Differential and complex geometry origins, abstractions and embeddings

CERN Document Server

Wells, Jr , Raymond O

2017-01-01

Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

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

An introduction to differential geometry

CERN Document Server

Willmore, T J

2012-01-01

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

On the formalism of local variational differential operators

NARCIS (Netherlands)

Igonin, S.; Verbovetsky, A.V.; Vitolo, R.

2002-01-01

The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the

Differential geometry of group lattices

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2003-01-01

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

Differential geometry on Hopf algebras and quantum groups

International Nuclear Information System (INIS)

Watts, P.

1994-01-01

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined

Differential geometry and mathematical physics

CERN Document Server

Rudolph, Gerd

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

Tensor analysis and elementary differential geometry for physicists and engineers

CERN Document Server

Nguyen-Schäfer, Hung

2017-01-01

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...

Multivariable calculus and differential geometry

CERN Document Server

Walschap, Gerard

2015-01-01

This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

Differential forms and the geometry of general relativity

CERN Document Server

Dray, Tevian

2015-01-01

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes

Geometry of the local equivalence of states

Energy Technology Data Exchange (ETDEWEB)

Sawicki, A; Kus, M, E-mail: assawi@cft.edu.pl, E-mail: marek.kus@cft.edu.pl [Center for Theoretical Physics, Polish Academy of Sciences, Al Lotnikow 32/46, 02-668 Warszawa (Poland)

2011-12-09

We present a description of locally equivalent states in terms of symplectic geometry. Using the moment map between local orbits in the space of states and coadjoint orbits of the local unitary group, we reduce the problem of local unitary equivalence to an easy part consisting of identifying the proper coadjoint orbit and a harder problem of the geometry of fibers of the moment map. We give a detailed analysis of the properties of orbits of 'equally entangled states'. In particular, we show connections between certain symplectic properties of orbits such as their isotropy and coisotropy with effective criteria of local unitary equivalence. (paper)

Numerical Simulation of Voltage Electric Field in Complex Geometries for Different Electrode Arrangements using Meshless Local MQ-DQ Method

DEFF Research Database (Denmark)

Jalaal, M.; Soleimani, Soheil; Domairry, G.

2011-01-01

In this paper the meshless Local Multi Quadrics-based Differential Quadrature (MQ-DQ) method is applied to obtain the electric field distribution for different applicable irregular geometries. This method is the combination of Differential Quadrature approximation of derivatives and function...

Differential geometry bundles, connections, metrics and curvature

CERN Document Server

Taubes, Clifford Henry

2011-01-01

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the

Differential geometry connections, curvature, and characteristic classes

CERN Document Server

Tu, Loring W

2017-01-01

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establ...

Differential geometry based multiscale models.

Science.gov (United States)

Wei, Guo-Wei

2010-08-01

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

Differential Geometry Based Multiscale Models

Science.gov (United States)

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 descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that

Index theory for locally compact noncommutative geometries

CERN Document Server

Carey, A L; Rennie, A; Sukochev, F A

2014-01-01

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

Aspects of differential geometry II

CERN Document Server

Gilkey, Peter

2015-01-01

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...

Tensor analysis and elementary differential geometry for physicists and engineers

CERN Document Server

Nguyen-Schäfer, Hung

2014-01-01

Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics, and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis, and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists, and practicing engineers.

Local analytic geometry

CERN Document Server

Abhyankar, Shreeram Shankar

1964-01-01

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

Differential geometry in string models

International Nuclear Information System (INIS)

Alvarez, O.

1986-01-01

In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold

Pseudo-differential operators groups, geometry and applications

CERN Document Server

Zhu, Hongmei

2017-01-01

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Foundations of arithmetic differential geometry

CERN Document Server

Buium, Alexandru

2017-01-01

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

Extended differential geometry as a basis for physical field theory

International Nuclear Information System (INIS)

Bruce, M.H.

1984-01-01

An extension of Riemann differential geometry is considered as a broadened uniform basis for physical field theory. The requirements for such a theory are set and interpreted as a generalized Ricci calculus capable of supporting certain physical affine motions and metric constraints. Both tensor and spinor languages are considered and a variational calculus is formulated within the geometry. The dominant emergent feature is the replacement of ordinary derivatives by generalized differential operators involving the usual Christoffel symbols as well as more general connection parameters. Then the Euler-Lagrange equations with constraints may be regarded as a general differential geometry and an action principle is formulated to give equations of motion in terms of generalized momentum operations. A cononical momentum tensor is employed which yields, by a generalized boundary variations of the action a set of conservation laws. The formulation is then applied to such diverse topics as the generalizing of the Dirac equation, the Lorentz and radiation terms for a charged particle, the relativistic rotator, and considerations on a geometric origin for the the Einstein energy density tensor

Introduction to differential geometry for engineers

CERN Document Server

Doolin, Brian F

2013-01-01

This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

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

CERN Document Server

James, I M

1962-01-01

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

Quantum κ-deformed differential geometry and field theory

Science.gov (United States)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Topics of differential geometry in hamiltonian and lagrangian mechanics and relativity

International Nuclear Information System (INIS)

Rodrigues, P.R.

1982-01-01

A little introduction to the tensor and exterior algebra just as to the differential geometry is made. Such a geometry is used in order to study the hamiltonian and lagrangian mechanics stressing their geometrical aspects. Some applications are done in relativity theory. (L.C.) [pt

Introduction to Dubois-Violette's non-commutative differential geometry

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs

On the influence of microphone array geometry on HRTF-based Sound Source Localization

DEFF Research Database (Denmark)

Farmani, Mojtaba; Pedersen, Michael Syskind; Tan, Zheng-Hua

2015-01-01

The direction dependence of Head Related Transfer Functions (HRTFs) forms the basis for HRTF-based Sound Source Localization (SSL) algorithms. In this paper, we show how spectral similarities of the HRTFs of different directions in the horizontal plane influence performance of HRTF-based SSL...... algorithms; the more similar the HRTFs of different angles to the HRTF of the target angle, the worse the performance. However, we also show how the microphone array geometry can assist in differentiating between the HRTFs of the different angles, thereby improving performance of HRTF-based SSL algorithms....... Furthermore, to demonstrate the analysis results, we show the impact of HRTFs similarities and microphone array geometry on an exemplary HRTF-based SSL algorithm, called MLSSL. This algorithm is well-suited for this purpose as it allows to estimate the Direction-of-Arrival (DoA) of the target sound using any...

Global differential geometry: An introduction for control engineers

Science.gov (United States)

Doolin, B. F.; Martin, C. F.

1982-01-01

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Partial Differential Equations

CERN Document Server

1988-01-01

The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

Thin shells joining local cosmic string geometries

Energy Technology Data Exchange (ETDEWEB)

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

2016-10-15

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

Thin shells joining local cosmic string geometries

International Nuclear Information System (INIS)

Eiroa, Ernesto F.; Rubin de Celis, Emilio; Simeone, Claudio

2016-01-01

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

Nonlinear Methods in Riemannian and Kählerian Geometry

CERN Document Server

Jost, Jürgen

1991-01-01

In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...

Geometry optimization of molecules within an LCGTO local-density functional approach

International Nuclear Information System (INIS)

Mintmire, J.W.

1990-01-01

We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach

Global Differential Geometry and Global Analysis

CERN Document Server

Pinkall, Ulrich; Simon, Udo; Wegner, Berd

1991-01-01

All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stabl...

A fast direct solver for boundary value problems on locally perturbed geometries

Science.gov (United States)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

System theory as applied differential geometry. [linear system

Science.gov (United States)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

A Qualitative Comparison between the Proportional Navigation and Differential Geometry Guidance Algorithms

Directory of Open Access Journals (Sweden)

Yunes Sh. ALQUDSI

2018-06-01

Full Text Available This paper discusses and presents an overview of the proportional navigation (PN guidance law as well as the differential geometry (DG guidance algorithm that are used to develop the intercept course of a certain target. The intent of this study is to illustrate the advantages of the guidance algorithm generated based on the concepts of differential geometry against the well-known PN guidance law. The basic principles behind the both algorithms are mentioned. Moreover, the different versions of the PN approach is briefly clarified to show the essential improvement from one version to the other. The paper terminated with numerous two-dimension simulation figures to give a great value of visual aids, illustrating the significant relations and main features and properties of both algorithms.

Minimal local Lagrangians for higher-spin geometry

International Nuclear Information System (INIS)

Francia, Dario; Sagnotti, Augusto

2005-01-01

The Fronsdal Lagrangians for free totally symmetric rank-s tensors φ μ 1 ...μ s rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator α μ 1 ...μ s-3 and a rank-(s-4) Lagrange multiplier β μ 1 ...μ s-4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψ μ 1 ...μ n can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator ξ μ 1 ...μ n-2 and a rank-(n-3) Lagrange multiplier λ μ 1 ...μ n-3

On some methods of achieving a continuous and differentiated assessment in Linear Algebra and Analytic and Differential Geometry courses and seminars

Directory of Open Access Journals (Sweden)

M. A.P. PURCARU

2017-12-01

Full Text Available This paper aims at highlighting some aspects related to assessment as regards its use as a differentiated training strategy for Linear Algebra and Analytic and Differential Geometry courses and seminars. Thus, the following methods of continuous differentiated assessment are analyzed and exemplified: the portfolio, the role play, some interactive methods and practical examinations.

Differential geometry based solvation model II: Lagrangian formulation.

Science.gov (United States)

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

2011-12-01

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

The algebraic approach to space-time geometry

International Nuclear Information System (INIS)

Heller, M.; Multarzynski, P.; Sasin, W.

