas. Rangel and Sirignano carried out both a linear and nonlinear invisid stability analysis that applies for any density ratio between the sheet liquid and the surrounding gas. Now there is renewed interest in sheet flows because of their possible application as low mass radiating surfaces. The objective of this study is to investigate the fluid dynamics of sheet flows that are of interest for a space radiator system. Analytical expressions that govern the sheet geometry are compared with experimental results. Since a space radiator will operate in a vacuum, the analysis does not include any drag force on the sheet flow.

  20. 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 ...

  1. An analytical approach for solid oxide cell electrode geometric design

    Science.gov (United States)

    Nelson, George J.

    2015-12-01

    An analytical model for gas distributions in porous solid oxide cell electrodes is applied to develop dimensionless metrics that describe electrode performance. These metrics include two forms of a dimensionless reactant depletion current density and a geometry sensitive Damköhler number used to assess electrode catalytic effectiveness. The first dimensionless depletion current density defines when reducing electrode thickness no longer benefits mass transfer performance for a given cell geometry. The second dimensionless depletion current density provides a gage of deviation from the limiting current behavior predicted using button-cell experimental and modeling approaches. The Damköhler number and related catalytic effectiveness quantify two-dimensional transport effects under non-depleted operating conditions, providing a means of generalizing insights from reactant depletion behavior for typical cell operating conditions. A finite element solution for gas transport based on the dusty-gas model is used as a benchmark for the analytical model and dimensionless metrics. Estimates of concentration polarization based on analytical and numerical models compare well to published experimental data. Analytical performance predictions provide clear demonstration of the influence of two-dimensional electrode geometry on solid oxide cell performance. These results agree with finite element predictions and suggest that reduction of electrode thickness does not exclusively benefit cell performance.

  2. 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.

  3. Symmetric airfoil geometry effects on leading edge noise.

    Science.gov (United States)

    Gill, James; Zhang, X; Joseph, P

    2013-10-01

    Computational aeroacoustic methods are applied to the modeling of noise due to interactions between gusts and the leading edge of real symmetric airfoils. Single frequency harmonic gusts are interacted with various airfoil geometries at zero angle of attack. The effects of airfoil thickness and leading edge radius on noise are investigated systematically and independently for the first time, at higher frequencies than previously used in computational methods. Increases in both leading edge radius and thickness are found to reduce the predicted noise. This noise reduction effect becomes greater with increasing frequency and Mach number. The dominant noise reduction mechanism for airfoils with real geometry is found to be related to the leading edge stagnation region. It is shown that accurate leading edge noise predictions can be made when assuming an inviscid meanflow, but that it is not valid to assume a uniform meanflow. Analytic flat plate predictions are found to over-predict the noise due to a NACA 0002 airfoil by up to 3 dB at high frequencies. The accuracy of analytic flat plate solutions can be expected to decrease with increasing airfoil thickness, leading edge radius, gust frequency, and Mach number. PMID:24116405

  4. Elliptic cylinder geometry for distinguishability analysis in impedance tomography.

    Science.gov (United States)

    Saka, Birsen; Yilmaz, Atila

    2004-01-01

    Electrical impedance tomography (EIT) is a technique that computes the cross-sectional impedance distribution within the body by using current and voltage measurements made on the body surface. It has been reported that the image reconstruction is distorted considerably when the boundary shape is considered to be more elliptical than circular as a more realistic shape for the measurement boundary. This paper describes an alternative framework for determining the distinguishability region with a finite measurement precision for different conductivity distributions in a body modeled by elliptic cylinder geometry. The distinguishable regions are compared in terms of modeling error for predefined inhomogeneities with elliptical and circular approaches for a noncircular measurement boundary at the body surface. Since most objects investigated by EIT are noncircular in shape, the analytical solution for the forward problem for the elliptical cross section approach is shown to be useful in order to reach a better assessment of the distinguishability region defined in a noncircular boundary. This paper is concentrated on centered elliptic inhomogeneity in the elliptical boundary and an analytic solution for this type of forward problem. The distinguishability performance of elliptical cross section with cosine injected current patterns is examined for different parameters of elliptical geometry. PMID:14723501

  5. Social Learning Analytics

    Science.gov (United States)

    Buckingham Shum, Simon; Ferguson, Rebecca

    2012-01-01

    We propose that the design and implementation of effective "Social Learning Analytics (SLA)" present significant challenges and opportunities for both research and enterprise, in three important respects. The first is that the learning landscape is extraordinarily turbulent at present, in no small part due to technological drivers. Online social…

  6. Analytics for Customer Engagement

    NARCIS (Netherlands)

    Bijmolt, Tammo H. A.; Leeflang, Peter S. H.; Block, Frank; Eisenbeiss, Maik; Hardie, Bruce G. S.; Lemmens, Aurelie; Saffert, Peter

    2010-01-01

    In this article, we discuss the state of the art of models for customer engagement and the problems that are inherent to calibrating and implementing these models. The authors first provide an overview of the data available for customer analytics and discuss recent developments. Next, the authors di

  7. Analytical Chemistry Laboratory

    Science.gov (United States)

    Anderson, Mark

    2013-01-01

    The Analytical Chemistry and Material Development Group maintains a capability in chemical analysis, materials R&D failure analysis and contamination control. The uniquely qualified staff and facility support the needs of flight projects, science instrument development and various technical tasks, as well as Cal Tech.

  8. Analytic number theory

    CERN Document Server

    Matsumoto, Kohji

    2002-01-01

    The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory

  9. Ada & the Analytical Engine.

    Science.gov (United States)

    Freeman, Elisabeth

    1996-01-01

    Presents a brief history of Ada Byron King, Countess of Lovelace, focusing on her primary role in the development of the Analytical Engine--the world's first computer. Describes the Ada Project (TAP), a centralized World Wide Web site that serves as a clearinghouse for information related to women in computing, and provides a Web address for…

  10. Geometry adaptive control of a composite reflector using PZT actuator

    Science.gov (United States)

    Lan, Lan; Jiang, Shuidong; Zhou, Yang; Fang, Houfei; Tan, Shujun; Wu, Zhigang

    2015-04-01

    Maintaining geometrical high precision for a graphite fiber reinforced composite (GFRC) reflector is a challenging task. Although great efforts have been placed to improve the fabrication precision, geometry adaptive control for a reflector is becoming more and more necessary. This paper studied geometry adaptive control for a GFRC reflector with piezoelectric ceramic transducer (PZT) actuators assembled on the ribs. In order to model the piezoelectric effect in finite element analysis (FEA), a thermal analogy was used in which the temperature was applied to simulate the actuation voltage, and the piezoelectric constant was mimicked by a Coefficient of Thermal Expansion (CTE). PZT actuator's equivalent model was validated by an experiment. The deformations of a triangular GFRC specimen with three PZT actuators were also measured experimentally and compared with that of simulation. This study developed a multidisciplinary analytical model, which includes the composite structure, thermal, thermal deformation and control system, to perform an optimization analysis and design for the adaptive GFRC reflector by considering the free vibration, gravity deformation and geometry controllability.

  11. Interplay between geometry and temperature in the Casimir effect

    Energy Technology Data Exchange (ETDEWEB)

    Weber, Alexej

    2010-06-23

    In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented. (orig.)

  12. Interplay between geometry and temperature in the Casimir effect

    International Nuclear Information System (INIS)

    In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented. (orig.)

  13. Multispectral analytical image fusion

    International Nuclear Information System (INIS)

    With new and advanced analytical imaging methods emerging, the limits of physical analysis capabilities and furthermore of data acquisition quantities are constantly pushed, claiming high demands to the field of scientific data processing and visualisation. Physical analysis methods like Secondary Ion Mass Spectrometry (SIMS) or Auger Electron Spectroscopy (AES) and others are capable of delivering high-resolution multispectral two-dimensional and three-dimensional image data; usually this multispectral data is available in form of n separate image files with each showing one element or other singular aspect of the sample. There is high need for digital image processing methods enabling the analytical scientist, confronted with such amounts of data routinely, to get rapid insight into the composition of the sample examined, to filter the relevant data and to integrate the information of numerous separate multispectral images to get the complete picture. Sophisticated image processing methods like classification and fusion provide possible solution approaches to this challenge. Classification is a treatment by multivariate statistical means in order to extract analytical information. Image fusion on the other hand denotes a process where images obtained from various sensors or at different moments of time are combined together to provide a more complete picture of a scene or object under investigation. Both techniques are important for the task of information extraction and integration and often one technique depends on the other. Therefore overall aim of this thesis is to evaluate the possibilities of both techniques regarding the task of analytical image processing and to find solutions for the integration and condensation of multispectral analytical image data in order to facilitate the interpretation of the enormous amounts of data routinely acquired by modern physical analysis instruments. (author)

  14. 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.

  15. 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. ...