1989-01-01

A differential manifold can be defined in terms of smooth real functions carried by it. By rejecting the postulate, in such a definition, demanding the local diffeomorphism of a manifold to the Euclidean space, one obtains the so-called differential space concept. Every subset of R n turns out to be a differential space. Extensive parts of differential geometry on differential spaces, developed by Sikorski, are reviewed and adapted to relativistic purposes. Differential space as a new model of space-time is proposed. The Lorentz structure and Einstein's field equations on differential spaces are discussed. 20 refs. (author)

Local p-Adic Differential Equations

NARCIS (Netherlands)

Put, Marius van der; Taelman, Lenny

2006-01-01

This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is

Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces

Energy Technology Data Exchange (ETDEWEB)

Hemmen, J. Leo van [Physik Department, Technical University of Munich, 85747 Garching (Germany)]. E-mail: lvh@tum.de; Leibold, Christian [Physik Department, Technical University of Munich, 85747 Garching (Germany)

2007-06-15

Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level.

Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces

International Nuclear Information System (INIS)

Hemmen, J. Leo van; Leibold, Christian

2007-01-01

Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level

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...

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...

Ordinary differential equation for local accumulation time.

Science.gov (United States)

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Differential geometry of groups in string theory

International Nuclear Information System (INIS)

Schmidke, W.B. Jr.

1990-09-01

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

Differential Geometry

CERN Document Server

Stoker, J J

2011-01-01

This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.

Differential geometry of curves and surfaces

CERN Document Server

Tapp, Kristopher

2016-01-01

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to carto...

Reduced differential transform method for partial differential equations within local fractional derivative operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

The Abel symposium 2008 on differential equations: geometry, symmetries and integrability

CERN Document Server

Lychagin, Valentin; Straume, Eldar; Abel symposium 2008; Differential equations; Geometry, symmetries and integrability

2008-01-01

The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

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

Triple differential cross-sections of Ne (2s2) in coplanar to perpendicular plane geometry

Science.gov (United States)

Chen, L. Q.; Khajuria, Y.; Chen, X. J.; Xu, K. Z.

2003-10-01

The distorted wave Born approximation (DWBA) with the spin averaged static exchange potential has been used to calculate the triple differential cross-sections (TDCSs) for Ne (2s^2) ionization by electron impact in coplanar to perpendicular plane symmetric geometry at 110.5 eV incident electron energy. The present theoretical results at gun angles Psi = 0^circ (coplanar symmetric geometry) and Psi = 90^circ (perpendicular plane geometry) are in satisfactory agreement with the available experimental data. A deep interference minimum appears in the TDCS in the coplanar symmetric geometry and a strong peak at scattering angle xi = 90^circ caused by the single collision mechanism has been observed in the perpendicular plane geometry. The TDCSs at the gun angles Psi = 30^circ, and Psi = 60^circ are predicted.

Geometric control theory and sub-Riemannian geometry

CERN Document Server

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

2014-01-01

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

Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry

OpenAIRE

Jurco, Branislav

2005-01-01

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| are shown to be one-to-one with stable equivalence classes of what we call crossed module gerbes bundle gerbes. We can also associate to a crossed module a 2-category C'. Then t...

Lie groups, differential equations, and geometry advances and surveys

CERN Document Server

2017-01-01

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

Indoor localization using unsupervised manifold alignment with geometry perturbation

KAUST Repository

Majeed, Khaqan

2014-04-01

The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment\\'s plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.

Indoor localization using unsupervised manifold alignment with geometry perturbation

KAUST Repository

Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh

2014-01-01

The main limitation of deploying/updating Received Signal Strength (RSS) based indoor localization is the construction of fingerprinted radio map, which is quite a hectic and time-consuming process especially when the indoor area is enormous and/or dynamic. Different approaches have been undertaken to reduce such deployment/update efforts, but the performance degrades when the fingerprinting load is reduced below a certain level. In this paper, we propose an indoor localization scheme that requires as low as 1% fingerprinting load. This scheme employs unsupervised manifold alignment that takes crowd sourced RSS readings and localization requests as source data set and the environment's plan coordinates as destination data set. The 1% fingerprinting load is only used to perturb the local geometries in the destination data set. Our proposed algorithm was shown to achieve less than 5 m mean localization error with 1% fingerprinting load and a limited number of crowd sourced readings, when other learning based localization schemes pass the 10 m mean error with the same information.

Gravitation, gauge theories and differential geometry

International Nuclear Information System (INIS)

Eguchi, T.; Chicago Univ., IL; Chicago Univ., IL; Gilkey, P.B.; California Univ., Los Angeles; Hanson, A.J.

1980-01-01

The purpose of this article is to outline various mathematical ideas, methods, and results, primarily from differential geometry and topology, and to show where they can be applied to Yang-Mills gauge theories and Einstein's theory of gravitation.We have several goals in mind. The first is to convey to physicists the bases for many mathematical concepts by using intuitive arguments while avoiding the detailed formality of most textbooks. Although a variety of mathematical theorems will be stated, we will generally give simple examples motivating the results instead of presenting abstract proofs. Another goal is to list a wide variety of mathematical terminology and results in a format which allows easy reference. The reader then has the option of supplementing the descriptions given here by consulting standard mathematical references and articles such as those listed in the bibliography. Finally, we intend this article to serve the dual purpose of acquainting mathematicians with some basic physical concepts which have mathematical ramifications; physical problems have often stimuladed new directions in mathematical thought. (orig./WL)

Localized excitations and the geometry of the 1nπ* excited states of pyrazine

International Nuclear Information System (INIS)

Kleier, D.A.; Martin, R.L.; Wadt, W.R.; Moomaw, W.R.

1982-01-01

Previous theoretical work has shown that the lowest excited singlet state of pyrazine, the π* 1 B 3 u state, is best described in terms of interacting excitations localized on each nitrogen. The present work refines the localized excitation model and considers its implications for the geometry of the 1 B 3 u state. Hartree-Fock calculations show that the best single configuration description of the nπ* state has broken ( 1 B 1 ) symmetry with the excitation strongly localized at one end of the molcule. If the symmetry-restricted hf result is used for reference, this localization describes an important correlation effect. The excited-state geometry was probed using configuration interaction wave functions based on the symmetry-restricted orbitals, as well as properly symmetrized ''valance-bond'' wave functions based on the broken symmetry solutions. Both descriptions lead to a very flat potential for a b/sub 1u/ vibrational mode. This mode reduces the molecular geometry from D/sub 2h/ to C/sub 2v/. We present spectroscopic evidence of our own and of other workers which is consistent with such a flat potential

On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

Effect of conductor geometry on source localization: Implications for epilepsy studies

International Nuclear Information System (INIS)

Schlitt, H.; Heller, L.; Best, E.; Ranken, D.; Aaron, R.

1994-01-01

We shall discuss the effects of conductor geometry on source localization for applications in epilepsy studies. The most popular conductor model for clinical MEG studies is a homogeneous sphere. However, several studies have indicated that a sphere is a poor model for the head when the sources are deep, as is the case for epileptic foci in the mesial temporal lobe. We believe that replacing the spherical model with a more realistic one in the inverse fitting procedure will improve the accuracy of localizing epileptic sources. In order to include a realistic head model in the inverse problem, we must first solve the forward problem for the realistic conductor geometry. We create a conductor geometry model from MR images, and then solve the forward problem via a boundary integral equation for the electric potential due to a specified primary source. One the electric potential is known, the magnetic field can be calculated directly. The most time-intensive part of the problem is generating the conductor model; fortunately, this needs to be done only once for each patient. It takes little time to change the primary current and calculate a new magnetic field for use in the inverse fitting procedure. We present the results of a series of computer simulations in which we investigate the localization accuracy due to replacing the spherical model with the realistic head model in the inverse fitting procedure. The data to be fit consist of a computer generated magnetic field due to a known current dipole in a realistic head model, with added noise. We compare the localization errors when this field is fit using a spherical model to the fit using a realistic head model. Using a spherical model is comparable to what is usually done when localizing epileptic sources in humans, where the conductor model used in the inverse fitting procedure does not correspond to the actual head

Nilpotent algebras of the generalized differential forms and the geometry of superfield theories

International Nuclear Information System (INIS)

Zupnik, B.M.

1991-01-01

We consider a new algebraic approach in the geometry of supergauge theories and supergravity. An introduction of nilpotent algebras simplifies significantly the analysis of D = 3, 4, N = 1 supergravity constraints. Different terms in the invariant action functionals of SG- and SYM-theories are constructed as the integrals of corresponding generalized differential forms. (orig.)

Non-Perturbative Quantum Geometry III

CERN Document Server

Krefl, Daniel

2016-08-02

The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

Differential geometry for physicists and mathematicians moving frames and differential forms : from Euclid past Riemann

CERN Document Server

Vargas, José G

2014-01-01

This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative - almost like a story being told - that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas

Real symplectic formulation of local special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

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

Theory of liquid crystal elastomers and polymer networks : Connection between neoclassical theory and differential geometry.

Science.gov (United States)

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

Complex analysis and CR geometry

CERN Document Server

Zampieri, Giuseppe

2008-01-01

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

A new approach for gravity localization in six-dimensional geometries

International Nuclear Information System (INIS)

Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de

2011-01-01

Full text: The idea that spacetime may have more than four dimensions is old, originally presented as an attempt to unify Maxwell's theory of Electromagnetism with the brand-new gravitation theory of Einstein. Such extra dimensions are in principle unobservable to the energy scales currently available. However, its effects can be seen in short distance gravity experiments and in observations in cosmology. Also, it is used as a mechanism to explain the difference between the energy scales of the weak force and gravity, which is called the hierarchy problem. The current framework for the extra dimension scenario is consider the four-dimensional known universe as embedded in a higher dimensional space called bulk. The form of this bulk determines how we perceive gravity in our universe; then, the behaviour of gravitational field depends on the geometry of the bulk. Metric solutions were already presented for string-like defect, with and without matter sources, where was shown that the gravity Newtonian potential grows with the inverse cube of distance. Such correction arises from a very particular mass spectrum for the gravitational field, which already contains the orbital angular momentum contributions. In this work we study the behaviour of gravitational field in a extra-dimensional braneworld scenario, using non-factorizable geometries (which preserves Poincare symmetry) and setting suitable matter distributions in order to verify its localization, for several geometries. For such geometries it is possible to find explicit solutions for the tensor fluctuations of the metric. (author)

Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time

Science.gov (United States)

Jumarie, Guy

2013-04-01

By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

Differential Geometry Applied to Rings and Möbius Nanostructures

DEFF Research Database (Denmark)

Lassen, Benny; Willatzen, Morten; Gravesen, Jens

2014-01-01

Nanostructure shape effects have become a topic of increasing interest due to advancements in fabrication technology. In order to pursue novel physics and better devices by tailoring the shape and size of nanostructures, effective analytical and computational tools are indispensable. In this chap......Nanostructure shape effects have become a topic of increasing interest due to advancements in fabrication technology. In order to pursue novel physics and better devices by tailoring the shape and size of nanostructures, effective analytical and computational tools are indispensable....... In this chapter, we present analytical and computational differential geometry methods to examine particle quantum eigenstates and eigenenergies in curved and strained nanostructures. Example studies are carried out for a set of ring structures with different radii and it is shown that eigenstate and eigenenergy...