  16. Automorphisms in Birational and Affine Geometry

    CERN Document Server

    Ciliberto, Ciro; Flenner, Hubert; McKernan, James; Prokhorov, Yuri; Zaidenberg, Mikhail

    2014-01-01

    The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference high...

  17. 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.

  18. Foliations dynamics, geometry and topology

    CERN Document Server

    Nicolau, Marcel

    2014-01-01

    This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods arising and used in the study of foliations. The lectures by A. El Kacimi Alaoui offer an introduction to Foliation Theory, with emphasis on examples and transverse structures. S. Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations, like limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, stable manifolds, Pesin Theory, and hyperbolic, parabolic, and elliptic types of foliations, all of them illustrated with examples. The lectures by M. Asaoka are devoted to the computation of the leafwise cohomology of orbit foliations given by locally free actions of certain Lie groups, and its application to the description of the deformation of those actions. In the lectures by K. Richardson, he studies the geometric and analytic properties ...

  19. Confocal X-ray fluorescence micro-spectroscopy experiment in tilted geometry

    International Nuclear Information System (INIS)

    This paper provides a generalized mathematical model to describe the intensity of primary X-ray fluorescence radiation collected in the tilted confocal geometry mode, where the collimating optics is rotated over an angle relative to a horizontal plane. The influence of newly introduced terms, which take into account the tilted geometry mode, is discussed. The model is verified with a multi-layer test sample scanned in depth. It is proved that for low-Z matrices, the rotation of the detection channel does not induce any significant differences in a reconstruction of the thickness and chemical composition of layers, so that it may safely be ignored. - Highlights: • A mathematical model for confocal XRF spectroscopy in tilted geometry was derived. • Tilted geometry influenced the analytical capabilities of XRF instrument slightly. • Thickness and the chemical composition of multi-layers were determined

  20. Stringlike structures in Kerr-Schild geometry: N=2 string, twistors and Calabi-Yau twofold

    CERN Document Server

    Burinskii, Alexander

    2013-01-01

    Four-dimensional Kerr-Schild geometry contains two stringy structures. The first one is the closed string formed by the Kerr singular ring, and the second one is an open complex string with was obtained in the complex structure of the Kerr-Schild geometry. The real and complex Kerr strings form together a membrane source of the over-rotating Kerr-Newman solution without horizon, $a =J/m >> m .$ It has also been obtained recently that the principal null congruence of the Kerr geometry, induced by the complex Kerr string, is determined by the Kerr theorem as a quartic in the projective twistor space, which corresponds to embedding of the Calabi-Yau twofold in the bulk of the Kerr geometry. In this paper we describe this embedding in details and show that the four folds of the twistorial K3 surface represent an analytic extension of the Kerr congruence created by antipodal involution.

  1. Absolute Parallelism Geometry: Developments, Applications and Problems

    OpenAIRE

    Wanas, M. I.

    2002-01-01

    Absolute parallelism geometry is frequently used for physical applications. It has two main defects, from the point of view of applications. The first is the identical vanishing of its curvature tensor. The second is that its autoparallel paths do not represent physical trajectories. The present work shows how these defects were treated in the course of development of the geometry. The new version of this geometry contains simultaneous non-vanishing torsion and curvatures. Also, the new paths...

  2. On the spacetime geometry of quantum nonlocality

    CERN Document Server

    Beil, Charlie

    2015-01-01

    We present a new geometry of spacetime where events may be positive dimensional. This geometry is obtained by applying the identity of indiscernibles, which is a fundamental principle of quantum statistics, to time. Quantum nonlocality arises as a natural consequence of this geometry. We also examine the ontology of the wavefunction in this framework. In particular, we show how entanglement swapping in spacetime invalidates the preparation assumption of the PBR theorem.

  3. Wormhole inspired by non-commutative geometry

    OpenAIRE

    Farook Rahaman; Sreya Karmakar; Indrani Karar; Saibal Ray

    2015-01-01

    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 gravitat...

  4. Symplectic spectral geometry of semiclassical operators

    OpenAIRE

    Pelayo, Álvaro

    2013-01-01

    In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and $\\hbar$-pseudodifferential operators. The paper emphasizes the interplay between spectral theory of operators (quantum theory) and symplectic geometry of Hamiltonians (classical theory), with an eye towards recent developments on the geometry of fini...

  5. On Profinite Hyperbolicity and Diophantine Geometry

    OpenAIRE

    Rastegar, Arash

    2012-01-01

    In this note, we explore the notion of hyperbolicity of topologically finitely generated profinite groups. Some applications to diophantine geometry are suggested and we try to reformulate certain problems in diophantine geometry in terms of hyperbolic profinite groups. Then, we introduce many occasions in which Galois groups are free profinite and try to explore implications of this condition in the world of diophantine geometry. In particular, we prove that, Grothendieck's "section conjectu...

  6. Supersymmetry and geometry of hyperbolic monopoles

    OpenAIRE

    Gharamti, Moustafa

    2015-01-01

    This thesis studies the geometry of hyperbolic monopoles using supersymmetry in four and six dimensions. On the one hand, we show that starting with a four dimensional supersymmetric Yang-Mills theory provides the necessary information to study the geometry of the complex moduli space of hyperbolic monopoles. On the other hand, we require to start with a six dimensional supersymmetric Yang-Mills theory to study the geometry of the real moduli space of hyperbolic monopoles. In c...

  7. 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

  8. Generalized geometries and scalar tensor theories

    International Nuclear Information System (INIS)

    Those generalized geometries satisfying the conditions that (a) parallel transfer with respect to the connection hamiltonian is path independent and (b) the geodesics of the metric g have the same trajectories as the auto-parallels of the connection hamiltonian, are determined. Some uniqueness theorems of the metric in terms of the curvature are shown for such generalized geometries. Geometries of this type may be useful for constructing geometrized theories of gravitation more general than Einstein's theory. (author)

  9. 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.

  10. 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...

  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./ppThe sequence of images being analysed can be viewed as supplementary material at: href="http://dx.doi.org/10.5334/ah.bz.s1"http://dx.doi.org/10.5334/ah.bz.s1

  12. Stochastic geometry in PRIZMA code

    International Nuclear Information System (INIS)

    The paper describes a method used to simulate radiation transport through random media - randomly placed grains in a matrix material. The method models the medium consequently from one grain crossed by particle trajectory to another. Like in the Limited Chord Length Sampling (LCLS) method, particles in grains are tracked in the actual grain geometry, but unlike LCLS, the medium is modeled using only Matrix Chord Length Sampling (MCLS) from the exponential distribution and it is not necessary to know the grain chord length distribution. This helped us extend the method to media with randomly oriented arbitrarily shaped convex grains. Other extensions include multicomponent media - grains of several sorts, and polydisperse media - grains of different sizes. Sort and size distributions of crossed grains were obtained and an algorithm was developed for sampling grain orientations and positions. Special consideration was given to medium modeling at the boundary of the stochastic region. The method was implemented in the universal 3D Monte Carlo code PRIZMA. The paper provides calculated results for a model problem where we determine volume fractions of modeled components crossed by particle trajectories. It also demonstrates the use of biased sampling techniques implemented in PRIZMA for solving a problem of deep penetration in model random media. Described are calculations for the spectral response of a capacitor dose detector whose anode was modeled with account for its stochastic structure. (authors)

  13. 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...

  14. 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

  15. Analytical chemists and dinosaurs

    International Nuclear Information System (INIS)

    The role of the analytical chemist in the development of the extraterrestrial impact theory for mass extinctions at the terminal Cretaceous Period is reviewed. High iridium concentrations in Cretaceous/Tertiary boundary clays have been linked to a terrestrial impact from an iridium-rich asteroid or large meteorite som 65 million years ago. Other evidence in favour of the occurrence of such an impact has been provided by the detection of shocked quartz grains originating from impact and of amorphous carbon particles similar to soot, derived presumably from wordwide wildfires at the terminal Cretaceous. Further evidence provided by the analytical chemist involves the determination of isotopic ratios such as 144Nd/143Nd, 187Os/186Os, and 87Sr/86Sr. Countervailing arguments put forward by the gradualist school (mainly palaeontological) as opposed to the catastrophists (mainly chemists and geochemists) are also presented and discussed

  16. Avatars in Analytical Gaming

    Energy Technology Data Exchange (ETDEWEB)

    Cowell, Andrew J.; Cowell, Amanda K.

    2009-08-29

    This paper discusses the design and use of anthropomorphic computer characters as nonplayer characters (NPC’s) within analytical games. These new environments allow avatars to play a central role in supporting training and education goals instead of planning the supporting cast role. This new ‘science’ of gaming, driven by high-powered but inexpensive computers, dedicated graphics processors and realistic game engines, enables game developers to create learning and training opportunities on par with expensive real-world training scenarios. However, there needs to be care and attention placed on how avatars are represented and thus perceived. A taxonomy of non-verbal behavior is presented and its application to analytical gaming discussed.