On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS{sub 3} geometries

Energy Technology Data Exchange (ETDEWEB)

Sheikh-Jabbari, M.M. [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Yavartanoo, H. [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China)

2016-09-15

Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Banados geometries, the most general solutions to the AdS{sub 3} Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Banados geometries. We discuss that the information as regards the Banados geometries falls into two categories: ''orbit invariant'' information and ''Virasoro hairs''. The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS{sub 3} Einstein gravity. (orig.)

An application of differential geometry to SSC magnet end winding

International Nuclear Information System (INIS)

Cook, J.M.

1990-04-01

It is expected that a large fraction of the total cost of the proposed Superconducting Supercollider will be spent on magnets, and, as Leon Lederman has remarked, ''most of the cost of making a magnet is in the ends.'' Among the mechanical problems to be solved there is the construction of an end-configuration for the superconducting cables which will minimize their strain energy. The purpose of this paper is to promote the use of differential geometry in this minimization. The use will be illustrated by a specific application to the winding of dipole ends. The cables are assumed to be clamped so firmly that their strain is not altered by Lorentz stresses. 15 refs

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

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

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

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

Geometry of convex polygons and locally minimal binary trees spanning these polygons

International Nuclear Information System (INIS)

Ivanov, A O; Tuzhilin, A A

1999-01-01

In previous works the authors have obtained an effective classification of planar locally minimal binary trees with convex boundaries. The main aim of the present paper is to find more subtle restrictions on the possible structure of such trees in terms of the geometry of the given boundary set. Special attention is given to the case of quasiregular boundaries (that is, boundaries that are sufficiently close to regular ones in a certain sense). In particular, a series of quasiregular boundaries that cannot be spanned by a locally minimal binary tree is constructed

Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ

DEFF Research Database (Denmark)

Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A

2012-01-01

This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of der...... in solution of partial differential equations (PDEs).......This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...

Modern Differential Geometry For Physicists. 2nd Edn

International Nuclear Information System (INIS)

Chrusciel, P T

2006-01-01

Most of us sometimes have to face a student asking: 'What do I need to get started on this'. (In my case 'this' would typically be a topic in general relativity.) After thinking about it for quite a while, and consulting candidate texts again and again, a few days later I usually end up saying: read this chapter in book I (but without going too much detail), then that chapter in book II (but ignore all those comments), then the first few sections of this review paper (but do not try to work out equations NN to NNN), and then come back to see me. In the unlikely event that the student comes back without changing the topic, there follows quite a bit of explaining on a blackboard over the following weeks. From now on I will say: get acquainted with the material covered by this book. As far as Isham's book is concerned, 'this' in the student's question above can stand for any topic in theoretical physics which touches upon differential geometry (and I can only think of very few which do not). Said plainly: this book contains most of the introductory material necessary to get started in general relativity, or those branches of mathematical physics which require differential geometry. A student who has mastered the notions presented in the book will have a solid basis to continue into specialized topics. I am not aware of any other book which would be as useful as this one in terms of the spectrum of topics covered, stopping at the right place to get sufficient introductory insight. According to the publisher, these lecture notes are the content of an introductory course on differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course 'Quantum Fields and Fundamental Forces' at Imperial College, London. The volume is divided into six chapters: - An Introduction to Topology; - Differential Manifolds; - Vector Fields and n-Forms; - Lie Groups; - Fibre Bundles; - Connections in a Bundle. It is a sad

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

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

Intercept Algorithm for Maneuvering Targets Based on Differential Geometry and Lyapunov Theory

Directory of Open Access Journals (Sweden)

Yunes Sh. ALQUDSI

2018-03-01

Full Text Available Nowadays, the homing guidance is utilized in the existed and under development air defense systems (ADS to effectively intercept the targets. The targets became smarter and capable to fly and maneuver professionally and the tendency to design missile with a small warhead became greater, then there is a pressure to produce a more precise and accurate missile guidance system based on intelligent algorithms to ensure effective interception of highly maneuverable targets. The aim of this paper is to present an intelligent guidance algorithm that effectively and precisely intercept the maneuverable and smart targets by virtue of the differential geometry (DG concepts. The intercept geometry and engagement kinematics, in addition to the direct intercept condition are developed and expressed in DG terms. The guidance algorithm is then developed by virtue of DG and Lyapunov theory. The study terminates with 2D engagement simulation with illustrative examples, to demonstrate that, the derived DG guidance algorithm is a generalized guidance approach and the well-known proportional navigation (PN guidance law is a subset of this approach.

A non-local variable for general relativity

International Nuclear Information System (INIS)

Kozameh, C.N.; Newman, E.T.

1983-01-01

The usual description of differential geometry and general relativity is in terms of local fields, e.g. the metric, the curvature tensor, etc, which satisfy local differential equations. The authors introduce a new non-local field (Z) from which the local fields can be derived. Basically Z, though it is non-local, should be thought of as a function on the bundle of null directions on a space-time. The program can be divided into two parts; first the authors want to show the geometric meaning of and the relationship between Z and the local field. Then they want to provide field equations (non-local) for Z which will be equivalent to the vacuum Einstein equations for the local field. (Auth.)

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

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

Architectural geometry

KAUST Repository

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

2014-01-01

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

Torso geometry reconstruction and body surface electrode localization using three-dimensional photography.

Science.gov (United States)

Perez-Alday, Erick A; Thomas, Jason A; Kabir, Muammar; Sedaghat, Golriz; Rogovoy, Nichole; van Dam, Eelco; van Dam, Peter; Woodward, William; Fuss, Cristina; Ferencik, Maros; Tereshchenko, Larisa G

We conducted a prospective clinical study (n=14; 29% female) to assess the accuracy of a three-dimensional (3D) photography-based method of torso geometry reconstruction and body surface electrodes localization. The position of 74 body surface electrocardiographic (ECG) electrodes (diameter 5mm) was defined by two methods: 3D photography, and CT (marker diameter 2mm) or MRI (marker size 10×20mm) imaging. Bland-Altman analysis showed good agreement in X (bias -2.5 [95% limits of agreement (LoA) -19.5 to 14.3] mm), Y (bias -0.1 [95% LoA -14.1 to 13.9] mm), and Z coordinates (bias -0.8 [95% LoA -15.6 to 14.2] mm), as defined by the CT/MRI imaging, and 3D photography. The average Hausdorff distance between the two torso geometry reconstructions was 11.17±3.05mm. Thus, accurate torso geometry reconstruction using 3D photography is feasible. Body surface ECG electrodes coordinates as defined by the CT/MRI imaging, and 3D photography, are in good agreement. Copyright © 2017 Elsevier Inc. All rights reserved.

Geometry of isotropic convex bodies

CERN Document Server

Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen

2014-01-01

The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...

Developments in special geometry

International Nuclear Information System (INIS)

Mohaupt, Thomas; Vaughan, Owen

2012-01-01

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

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

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

Differential evolution to enhance localization of mobile robots

DEFF Research Database (Denmark)

Lisowski, Michal; Fan, Zhun; Ravn, Ole

2011-01-01

. In addition, a novel mechanism for effective robot kidnap detection was proposed. Experiments were performed using computer simulations based on the odometer data and laser range finder measurements collected in advance by a robot in real-life. Experimental results showed that integrating DE enables MCL...... to provide more accurate robot pose estimations in shorter time while using fewer particles.......This paper focuses on the mobile robot localization problems: pose tracking, global localization and robot kidnap. Differential Evolution (DE) applied to extend Monte Carlo Localization (MCL) was investigated to better solve localization problem by increasing localization reliability and speed...

Nonlocality, no-signalling, and Bellʼs theorem investigated by Weyl conformal differential geometry

Science.gov (United States)

De Martini, Francesco; Santamato, Enrico

2014-12-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-\\frac{1}{2} leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-\\frac{1}{2} in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.

Nonlocality, no-signalling, and Bell's theorem investigated by Weyl conformal differential geometry

International Nuclear Information System (INIS)

Martini, Francesco De; Santamato, Enrico

2014-01-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-(1/2) leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-(1/2) in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality. (paper)

Topics in modern differential geometry

CERN Document Server

Verstraelen, Leopold

2017-01-01

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

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Topics in Riemannian geometry

International Nuclear Information System (INIS)

Ezin, J.P.

1988-08-01

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

Guide to Computational Geometry Processing

DEFF Research Database (Denmark)

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

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

The Effect of Teaching Geometry Which is Differentiated Based on the Parallel Curriculum for Gifted/Talented Students on Spatial Ability

Directory of Open Access Journals (Sweden)

Basak KOK

2014-06-01

Full Text Available The purpose of this research is to evaluate the effects of teaching geometry which is differentiated based on the parallel curriculum for gifted/talented students on spatial ability. For this purpose; two units as “Polygons” and “Geometric Objects” of 5th grade mathematics book has been taken and formed a new differentiated geometry unit. In this study, pretest and posttest designs of experimental model were used. The study was conducted in Istanbul Science and Art Center, which offers differentiated program to those who are gifted and talented students after school, in the city of İstanbul and participants were 30 students being 15 of them are experimental group and the other 15 are control group. Experimental group students were underwent a differentiated program on “Polygons” and “Geometric Objects” whereas the other group continued their normal program without any differentiation. Spatial Ability Test developed by Talented Youth Center of John Hopkins University was used to collect data. Above mentioned test was presented to both groups of the study. Collected data was analyzed by Mann Whitney-U and Wilcoxon Signed Rank Test which is in the statistics program. It is presented as a result of the study that the program prepared for the gifted and talented students raised their spatial thinking ability.

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,

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

International Nuclear Information System (INIS)

Thierry-Mieg, Jean

2006-01-01

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

A non-differentiable solution for the local fractional telegraph equation

Directory of Open Access Journals (Sweden)

Li Jie

2017-01-01

Full Text Available In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

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

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

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

Open problems in the geometry and analysis of Banach spaces

CERN Document Server

Guirao, Antonio J; Zizler, Václav

2016-01-01

This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...

Information geometry near randomness and near independence

CERN Document Server

Arwini, Khadiga A

2008-01-01

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

Geometry of surfaces a practical guide for mechanical engineers

CERN Document Server

Radzevich, Stephen P

2012-01-01

Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry an...

The theory of pseudo-differential operators on the noncommutative n-torus

Science.gov (United States)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

Expression-robust 3D face recognition via weighted sparse representation of multi-scale and multi-component local normal patterns

KAUST Repository

Li, Huibin; Huang, Di; Morvan, Jean-Marie; Chen, Liming; Wang, Yunhong

2014-01-01

In the theory of differential geometry, surface normal, as a first order surface differential quantity, determines the orientation of a surface at each point and contains informative local surface shape information. To fully exploit this kind

Indoor Localization and Radio Map Estimation using Unsupervised Manifold Alignment with Geometry Perturbation

KAUST Repository

Majeed, Khaqan

2015-12-22

The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.

Indoor Localization and Radio Map Estimation using Unsupervised Manifold Alignment with Geometry Perturbation

KAUST Repository

Majeed, Khaqan; Sorour, Sameh; Al-Naffouri, Tareq Y.; Valaee, Shahrokh

2015-01-01

The Received Signal Strength (RSS) based fingerprinting approaches for indoor localization pose a need for updating the fingerprint databases due to dynamic nature of the indoor environment. This process is hectic and time-consuming when the size of the indoor area is large. The semi-supervised approaches reduce this workload and achieve good accuracy around 15% of the fingerprinting load but the performance is severely degraded if it is reduced below this level. We propose an indoor localization framework that uses unsupervised manifold alignment. It requires only 1% of the fingerprinting load, some crowd sourced readings and plan coordinates of the indoor area. The 1% fingerprinting load is used only in perturbing the local geometries of the plan coordinates. The proposed framework achieves less than 5m mean localization error, which is considerably better than semi-supervised approaches at very small amount of fingerprinting load. In addition, the few location estimations together with few fingerprints help to estimate the complete radio map of the indoor environment. The estimation of radio map does not demand extra workload rather it employs the already available information from the proposed indoor localization framework. The testing results for radio map estimation show almost 50% performance improvement by using this information as compared to using only fingerprints.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

Science.gov (United States)

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

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)

Commutative algebra with a view toward algebraic geometry

CERN Document Server

Eisenbud, David

1995-01-01

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

RDEL: Restart Differential Evolution algorithm with Local Search Mutation for global numerical optimization

Directory of Open Access Journals (Sweden)

Ali Wagdy Mohamed

2014-11-01

Full Text Available In this paper, a novel version of Differential Evolution (DE algorithm based on a couple of local search mutation and a restart mechanism for solving global numerical optimization problems over continuous space is presented. The proposed algorithm is named as Restart Differential Evolution algorithm with Local Search Mutation (RDEL. In RDEL, inspired by Particle Swarm Optimization (PSO, a novel local mutation rule based on the position of the best and the worst individuals among the entire population of a particular generation is introduced. The novel local mutation scheme is joined with the basic mutation rule through a linear decreasing function. The proposed local mutation scheme is proven to enhance local search tendency of the basic DE and speed up the convergence. Furthermore, a restart mechanism based on random mutation scheme and a modified Breeder Genetic Algorithm (BGA mutation scheme is combined to avoid stagnation and/or premature convergence. Additionally, an exponent increased crossover probability rule and a uniform scaling factors of DE are introduced to promote the diversity of the population and to improve the search process, respectively. The performance of RDEL is investigated and compared with basic differential evolution, and state-of-the-art parameter adaptive differential evolution variants. It is discovered that the proposed modifications significantly improve the performance of DE in terms of quality of solution, efficiency and robustness.

The geometry of geodesics

CERN Document Server

Busemann, Herbert

2005-01-01

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

Geometry and analysis on manifolds in memory of professor Shoshichi Kobayashi

CERN Document Server

Mabuchi, Toshiki; Maeda, Yoshiaki; Noguchi, Junjiro; Weinstein, Alan

2015-01-01

This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables ...

Chiral anomalies and differential geometry

International Nuclear Information System (INIS)

Zumino, B.

1983-10-01

Some properties of chiral anomalies are described from a geometric point of view. Topics include chiral anomalies and differential forms, transformation properties of the anomalies, identification and use of the anomalies, and normalization of the anomalies. 22 references

Geometry and Hamiltonian mechanics on discrete spaces

International Nuclear Information System (INIS)

Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

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.

Local first integrals for systems of differential equations

International Nuclear Information System (INIS)

Zhang Xiang

2003-01-01

The main purpose of this paper is to provide some sufficient conditions for a system of differential equations to have local first integrals in a certain neighbourhood of a singularity. Our results generalize those given in Kwek et al (2003 Z. Angew. Math. Phys. 54 26) and Li et al (2003 Z. Angew. Math. Phys. 54 235)

GEOMETRY – AN IMPORTANT MEANS OF EDUCATION IN THE CIVILISATION SCOPE

OpenAIRE

Liliana TOCARIU, PhD

2017-01-01

Geometry (from the Greek: γεωμετρία; geo = earth, metria = measure) is a genuine science, rooted in mathematics, which studies the plane and spatial forms of bodies from the objective or conceptual reality and the nature of the relationship that exists between them. Due to its complexity, geometry is divided into: Euclidian geometry, analytical geometry, descriptive geometry, projective geometry, kinematic geometry, surface and curve differential geometry, axiomatic geometry,...

Geometry and dynamics of integrable systems

CERN Document Server

Matveev, Vladimir

2016-01-01

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

Geometry and Cloaking Devices

Science.gov (United States)

Ochiai, T.; Nacher, J. C.

2011-09-01

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

Symplectic geometry and Fourier analysis

CERN Document Server

Wallach, Nolan R

2018-01-01

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

Local bifurcations in differential equations with state-dependent delay.

Science.gov (United States)

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

Local bifurcations in differential equations with state-dependent delay

Science.gov (United States)

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

Intrinsic geometry of biological surface growth

CERN Document Server

Todd, Philip H

1986-01-01

1.1 General Introduction The work which comprises this essay formed part of a multidiscip­ linary project investigating the folding of the developing cerebral cortex in the ferret. The project as a whole combined a study, at the histological level, of the cytoarchitectural development concom­ itant with folding and a mathematical study of folding viewed from the perspective of differential geometry. We here concentrate on the differential geometry of brain folding. Histological results which have some significance to the geometry of the cortex are re­ ferred to, but are not discussed in any depth. As with any truly multidisciplinary work, this essay has objectives which lie in each of its constituent disciplines. From a neuroana­ tomical point of view, the work explores the use of the surface geo­ metry of the developing cortex as a parameter for the underlying growth process. Geometrical parameters of particular interest and theoretical importance are surface curvatures. Our experimental portion reports...

Compounding local invariant features and global deformable geometry for medical image registration.

Directory of Open Access Journals (Sweden)

Jianhua Zhang

Full Text Available Using deformable models to register medical images can result in problems of initialization of deformable models and robustness and accuracy of matching of inter-subject anatomical variability. To tackle these problems, a novel model is proposed in this paper by compounding local invariant features and global deformable geometry. This model has four steps. First, a set of highly-repeatable and highly-robust local invariant features, called Key Features Model (KFM, are extracted by an effective matching strategy. Second, local features can be matched more accurately through the KFM for the purpose of initializing a global deformable model. Third, the positional relationship between the KFM and the global deformable model can be used to precisely pinpoint all landmarks after initialization. And fourth, the final pose of the global deformable model is determined by an iterative process with a lower time cost. Through the practical experiments, the paper finds three important conclusions. First, it proves that the KFM can detect the matching feature points well. Second, the precision of landmark locations adjusted by the modeled relationship between KFM and global deformable model is greatly improved. Third, regarding the fitting accuracy and efficiency, by observation from the practical experiments, it is found that the proposed method can improve 6~8% of the fitting accuracy and reduce around 50% of the computational time compared with state-of-the-art methods.

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

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

On Theories of Superalgebras of Differentiable Functions

NARCIS (Netherlands)

Carchedi, D.J.; Roytenberg, D.