  17. Nuclear analytical chemistry

    International Nuclear Information System (INIS)

    This book covers the general theories and techniques of nuclear chemical analysis, directed at applications in analytical chemistry, nuclear medicine, radiophysics, agriculture, environmental sciences, geological exploration, industrial process control, etc. The main principles of nuclear physics and nuclear detection on which the analysis is based are briefly outlined. An attempt is made to emphasise the fundamentals of activation analysis, detection and activation methods, as well as their applications. The book provides guidance in analytical chemistry, agriculture, environmental and biomedical sciences, etc. The contents include: the nuclear periodic system; nuclear decay; nuclear reactions; nuclear radiation sources; interaction of radiation with matter; principles of radiation detectors; nuclear electronics; statistical methods and spectral analysis; methods of radiation detection; neutron activation analysis; charged particle activation analysis; photon activation analysis; sample preparation and chemical separation; nuclear chemical analysis in biological and medical research; the use of nuclear chemical analysis in the field of criminology; nuclear chemical analysis in environmental sciences, geology and mineral exploration; and radiation protection

  18. Analytic ICF Hohlraum Energetics

    Energy Technology Data Exchange (ETDEWEB)

    Rosen, M D; Hammer, J

    2003-08-27

    We apply recent analytic solutions to the radiation diffusion equation to problems of interest for ICF hohlraums. The solutions provide quantitative values for absorbed energy which are of use for generating a desired radiation temperature vs. time within the hohlraum. Comparison of supersonic and subsonic solutions (heat front velocity faster or slower, respectively, than the speed of sound in the x-ray heated material) suggests that there may be some advantage in using high Z metallic foams as hohlraum wall material to reduce hydrodynamic losses, and hence, net absorbed energy by the walls. Analytic and numerical calculations suggest that the loss per unit area might be reduced {approx} 20% through use of foam hohlraum walls. Reduced hydrodynamic motion of the wall material may also reduce symmetry swings, as found for heavy ion targets.

  19. An Analytical Delay Model

    Institute of Scientific and Technical Information of China (English)

    MIN Yinghua; LI Zhongcheng

    1999-01-01

    Delay consideration has been a majorissue in design and test of high performance digital circuits. Theassumption of input signal change occurring only when all internal nodesare stable restricts the increase of clock frequency. It is no longertrue for wave pipelining circuits. However, previous logical delaymodels are based on the assumption. In addition, the stable time of arobust delay test generally depends on the longest sensitizable pathdelay. Thus, a new delay model is desirable. This paper explores thenecessity first. Then, Boolean process to analytically describe thelogical and timing behavior of a digital circuit is reviewed. Theconcept of sensitization is redefined precisely in this paper. Based onthe new concept of sensitization, an analytical delay model isintroduced. As a result, many untestable delay faults under thelogical delay model can be tested if the output waveforms can be sampledat more time points. The longest sensitizable path length is computedfor circuit design and delay test.

  20. Nuclear analytical chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Brune, D.; Forkman, B.; Persson, B.

    1984-01-01

    This book covers the general theories and techniques of nuclear chemical analysis, directed at applications in analytical chemistry, nuclear medicine, radiophysics, agriculture, environmental sciences, geological exploration, industrial process control, etc. The main principles of nuclear physics and nuclear detection on which the analysis is based are briefly outlined. An attempt is made to emphasise the fundamentals of activation analysis, detection and activation methods, as well as their applications. The book provides guidance in analytical chemistry, agriculture, environmental and biomedical sciences, etc. The contents include: the nuclear periodic system; nuclear decay; nuclear reactions; nuclear radiation sources; interaction of radiation with matter; principles of radiation detectors; nuclear electronics; statistical methods and spectral analysis; methods of radiation detection; neutron activation analysis; charged particle activation analysis; photon activation analysis; sample preparation and chemical separation; nuclear chemical analysis in biological and medical research; the use of nuclear chemical analysis in the field of criminology; nuclear chemical analysis in environmental sciences, geology and mineral exploration; and radiation protection.

  1. Inorganic Analytical Chemistry

    DEFF Research Database (Denmark)

    Berg, Rolf W.

    The book is a treatise on inorganic analytical reactions in aqueous solution. It covers about half of the elements in the periodic table, i.e. the most important ones : H, Li, B, C, N, O, Na, Mg, Al, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Br, Sr, Mo, Ag, Cd, Sn, Sb, I, Ba, W...