2013-01-01

This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be

Surface geometry of protoplanetary disks inferred from near-infrared imaging polarimetry

Energy Technology Data Exchange (ETDEWEB)

Takami, Michihiro; Hasegawa, Yasuhiro; Gu, Pin-Gao; Karr, Jennifer L.; Chapillon, Edwige; Tang, Ya-Wen [Institute of Astronomy and Astrophysics, Academia Sinica, PO Box 23-141, Taipei 10617, Taiwan, ROC (China); Muto, Takayuki [Division of Liberal Arts, Kogakuin University, 1-24-2, Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677 (Japan); Dong, Ruobing [Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Hashimoto, Jun [H. L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St. Norman, OK 73019 (United States); Kusakabe, Nobuyuki; Akiyama, Eiji; Kwon, Jungmi [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan); Itoh, Youchi [Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo, 407-2 Nishigaichi, Sayo, Sayo, Hyogo 679-5313 (Japan); Carson, Joseph [Department of Physics and Astronomy, College of Charleston, 58 Coming Street, Charleston, SC 29424 (United States); Follette, Katherine B. [Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States); Mayama, Satoshi [The Center for the Promotion of Integrated Sciences, The Graduate University for Advanced Studies (SOKENDAI), Shonan International Village, Hayama-cho, Miura-gun, Kanagawa 240-0193 (Japan); Sitko, Michael [Department of Physics, University of Cincinnati, Cincinnati, OH 45221 (United States); Janson, Markus [Astrophysics Research Center, Queen' s University Belfast, BT7 1NN (United Kingdom); Grady, Carol A. [Eureka Scientific, 2452 Delmer Suite 100, Oakland, CA 96402 (United States); Kudo, Tomoyuki, E-mail: hiro@asiaa.sinica.edu.tw [Subaru Telescope, 650 North Aohoku Place, Hilo, HI 96720 (United States); and others

2014-11-01

We present a new method of analysis for determining the surface geometry of five protoplanetary disks observed with near-infrared imaging polarimetry using Subaru-HiCIAO. Using as inputs the observed distribution of polarized intensity (PI), disk inclination, assumed properties for dust scattering, and other reasonable approximations, we calculate a differential equation to derive the surface geometry. This equation is numerically integrated along the distance from the star at a given position angle. We show that, using these approximations, the local maxima in the PI distribution of spiral arms (SAO 206462, MWC 758) and rings (2MASS J16042165-2130284, PDS 70) are associated with local concave-up structures on the disk surface. We also show that the observed presence of an inner gap in scattered light still allows the possibility of a disk surface that is parallel to the light path from the star, or a disk that is shadowed by structures in the inner radii. Our analysis for rings does not show the presence of a vertical inner wall as often assumed in studies of disks with an inner gap. Finally, we summarize the implications of spiral and ring structures as potential signatures of ongoing planet formation.

Surface geometry of protoplanetary disks inferred from near-infrared imaging polarimetry

International Nuclear Information System (INIS)

Takami, Michihiro; Hasegawa, Yasuhiro; Gu, Pin-Gao; Karr, Jennifer L.; Chapillon, Edwige; Tang, Ya-Wen; Muto, Takayuki; Dong, Ruobing; Hashimoto, Jun; Kusakabe, Nobuyuki; Akiyama, Eiji; Kwon, Jungmi; Itoh, Youchi; Carson, Joseph; Follette, Katherine B.; Mayama, Satoshi; Sitko, Michael; Janson, Markus; Grady, Carol A.; Kudo, Tomoyuki

2014-01-01

We present a new method of analysis for determining the surface geometry of five protoplanetary disks observed with near-infrared imaging polarimetry using Subaru-HiCIAO. Using as inputs the observed distribution of polarized intensity (PI), disk inclination, assumed properties for dust scattering, and other reasonable approximations, we calculate a differential equation to derive the surface geometry. This equation is numerically integrated along the distance from the star at a given position angle. We show that, using these approximations, the local maxima in the PI distribution of spiral arms (SAO 206462, MWC 758) and rings (2MASS J16042165-2130284, PDS 70) are associated with local concave-up structures on the disk surface. We also show that the observed presence of an inner gap in scattered light still allows the possibility of a disk surface that is parallel to the light path from the star, or a disk that is shadowed by structures in the inner radii. Our analysis for rings does not show the presence of a vertical inner wall as often assumed in studies of disks with an inner gap. Finally, we summarize the implications of spiral and ring structures as potential signatures of ongoing planet formation.

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

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

Graphic constructions of characteristic diagrams in chemical engineering and the application of differential geometry

Directory of Open Access Journals (Sweden)

Pejović Branko B.

2012-01-01

Full Text Available Starting from the experimental concentration-time ( cA,t diagram this work gives the construction of the rate of reaction-time (rA,t diagram using the pure graphic method. The diagram was constructed based on the constructed tangents in arbitrary points of the starting diagram by drawing lines parallel to them in the predetermined pole. The evidence of the construction was derived using differential geometry, i.e. the main theorem of differential calculus. Differential properties between the observed values were used in the method. Starting from the analytic relations rA = rA(t and cA = cA(t, which can be very complex (polynomes of the n-th order, and, eliminating time t in order to give a full description of the process, we obtain the analytical relation rA = rA(cA, which is then graphically represented. Hoewever, this elimination of time can also be done graphically, in a relatively simple way. After that, through the use of the integral calculus, it was shown that concentration increase in a time interval is proportional to the (rA,t diagram surface area. Using a similar procedure, further in the paper, it was shown that the time increase is proportional to the (1/rA, cA diagram surface area. In order for the method to be applicable in practice, we have derived relations for appropriate coefficients of proportionality. Verification of the method is illustrated by the two characteristic examples from chemical kinetics at different monotonies of the starting experimental functions.

An introduction to Lie groups and the geometry of homogeneous spaces

CERN Document Server

Arvanitoyeorgos, Andreas

2003-01-01

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differenti...

Ionic diffusion through confined geometries: from Langevin equations to partial differential equations

International Nuclear Information System (INIS)

Nadler, Boaz; Schuss, Zeev; Singer, Amit; Eisenberg, R S

2004-01-01

Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels

Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures

CERN Document Server

Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre

2002-01-01

Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...

Ionisation differential cross section measurements for N2 at low incident energy in coplanar and non-coplanar geometries

International Nuclear Information System (INIS)

Sakaamini, Ahmad; Murray, Andrew James; Amami, Sadek; Madison, Don; Ning, Chuangang

2016-01-01

Ionisation triple differential cross sections have been determined experimentally and theoretically for the neutral molecule N 2 over a range of geometries from coplanar to the perpendicular plane. Data were obtained at incident electron energies ∼10 and ∼20 eV above the ionisation potential of the 3 σ g , 1 π u and 2 σ g states, using both equal and non-equal outgoing electron energies. The data were taken with the incident electron beam in the scattering plane ( ψ = 0°), at 45° to this plane and orthogonal to the plane ( ψ = 90°). The set of nine measured differential cross sections at a given energy were then inter-normalised to each other. The data are compared to new calculations using various distorted wave methods, and differences between theory and experiment are discussed. (paper)

Relative-locality distant observers and the phenomenology of momentum-space geometry

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Rosati, Giacomo; Trevisan, Gabriele; Arzano, Michele; Kowalski-Glikman, Jerzy

2012-01-01

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincare-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincare connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source. (paper)

Relative-locality distant observers and the phenomenology of momentum-space geometry

Science.gov (United States)

Amelino-Camelia, Giovanni; Arzano, Michele; Kowalski-Glikman, Jerzy; Rosati, Giacomo; Trevisan, Gabriele

2012-04-01

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincaré-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincaré connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source.

Localized decrease of β-catenin contributes to the differentiation of human embryonic stem cells

International Nuclear Information System (INIS)

Lam, Hayley; Patel, Shyam; Wong, Janelle; Chu, Julia; Li, Adrian; Li, Song

2008-01-01

Human embryonic stem cells (hESC) are pluripotent, and can be directed to differentiate into different cell types for therapeutic applications. To expand hESCs, it is desirable to maintain hESC growth without differentiation. As hESC colonies grow, differentiated cells are often found at the periphery of the colonies, but the underlying mechanism is not well understood. Here, we utilized micropatterning techniques to pattern circular islands or strips of matrix proteins, and examined the spatial pattern of hESC renewal and differentiation. We found that micropatterned matrix restricted hESC differentiation at colony periphery but allowed hESC growth into multiple layers in the central region, which decreased hESC proliferation and induced hESC differentiation. In undifferentiated hESCs, β-catenin primarily localized at cell-cell junctions but not in the nucleus. The amount of β-catenin in differentiating hESCs at the periphery of colonies or in multiple layers decreased significantly at cell-cell junctions. Consistently, knocking down β-catenin decreased Oct-4 expression in hESCs. These results indicate that localized decrease of β-catenin contributes to the spatial pattern of differentiation in hESC colonies

Quantum symplectic geometry. 1. The matrix Hamiltonian formalism

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

The main purpose of this work is to describe the quantum analogue of the usual classical symplectic geometry and then to formulate the quantum mechanics as a (quantum) non-commutative symplectic geometry. In this first part, we define the quantum symplectic structure in the context of the matrix differential geometry by using the discrete Weyl-Schwinger realization of the Heisenberg group. We also discuss the continuous limit and give an expression of the quantum structure constants. (author). 42 refs

Geometry, algebra and applications from mechanics to cryptography

CERN Document Server

Encinas, Luis; Gadea, Pedro; María, Mª

2016-01-01

This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

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

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

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

Experimental data and calculation studies of critical heat fluxes at local disturbances of geometry of WWER fuel assemblies

International Nuclear Information System (INIS)

Kobzar, L.L.; Oleksyuk, D.A.

2001-01-01

The results of experiments executed in RRC 'Kurchatov Institute on the thermal-physical critical facility SVD are presented herein. The experiments modeled the drawing of two fuel rods to each other till touching WWER-1000 reactor in FA. The experimental model is a 7-rod bundle with the heated length of 1 m. The primary goal of experiments was to acquire the quantitative factors of the reduction in the critical heat fluxes as contrasted to the basic model (without disturbances of FA geometry) at the expense of local disturbance of a rod bundle geometry. As it follows from the experiment, the effect of decrease of the critical heat rate depends on combination of regime parameters and it makes 15% in the most unfavorable case (Authors)

Pseudo-differential operators and generalized functions

CERN Document Server

Toft, Joachim

2015-01-01

This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.

An Enhanced Differential Evolution with Elite Chaotic Local Search

Directory of Open Access Journals (Sweden)

Zhaolu Guo

2015-01-01

Full Text Available Differential evolution (DE is a simple yet efficient evolutionary algorithm for real-world engineering problems. However, its search ability should be further enhanced to obtain better solutions when DE is applied to solve complex optimization problems. This paper presents an enhanced differential evolution with elite chaotic local search (DEECL. In DEECL, it utilizes a chaotic search strategy based on the heuristic information from the elite individuals to promote the exploitation power. Moreover, DEECL employs a simple and effective parameter adaptation mechanism to enhance the robustness. Experiments are conducted on a set of classical test functions. The experimental results show that DEECL is very competitive on the majority of the test functions.