  2. Competing on analytics.

    Science.gov (United States)

    Davenport, Thomas H

    2006-01-01

    We all know the power of the killer app. It's not just a support tool; it's a strategic weapon. Companies questing for killer apps generally focus all their firepower on the one area that promises to create the greatest competitive advantage. But a new breed of organization has upped the stakes: Amazon, Harrah's, Capital One, and the Boston Red Sox have all dominated their fields by deploying industrial-strength analytics across a wide variety of activities. At a time when firms in many industries offer similar products and use comparable technologies, business processes are among the few remaining points of differentiation--and analytics competitors wring every last drop of value from those processes. Employees hired for their expertise with numbers or trained to recognize their importance are armed with the best evidence and the best quantitative tools. As a result, they make the best decisions. In companies that compete on analytics, senior executives make it clear--from the top down--that analytics is central to strategy. Such organizations launch multiple initiatives involving complex data and statistical analysis, and quantitative activity is managed atthe enterprise (not departmental) level. In this article, professor Thomas H. Davenport lays out the characteristics and practices of these statistical masters and describes some of the very substantial changes other companies must undergo in order to compete on quantitative turf. As one would expect, the transformation requires a significant investment in technology, the accumulation of massive stores of data, and the formulation of company-wide strategies for managing the data. But, at least as important, it also requires executives' vocal, unswerving commitment and willingness to change the way employees think, work, and are treated. PMID:16447373

  3. Analytical and physical electrochemistry

    CERN Document Server

    Girault, Hubert H

    2004-01-01

    The study of electrochemistry is pertinent to a wide variety of fields, including bioenergetics, environmental sciences, and engineering sciences. In addition, electrochemistry plays a fundamental role in specific applications as diverse as the conversion and storage of energy and the sequencing of DNA.Intended both as a basic course for undergraduate students and as a reference work for graduates and researchers, Analytical and Physical Electrochemistry covers two fundamental aspects of electrochemistry: electrochemistry in solution and interfacial electrochemistry. By bringing these two subj

  4. Analytic stacks and hyperbolicity

    OpenAIRE

    Borghesi, Simone; Tomassini, Giuseppe

    2012-01-01

    The classical Brody's theorem asserts the equivalence between two notions of hyperbolicity for compact complex spaces, one named after Kobayashi and one expressed in terms of lack of non constant holomorphic entire functions (compactness is only used to prove the harder implication). We extend this theorem to Deligne-Mumford analytic stacks, by first providing definitions of what we think of Kobayashi and Brody hyperbolicity for such objects and then proving the equivalence of these concepts ...

  5. An analytical model and verification for MEMS Pirani gauges

    International Nuclear Information System (INIS)

    A new analytical model for the design of micromachined Pirani gauges operating in constant current mode is presented. This model expresses the pressure range as a closed-form analytical function of the design variables such as geometry and biasing. Furthermore, it yields simplified expressions for other performance parameters such as the sensitivity, output swing and power consumption. A Pirani gauge has been designed according to the presented model and has been fabricated and characterized in order to verify the validity of the model. The measurements match the theory closely. The model will be useful to designers who need to trade off performance against the costs of chip area and biasing power.

  6. Explosion modelling for complex geometries

    Science.gov (United States)

    Nehzat, Naser

    A literature review suggested that the combined effects of fuel reactivity, obstacle density, ignition strength, and confinement result in flame acceleration and subsequent pressure build-up during a vapour cloud explosion (VCE). Models for the prediction of propagating flames in hazardous areas, such as coal mines, oil platforms, storage and process chemical areas etc. fall into two classes. One class involves use of Computation Fluid Dynamics (CFD). This approach has been utilised by several researchers. The other approach relies upon a lumped parameter approach as developed by Baker (1983). The former approach is restricted by the appropriateness of sub-models and numerical stability requirements inherent in the computational solution. The latter approach raises significant questions regarding the validity of the simplification involved in representing the complexities of a propagating explosion. This study was conducted to investigate and improve the Computational Fluid Dynamic (CFD) code EXPLODE which has been developed by Green et al., (1993) for use on practical gas explosion hazard assessments. The code employs a numerical method for solving partial differential equations by using finite volume techniques. Verification exercises, involving comparison with analytical solutions for the classical shock-tube and with experimental (small-scale, medium and large-scale) results, demonstrate the accuracy of the code and the new combustion models but also identify differences between predictions and the experimental results. The project has resulted in a developed version of the code (EXPLODE2) with new combustion models for simulating gas explosions. Additional features of this program include the physical models necessary to simulate the combustion process using alternative combustion models, improvement to the numerical accuracy and robustness of the code, and special input for simulation of different gas explosions. The present code has the capability of