Some questions of differential geometry in the large

CERN Document Server

Shikin, E V

1996-01-01

This collection contains articles that present recent results by geometers in Russia and the Ukraine. Papers in the collection deal with various questions related to the structure, symmetries, and embeddings of submanifolds in Euclidean and pseudo-Euclidian spaces. This collection offers a review of the challenges facing specialists in geometry in the large and features current research in the field.

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

VIII International Meeting on Lorentzian Geometry

CERN Document Server

Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics

2017-01-01

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...

Cubical version of combinatorial differential forms

DEFF Research Database (Denmark)

Kock, Anders

2010-01-01

The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....

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. ...

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

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

Determination of a basic set of Eigen-functions and of the corresponding norm in the case of the one-velocity integral differential Boltzmann equation in spherical geometry

International Nuclear Information System (INIS)

Lafore, P.

1965-01-01

The object of the present work is to draw up a basic set of orthogonal eigenfunctions; resolution of the one-velocity integral-differential Boltzmann equation; this in the case of a spherical geometry system. (author) [fr

Unusual metastatic localizations of differentiated thyroid carcinoma

International Nuclear Information System (INIS)

Ben Rais, N.; Ghfir, I.

2007-01-01

Full text: Introduction: The majority of thyroid cancers have a slow evolution, a more often loco-regional extension, and a good forecast. Remote metastases, when they exist, generally touch the osseous skeleton and/or pulmonary tissue. However, unusual metastatic localizations much more exceptional are possible. The authors report through these work five cases of atypical metastasis of differentiated thyroid carcinoma followed in Nuclear Medicine department of Ibn Sina hospital in Rabat under the directives of Professor N Ben Rais. Materials and methods: Our five patients had initially undergone a total thyroidectomy for differentiated thyroid carcinoma histologically confirmed. They had profited 4 weeks after the surgical gesture from a reference isotopic exploration (131 Iodine whole body scan and thyroglobulin dosage). The paraclinic assessment was supplemented by a computed tomography (CT). Results: Revealing symptomatology in the first 69 year old patient was dominated by blindness associated with an elective up-take of radioactive 131-Iodine on the level of hypophyseal gland extending to the sphenoid bone. The second 55 year old patient reported right basithoracic pains resisting to the usual antalgic treatment with a bulky mass driving back the kidney right to the bottom at CT with and important up-take 131-Iodine at whole body scan; a surrenalectomy was thus carried out with conservation of the kidney. The three other patients presented at the clinical examination dermohypodermic nodular lesions of various localizations whose anatomopathologic study had confirmed their thyroid metastatic origin. In the 5 patients the rate of thyroglobulin was considerably high. An activity of 3,7 GBq 131-Iodine was managed with the 5 patients. The evolution was marked, in the short run, at the first patient by a recovery partial of the sight, the disappearance of pain in the second patient and a remarkable reduction of thyroglobulin level for all our patients. Conclusion

Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

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

Cell-geometry-dependent changes in plasma membrane order direct stem cell signalling and fate

Science.gov (United States)

von Erlach, Thomas C.; Bertazzo, Sergio; Wozniak, Michele A.; Horejs, Christine-Maria; Maynard, Stephanie A.; Attwood, Simon; Robinson, Benjamin K.; Autefage, Hélène; Kallepitis, Charalambos; del Río Hernández, Armando; Chen, Christopher S.; Goldoni, Silvia; Stevens, Molly M.

2018-03-01

Cell size and shape affect cellular processes such as cell survival, growth and differentiation1-4, thus establishing cell geometry as a fundamental regulator of cell physiology. The contributions of the cytoskeleton, specifically actomyosin tension, to these effects have been described, but the exact biophysical mechanisms that translate changes in cell geometry to changes in cell behaviour remain mostly unresolved. Using a variety of innovative materials techniques, we demonstrate that the nanostructure and lipid assembly within the cell plasma membrane are regulated by cell geometry in a ligand-independent manner. These biophysical changes trigger signalling events involving the serine/threonine kinase Akt/protein kinase B (PKB) that direct cell-geometry-dependent mesenchymal stem cell differentiation. Our study defines a central regulatory role by plasma membrane ordered lipid raft microdomains in modulating stem cell differentiation with potential translational applications.

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

International Nuclear Information System (INIS)

McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.

2010-01-01

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)

A geometry calibration method for rotation translation trajectory

International Nuclear Information System (INIS)

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

2013-01-01

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

The Cellular Differential Evolution Based on Chaotic Local Search

Directory of Open Access Journals (Sweden)

Qingfeng Ding

2015-01-01

Full Text Available To avoid immature convergence and tune the selection pressure in the differential evolution (DE algorithm, a new differential evolution algorithm based on cellular automata and chaotic local search (CLS or ccDE is proposed. To balance the exploration and exploitation tradeoff of differential evolution, the interaction among individuals is limited in cellular neighbors instead of controlling parameters in the canonical DE. To improve the optimizing performance of DE, the CLS helps by exploring a large region to avoid immature convergence in the early evolutionary stage and exploiting a small region to refine the final solutions in the later evolutionary stage. What is more, to improve the convergence characteristics and maintain the population diversity, the binomial crossover operator in the canonical DE may be instead by the orthogonal crossover operator without crossover rate. The performance of ccDE is widely evaluated on a set of 14 bound constrained numerical optimization problems compared with the canonical DE and several DE variants. The simulation results show that ccDE has better performances in terms of convergence rate and solution accuracy than other optimizers.

Differential geometry of CR-submanifolds of a normal almost para contact manifold

International Nuclear Information System (INIS)

Shahid, M.H.

1992-12-01

The aim of this paper is to study the geometry of CR-submanifolds of a normal almost para contact manifold. We discuss the integrability conditions of distributions involved in the definition and geometry of leaves of CR-submanifolds, some results on CR-submanifolds with parallel structures and contact CR-product are also given. (author). 10 refs

Electrodynamics and Spacetime Geometry: Foundations

Science.gov (United States)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Somatic stem cell differentiation is regulated by PI3K/Tor signaling in response to local cues.

Science.gov (United States)

Amoyel, Marc; Hillion, Kenzo-Hugo; Margolis, Shally R; Bach, Erika A

2016-11-01

Stem cells reside in niches that provide signals to maintain self-renewal, and differentiation is viewed as a passive process that depends on loss of access to these signals. Here, we demonstrate that the differentiation of somatic cyst stem cells (CySCs) in the Drosophila testis is actively promoted by PI3K/Tor signaling, as CySCs lacking PI3K/Tor activity cannot differentiate properly. We find that an insulin peptide produced by somatic cells immediately outside of the stem cell niche acts locally to promote somatic differentiation through Insulin-like receptor (InR) activation. These results indicate that there is a local 'differentiation' niche that upregulates PI3K/Tor signaling in the early daughters of CySCs. Finally, we demonstrate that CySCs secrete the Dilp-binding protein ImpL2, the Drosophila homolog of IGFBP7, into the stem cell niche, which blocks InR activation in CySCs. Thus, we show that somatic cell differentiation is controlled by PI3K/Tor signaling downstream of InR and that the local production of positive and negative InR signals regulates the differentiation niche. These results support a model in which leaving the stem cell niche and initiating differentiation are actively induced by signaling. © 2016. Published by The Company of Biologists Ltd.

Application of stochastic differential geometry to the term structure of interst rates in developed markets

Energy Technology Data Exchange (ETDEWEB)

Taranenko, Y.; Barnes, C.

1996-12-31

This paper deals with further developments of the new theory that applies stochastic differential geometry (SDG) to dynamics of interest rates. We examine mathematical constraints on the evolution of interest rate volatilities that arise from stochastic differential calculus under assumptions of an arbitrage free evolution of zero coupon bonds and developed markets (i.e., none of the party/factor can drive the whole market). The resulting new theory incorporates the Heath-Jarrow-Morton (HJM) model of interest rates and provides new equations for volatilities which makes the system of equations for interest rates and volatilities complete and self consistent. It results in much smaller amount of volatility data that should be guessed for the SDG model as compared to the HJM model. Limited analysis of the market volatility data suggests that the assumption of the developed market is violated around maturity of two years. Such maturities where the assumptions of the SDG model are violated are suggested to serve as boundaries at which volatilities should be specified independently from the model. Our numerical example with two boundaries (two years and five years) qualitatively resembles the market behavior. Under some conditions solutions of the SDG model become singular that may indicate market crashes. More detail comparison with the data is needed before the theory can be established or refuted.

Solution of multigroup diffusion equations in cylindrical configuration by local polynomial approximation

International Nuclear Information System (INIS)

Jakab, J.

1979-05-01

Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)

Hepatocellular differentiation status is characterized by distinct subnuclear localization and form of the chanzyme TRPM7.

Science.gov (United States)

Ogunrinde, Adenike; Pereira, Robyn D; Beaton, Natalie; Lam, D Hung; Whetstone, Christiane; Hill, Ceredwyn E

The channel-kinase TRPM7 is important for the survival, proliferation, and differentiation, of many cell types. Both plasma membrane channel activity and kinase function are implicated in these roles. Channel activity is greater in less differentiated hepatoma cells compared with non-dividing, terminally differentiated adult hepatocytes, suggesting differences in protein expression and/or localization. We used electrophysiological and immunofluorescence approaches to establish whether hepatocellular differentiation is associated with altered TRPM7 expression. Mean outward current decreased by 44% in WIF-B hepatoma cells incubated with the established hepatic differentiating factors oncostatin M/dexamethasone for 1-8 days. Pre-incubation with pyridone 6, a pan-JAK inhibitor, blocked the current reduction. An antibody targeted to the C-terminus of TRPM7 labelled the cytoplasm in WIF-B cells and intact rat liver. Significant label also localized to the nuclear envelope (NE), with relatively more detected in adult hepatocytes compared with WIF-B cells. Hepatoma cells also exhibited nucleoplasmic labelling with intense signal in the nucleolus. The endogenous labelling pattern closely resembles that of HEK293T cells heterologously expressing a TRPM7 kinase construct containing a putative nucleolar localization sequence. These results suggest that TRPM7 form and distribution between the plasma membrane and nucleus, rather than expression, is altered in parallel with differentiation status in rat hepatic cells. Copyright © 2017 International Society of Differentiation. Published by Elsevier B.V. All rights reserved.