  7. Quantum groups: Geometry and applications

    International Nuclear Information System (INIS)

    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

  8. Detonation diffraction through different geometries

    Science.gov (United States)

    Sorin, Rémy; Zitoun, Ratiba; Khasainov, Boris; Desbordes, Daniel

    2009-04-01

    We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d c = k c · λ (with λ the detonation cell size and k c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter ( D/ d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/ λ. For ratios below k c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k lim (which depends on D/ d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k c by 50%. The results in configuration C show that the re-ignition process depends both on d/ λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D ch = 200 mm) at as small d/ λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

  9. 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.

  10. Developments and retrospectives in Lie theory geometric and analytic methods

    CERN Document Server

    Penkov, Ivan; Wolf, Joseph

    2014-01-01

    This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...

  11. Geometry behind chordal Loewner chains

    CERN Document Server

    Contreras, Manuel D; Gumenyuk, Pavel

    2010-01-01

    Loewner Theory is a deep technique in Complex Analysis affording a basis for many further important developments such as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner Evolution (SLE). It provides analytic description of expanding domains dynamics in the plane. Two cases have been developed in the classical theory, namely the {\\it radial} and the {\\it chordal} Loewner evolutions, referring to the associated families of holomorphic self-mappings being normalized at an internal or boundary point of the reference domain, respectively. Recently there has been introduced a new approach [arXiv:0807.1594v1, arXiv:0807.1715v1, arXiv:0902.3116v1] bringing together, and containing as quite special cases, radial and chordal variants of Loewner Theory. In the framework of this approach we address the question what kind of systems of simply connected domains can be described by means of Loewner chains of chordal type. As an answer to this question we establish a necessary and ...

  12. Business analytics a practitioner's guide

    CERN Document Server

    Saxena, Rahul

    2013-01-01

    This book provides a guide to businesses on how to use analytics to help drive from ideas to execution. Analytics used in this way provides "full lifecycle support" for business and helps during all stages of management decision-making and execution.The framework presented in the book enables the effective interplay of business, analytics, and information technology (business intelligence) both to leverage analytics for competitive advantage and to embed the use of business analytics into the business culture. It lays out an approach for analytics, describes the processes used, and provides gu

  13. 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.

  14. Teaching Molecular Geometry with the VSEPR Model

    Science.gov (United States)

    Gillespie, Ronald J.

    2004-01-01

    The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…

  15. Noncommutative geometry inspired dirty black holes

    OpenAIRE

    Nicolini, Piero; Spallucci, Euro

    2009-01-01

    We provide a new exact solution of the Einstein equations which generalizes the noncommutative geometry inspired Schwarzschild metric, we previously obtained. We consider here more general relations between the energy density and the radial pressure and find new a geometry describing a regular ``dirty black hole''. We discuss strong and weak energy condition violations and various aspects of the regular dirty black hole thermodynamics.

  16. Quantum anticentrifugal force for wormhole geometry

    OpenAIRE

    Dandoloff, Rossen

    2009-01-01

    We show the existence of an anticentrifugal force in a wormhole geometry in $R^3$. This counterintuitive force was shown to exist in a flat $R^2$ space. The role the geometry plays in the appearance of this force is discussed.

  17. Some Types of Recurrence in Finsler geometry

    CERN Document Server

    Soleiman, A

    2016-01-01

    The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of recurrence are studied. The generalized concircular recurrence, as a new concept, is singled out.

  18. 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....

  19. Backgrounds of arithmetic and geometry an introduction

    CERN Document Server

    Miron, Radu

    1995-01-01

    The book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures.

  20. Magnetic surfaces in the reversed field geometry

    International Nuclear Information System (INIS)

    The achievement of field reversal is shown not to ensure a closed magnetic geometry. The closure of the reversed field geometry is found to be critically dependent on the shape of the toroidal component of the magnetic field no matter how small it may be

  1. Quilt Blocks: Writing in the Geometry Classroom

    Science.gov (United States)

    Gibson, Michelle; Thomas, Timothy G.

    2005-01-01

    The introduction of quilt pattern consisting of many quilt blocks formed by congruent triangles, for writing by the students in the geometry classrooms, is studied. It is found that the students enjoyed this method and writing also helped in understanding the geometric concepts expanding their vocabulary in geometry.