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

International Nuclear Information System (INIS)

Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru

2013-01-01

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.

Classification of digital affine noncommutative geometries

Science.gov (United States)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Geometry effects on the (e, 2e) cross section on ionic targets

International Nuclear Information System (INIS)

Khajuria, Y.

2005-01-01

The three body distorted wave Born approximation (DWBA) with spin averaged static exchange potential has been used to calculate the electron impact triple-differential cross section of Li + , Na + and K + ions in different geometries and kinematics. In coplanar geometry at high incident energy (≥ 500 eV) and scattering angle ∼10deg, both recoil and binary peaks in case of p-orbital electrons splits into two. The value of the binary to the recoil peak ratio for the specific value of the momentum transfer has been determined to understand the collision dynamics. In the non-coplanar geometry a strong interference resulting in a dip in triple differential cross section (TDCS) has been noticed. (author)

Surfaces in classical geometries a treatment by moving frames

CERN Document Server

Jensen, Gary R; Nicolodi, Lorenzo

2016-01-01

Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep relationships, such as the Lawson correspondence. The nearly 300 problems and exercises range from simple applications to open problems. Exercises are embedded in the text as essential parts of the exposition. Problems are collected at the end of each chapter; solutions to select problems are given at the end of the book. Mathematica®, Matlab™, and Xfig are used to illustrate selected concepts and results. The careful selection of results serves to show the reader how to prove the most important theorems in the subject, which may become the foundation of future progress...

Differential manifolds

CERN Document Server

Kosinski, Antoni A

2007-01-01

The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

Energy Technology Data Exchange (ETDEWEB)

De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

2017-09-15

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)

Differential geometry techniques for sets of nonlinear partial differential equations

Science.gov (United States)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

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...

Comparison between two differential graded algebras in ...

Indian Academy of Sciences (India)

76

A differential calculus on a “space” means the specification of a differential graded algebra (dga), often interpreted as space of forms. In classical geometry the “space” is a manifold and we have the de-Rham dga, whereas in noncommutative geometry a “space” is described by a triple called spectral triple. A spectral triple is ...

Local Instruction Theory (LIT) on spherical geometry for enhancement students’ strategic competence

Science.gov (United States)

Nuraida, I.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-03-01

This research focused on the analysis of the materials spherical geometry of the wake in an attempt to enhancemet the strategic competence of students and to produce learning trajectory. That is because the materials that are used less catchy concept gives students. Learning materials with Local Instructional Theory (LIT) can enhancemet the strategic competence of the students. This research aims to study the difference of achievement and improving the strategic competence of the students who got the Realistics Mathematics Education (RME) and (LIT) with conventional learning. This research is the Design Research with two cycles. This research has three phases i.e. 1) preparing for the experiment/preliminary; 2) teaching eksperiment; 3) retrospective analysis. The population of the research was the whole IX group junior high school 1 Rajapolah with samples of IXg and IXj group. Results of the analysis of the data shows that students based on Mathematical Prior Knowledge (MPK) acquire learning achievement have RME and LIT and enhancement strategic competence of the mathematical that are higher than those of students who obtain the conventional learning.

Geometry, topology, and string theory

Energy Technology Data Exchange (ETDEWEB)

Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

2003-01-01

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.

Geometry, topology, and string theory

International Nuclear Information System (INIS)

Varadarajan, Uday

2003-01-01

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

Local fractional variational iteration algorithm iii for the diffusion model associated with non-differentiable heat transfer

Directory of Open Access Journals (Sweden)

Meng Zhi-Jun

2016-01-01

Full Text Available This paper addresses a new application of the local fractional variational iteration algorithm III to solve the local fractional diffusion equation defined on Cantor sets associated with non-differentiable heat transfer.

Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

Directory of Open Access Journals (Sweden)

Xinwei Wang

2016-11-01

Full Text Available Sandwich structures are widely used in practice and thus various engineering theories adopting simplifying assumptions are available. However, most engineering theories of beams, plates and shells cannot recover all stresses accurately through their constitutive equations. Therefore, the soft-core is directly modeled by two-dimensional (2D elasticity theory without any pre-assumption on the displacement field. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. The differential equations of the 2D core are then solved by the harmonic differential quadrature method (HDQM. To circumvent the difficulties in dealing with the locally distributed load by point discrete methods such as the HDQM, a general and rigorous way is proposed to treat the locally distributed load. Detailed formulations are provided. The static behavior of sandwich panels under different locally distributed loads is investigated. For verification, results are compared with data obtained by ABAQUS with very fine meshes. A high degree of accuracy on both displacement and stress has been observed.

Braided affine geometry and q-analogs of wave operators

International Nuclear Information System (INIS)

Gurevich, Dimitri; Saponov, Pavel

2009-01-01

The main goal of this review is to compare different approaches to constructing the geometry associated with a Hecke type braiding (in particular, with that related to the quantum group U q (sl(n))). We place emphasis on the affine braided geometry related to the so-called reflection equation algebra (REA). All objects of such a type of geometry are defined in the spirit of affine algebraic geometry via polynomial relations on generators. We begin by comparing the Poisson counterparts of 'quantum varieties' and describe different approaches to their quantization. Also, we exhibit two approaches to introducing q-analogs of vector bundles and defining the Chern-Connes index for them on quantum spheres. In accordance with the Serre-Swan approach, the q-vector bundles are treated as finitely generated projective modules over the corresponding quantum algebras. Besides, we describe the basic properties of the REA used in this construction and compare different ways of defining q-analogs of partial derivatives and differentials on the REA and algebras close to them. In particular, we present a way of introducing a q-differential calculus via Koszul type complexes. The elements of the q-calculus are applied to defining q-analogs of some relativistic wave operators. (topical review)

The Cx43-like connexin protein Cx40.8 is differentially localized during fin ontogeny and fin regeneration.

Directory of Open Access Journals (Sweden)

Sarah V Gerhart

Full Text Available Connexins (Cx are the subunits of gap junctions, membraneous protein channels that permit the exchange of small molecules between adjacent cells. Cx43 is required for cell proliferation in the zebrafish caudal fin. Previously, we found that a Cx43-like connexin, cx40.8, is co-expressed with cx43 in the population of proliferating cells during fin regeneration. Here we demonstrate that Cx40.8 exhibits novel differential subcellular localization in vivo, depending on the growth status of the fin. During fin ontogeny, Cx40.8 is found at the plasma membrane, but Cx40.8 is retained in the Golgi apparatus during regeneration. We next identified a 30 amino acid domain of Cx40.8 responsible for its dynamic localization. One possible explanation for the differential localization is that Cx40.8 contributes to the regulation of Cx43 in vivo, perhaps modifying channel activity during ontogenetic growth. However, we find that the voltage-gating properties of Cx40.8 are similar to Cx43. Together our findings reveal that Cx40.8 exhibits differential subcellular localization in vivo, dependent on a discrete domain in its carboxy terminus. We suggest that the dynamic localization of Cx40.8 differentially influences Cx43-dependent cell proliferation during ontogeny and regeneration.

Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow

Directory of Open Access Journals (Sweden)

Yu Zhang

2015-10-01

Full Text Available In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.

The non-differentiable solution for local fractional Laplace equation in steady heat-conduction problem

Directory of Open Access Journals (Sweden)

Chen Jie-Dong

2016-01-01

Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.

The Persistification of the ATLAS Geometry

CERN Document Server

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

2016-01-01

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

Granular flows in constrained geometries

Science.gov (United States)

Murthy, Tejas; Viswanathan, Koushik

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

Average methods and their applications in Differential Geometry I

OpenAIRE

Vincze, Csaba

2013-01-01

In Minkowski geometry the metric features are based on a compact convex body containing the origin in its interior. This body works as a unit ball with its boundary formed by the unit vectors. Using one-homogeneous extension we have a so-called Minkowski functional to measure the lenght of vectors. The half of its square is called the energy function. Under some regularity conditions we can introduce an average Euclidean inner product by integrating the Hessian matrix of the energy function o...

Normal forms in Poisson geometry

NARCIS (Netherlands)

Marcut, I.T.

2013-01-01

The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

Advances in geometry and Lie algebras from supergravity

CERN Document Server

Frè, Pietro Giuseppe

2018-01-01

This book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject. .

A variational solution of transport equation based on spherical geometry

International Nuclear Information System (INIS)

Liu Hui; Zhang Ben'ai

2002-01-01

A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods

The geometry of some natural conjugacies in ℂn dynamics

Directory of Open Access Journals (Sweden)

John W. Robertson

2004-01-01

Full Text Available We show that under some simple conditions a topological conjugacy h between two holomorphic self-maps f1 and f2 of complex n-dimensional projective space ℙn lifts canonically to a topological conjugacy H between the two corresponding polynomial self-maps of ℂn+1, and this conjugacy relates the two Green functions of f1 and f2. These conjugacies are interesting because their geometry is not inherited entirely from the geometry of the conjugacy on ℙn. Part of the geometry of such a conjugacy is given (locally by a complex-valued function whose absolute value is determined by the Green functions for the two maps, but whose argument seems to appear out of thin air. We work out the local geometry of such conjugacies over the Fatou set and over Fatou varieties of the original map.

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

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

Topography printing to locally control wettability.