  2. Line geometry and electromagnetism I: basic structures

    OpenAIRE

    Delphenich, D. H.

    2013-01-01

    Some key notions of line geometry are recalled, along with their application to mechanics. It is then shown that most of the basic structures that one introduces in the pre-metric formulation of electromagnetism can be interpreted directly in terms of corresponding concepts in line geometry. The results are summarized in a table.

  3. Different lattice geometries with synthetic dimension

    OpenAIRE

    Suszalski, Dominik; Zakrzewski, Jakub

    2016-01-01

    The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. Additional linear potential and Raman assisted tunnelings are used to engineer well controlled tunnelings between available states. The great flexibility of the system allows us to obtain different geometries of synthetic lattices with possibility of adding synthetic gauge fields.

  4. 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.

  5. Wave-induced set-up and flow over shoals and coral reefs. Part 1. A simplified bottom geometry case

    OpenAIRE

    Stanis³aw R. Massel; Richard M. Brinkman

    2001-01-01

    An analytical approach was used to model the wave-induced set-up and flow through simple shoal geometry when water depth is a linear function of the distance. Two different approaches were applied to parameterize the energy dissipation due to wave breaking. The resulting set-up height and flow velocity were determined and their dependence on the geometry of the shoal and offshore forcing was demonstrated. The extension of the solution to a more complicated bathymetry and verification agai...

  6. Experimental and Analytical Research on Fracture Processes in ROck

    Energy Technology Data Exchange (ETDEWEB)

    Herbert H.. Einstein; Jay Miller; Bruno Silva

    2009-02-27

    Experimental studies on fracture propagation and coalescence were conducted which together with previous tests by this group on gypsum and marble, provide information on fracturing. Specifically, different fracture geometries wsere tested, which together with the different material properties will provide the basis for analytical/numerical modeling. INitial steps on the models were made as were initial investigations on the effect of pressurized water on fracture coalescence.

  7. 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.

  8. Elementary differential geometry from a generalized standpoint

    International Nuclear Information System (INIS)

    The authors describe the essential ingredients of differential geometry-vielbeins, connections, curvatures and isometries-on a level somewhat more general than is commonly found in the literature of physics and mathematics. Most often, one finds differential geometry discussed in terms either of a metric (especially in the older textbooks), or equivalently in terms of a vielbein together with a principle of invariance under independent rotations or Lorentz transformations at each point, as well as invariance under general coordinate transformations. They adopt the same general framework, but keep an open mind as to whether the local invariance group is a rotation or Lorentz group or something quite different. Differential geometry based on a metric or on local rotational or Lorentz invariance is called Riemannian geometry; the more general quasi-Riemannian geometry described here is known in the mathematical literature as the theory of G-structures

  9. Final Report: Geometry And Elementary Particle Physics

    International Nuclear Information System (INIS)

    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.

  10. Physical meaning of the optical reference geometry

    International Nuclear Information System (INIS)

    I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

  11. 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.

  12. 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...

  13. 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…

  14. 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…

  15. On Special Cases of General Geometry: geometries with changing length of vectors

    OpenAIRE

    Shahverdiyev, S. S.

    2006-01-01

    We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. We show that the length of a vector changes along a curve in these geometries.

  16. A Vector Approach to Euclidean Geometry: Vector Spaces and Affine Geometry, Volume 1. Teacher's Edition.

    Science.gov (United States)

    Vaughan, Herbert E.; Szabo, Steven

    This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

  17. 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

  18. 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

  19. Contribution to analytical theory of neutron resonance absorption in heterogeneous reactor systems with cylindrical geometry

    International Nuclear Information System (INIS)

    Following a review of the existing theories od resonance absorption this thesis includes a new approach for calculating the effective resonance integral of absorbed neutrons, new approximate formula for the penetration factor, an analysis of the effective resonance integral and the correction of the resonance integral taking into account the interference of potential and resonance dissipation. A separate chapter is devoted to calculation of the effective resonance integral for the regular reactor lattice with cylindrical fuel elements

  20. Functions, Analytic Geometry, Probability and Statistics. A Study Guide of the Science and Engineering Technician Curriculum.

    Science.gov (United States)

    Melton, Roger

    This study guide is part of an interdisciplinary course entitled the Science and Engineering Technician (SET) Curriculum. The course integrates elements from the disciplines of chemistry, physics, mathematics, mechanical technology, and electronic technology, with the objective of training technicians in the use of electronic instruments and their…