Science.gov (United States)

Zheng, Zijian; Azzaroni, Omar; Zhou, Feng; Huck, Wilhelm T S

2006-06-21

This paper reports a new patterning method, which utilizes NaOH to facilitate the irreversible binding between the PDMS stamp and substrates and subsequent cohesive mechanical failure to transfer the PDMS patterns. Our method shows high substrate tolerance and can be used to "print" various PDMS geometries on a wide range of surfaces, including Si100, glass, gold, polymers, and patterned SU8 photoresist. Using this technique, we are able to locally change the wettability of substrate surfaces by printing well-defined PDMS architectures on the patterned SU8 photoresist. It is possible to generate differential wetting and dewetting properties in microchannels and in the PDMS printed area, respectively.

Differential migration and proliferation of geometrical ensembles of cell clusters

International Nuclear Information System (INIS)

Kumar, Girish; Chen, Bo; Co, Carlos C.; Ho, Chia-Chi

2011-01-01

Differential cell migration and growth drives the organization of specific tissue forms and plays a critical role in embryonic development, tissue morphogenesis, and tumor invasion. Localized gradients of soluble factors and extracellular matrix have been shown to modulate cell migration and proliferation. Here we show that in addition to these factors, initial tissue geometry can feedback to generate differential proliferation, cell polarity, and migration patterns. We apply layer by layer polyelectrolyte assembly to confine multicellular organization and subsequently release cells to demonstrate the spatial patterns of cell migration and growth. The cell shapes, spreading areas, and cell-cell contacts are influenced strongly by the confining geometry. Cells within geometric ensembles are morphologically polarized. Symmetry breaking was observed for cells on the circular pattern and cells migrate toward the corners and in the direction parallel to the longest dimension of the geometric shapes. This migration pattern is disrupted when actomyosin based tension was inhibited. Cells near the edge or corner of geometric shapes proliferate while cells within do not. Regions of higher rate of cell migration corresponded to regions of concentrated growth. These findings demonstrate that multicellular organization can result in spatial patterns of migration and proliferation.

Tensor and vector analysis with applications to differential geometry

CERN Document Server

Springer, C E

2012-01-01

Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics.Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in three-space, transformation of coordinates in space and differentiation, tensor algebra and analysis, and vector analysis and algebra. Additional topics include differentiation of vect

Integrable systems, geometry, and topology

CERN Document Server

Terng, Chuu-Lian

2006-01-01

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

Differential equation of transverse vibrations of a beam with local stroke change of stiffness

Directory of Open Access Journals (Sweden)

Stanisław Kasprzyk

2007-01-01

Full Text Available The aim of this paper is to derive a differential equation of transverse vibrations of a beam with a local, stroke change of stiffness, and to solve it. The presented method is based on the theory of distributions.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

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

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

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

Indium local geometry in In-Sb-Te thin films using XANES and DFT calculations

Science.gov (United States)

Bilovol, V.; Gil Rebaza, A. V.; Mudarra Navarro, A. M.; Errico, L.; Fontana, M.; Arcondo, B.

2017-12-01

In-Sb-Te when is a thin film presents a huge difference in its electrical resistivity when transform from the amorphous (insulating) to the crystalline (conducting) phase. This property made this system one of the main phase-change materials used in the data storage industry. The change in the electrical conductivity is probably associated to a change in the bonding geometry of some of its constituents. To explore this point, we present in this work an study of the bonding geometry of In atoms in In-Sb-Te films by means of In K-edge X-ray absorption near edge structure (XANES) spectroscopy using synchrotron radiation in both as deposited (amorphous) and crystalline thin films obtained as a result of resistance (R) vs temperature (T) measurements. Comparison of the XANES spectra obtained for ternary amorphous films and binary crystalline reference films suggests that in amorphous films the bonding geometry of In atoms is tetrahedral-like. After the thermal annealing has been carried out the differences in the XANES spectra of the as deposited and the annealed films indicate that the bonding geometry of In atoms changes. Based on X-ray diffraction results and ab initio calculations in the framework of the Density Functional Theory (DFT) we show that the new coordination geometry is associated with a tendency of In atoms towards octahedral-like.

Introduction to differentiable manifolds

CERN Document Server

Auslander, Louis

2009-01-01

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff

Perception of global facial geometry is modulated through experience

Directory of Open Access Journals (Sweden)

Meike Ramon

2015-03-01

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

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.

Polygons, Pillars and Pavilions: Discovering Connections between Geometry and Architecture

Science.gov (United States)

Madden, Sean Patrick

2017-01-01

Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical…

International conference on Algebraic and Complex Geometry

CERN Document Server

Kloosterman, Remke; Schütt, Matthias

2014-01-01

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

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...

A study of complexity of oral mucosa using fractal geometry

Directory of Open Access Journals (Sweden)

S R Shenoi

2017-01-01

Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.

Smooth functors vs. differential forms

NARCIS (Netherlands)

Schreiber, U.; Waldorf, K.

2011-01-01

We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth

On Degenerate Partial Differential Equations

OpenAIRE

Chen, Gui-Qiang G.

2010-01-01

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...

Differential Calculus on Quantum Spheres

OpenAIRE

Welk, Martin

1998-01-01

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

Parareal algorithms with local time-integrators for time fractional differential equations

Science.gov (United States)

Wu, Shu-Lin; Zhou, Tao

2018-04-01

It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal method to such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions.

Wage Differentials between Foreign Multinationals and Local Plants and Worker Quality in Malaysian Manufacturing

OpenAIRE

Eric D. Ramstetter

2014-01-01

Using industrial census data for 2000, and smaller sets of survey data for 2001–2004, this paper examines the extent of wage differentials between medium-large (20 or more workers) foreign multinational enterprises (MNEs) and local plants in Malaysia's manufacturing industries. On average, wages in sample MNEs were higher than in local plants by two-fifths or more. In addition to being more capital-intensive and relatively large, MNEs also hired higher shares of workers in highly paid occup...

Wage Differentials between Foreign Multinationals and Local Plants and Worker Quality in Malaysian Manufacturing

OpenAIRE

エリック D., ラムステッター; Eric D. , Ramstetter

2013-01-01

Using industrial census data for 2000, and smaller sets of survey data for 2001-2004, this paper examines the extent of wage differentials between medium-large (20 or more workers) foreign multinational enterprises (MNEs) and local plants in Malaysia’s manufacturing industries. On average, wages in sample MNEs were higher than in local plants by two-fifths or more. MNEs also hired higher shares of workers in highly paid occupations and with moderate or high education, in addition to being mor...

PREFACE: The 7th International Seminar on Geometry, Continua and Microstructures

Science.gov (United States)

Burton, David A.

2007-04-01

It gives me great pleasure to present the proceedings of the 7th International Seminar on Geometry, Continua and Microstructures (GCM 7). The conference took place on 25-27 September 2006 at Lancaster University and the local organisers were Robin Tucker, Tim Walton, myself and Jonathan Gratus of the Lancaster University Mathematical Physics Group. Modern field theories of mechanically and electrically responsive continua have a wealth of interesting applications in physics. Such theories provide effective macroscopic models of complex systems, such as living tissue and material with dynamical defects, that capture macroscopic consequences of microscopic phenomena. GCM is an interdisciplinary conference series, initiated by the Eringen medallist Gérard A Maugin, that brings together physicists and applied mathematicians who have interests in continuum mechanics and differential geometry and who aim to develop new and powerful methods for analysing the behaviour of complex mechanical systems. The earlier conferences in the series were held in Paris, Madrid, Mannheim, Turin, Sinaia and Belgrade. This volume addresses a variety of topics including the physics of saturated porous media, the relationship between growth in living tissue and molecular transport, the mechanics of polymer bonds, the macroscopic properties of damaged elastomers, the mechanics of carbon nanotubes, the geometry of balance systems in Continuum Thermodynamics and wave propagation in the material manifold. I would like to warmly thank the rest of the organising committee and the conference participants for making GCM 7 an enjoyable and rewarding occasion. Photographs may be found at http://www.lancs.ac.uk/depts/spc/conf/gcm7/wss/index.htm David A Burton Editor

Quantum groups, non-commutative differential geometry and applications

International Nuclear Information System (INIS)

Schupp, P.; California Univ., Berkeley, CA

1993-01-01

The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity

Ca2+-dependent localization of integrin-linked kinase to cell junctions in differentiating keratinocytes.

Science.gov (United States)

Vespa, Alisa; Darmon, Alison J; Turner, Christopher E; D'Souza, Sudhir J A; Dagnino, Lina

2003-03-28

Integrin complexes are necessary for proper proliferation and differentiation of epidermal keratinocytes. Differentiation of these cells is accompanied by down-regulation of integrins and focal adhesions as well as formation of intercellular adherens junctions through E-cadherin homodimerization. A central component of integrin adhesion complexes is integrin-linked kinase (ILK), which can induce loss of E-cadherin expression and epithelial-mesenchymal transformation when ectopically expressed in intestinal and mammary epithelia. In cultured primary mouse keratinocytes, we find that ILK protein levels are independent of integrin expression and signaling, since they remain constant during Ca(2+)-induced differentiation. In contrast, keratinocyte differentiation is accompanied by marked reduction in kinase activity in ILK immunoprecipitates and altered ILK subcellular distribution. Specifically, ILK distributes in close apposition to actin fibers along intercellular junctions in differentiated but not in undifferentiated keratinocytes. ILK localization to cell-cell borders occurs independently of integrin signaling and requires Ca(2+) as well as an intact actin cytoskeleton. Further, and in contrast to what is observed in other epithelial cells, ILK overexpression in differentiated keratinocytes does not promote E-cadherin down-regulation and epithelial-mesenchymal transition. Thus, novel tissue-specific mechanisms control the formation of ILK complexes associated with cell-cell junctions in differentiating murine epidermal keratinocytes.

Algebraic theory of locally nilpotent derivations

CERN Document Server

Freudenburg, Gene

2017-01-01

This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factoriza...

Utility of COX1 phylogenetics to differentiate between locally acquired and imported Plasmodium knowlesi infections in Singapore

Science.gov (United States)

Loh, Jin Phang; Gao, Qiu Han Christine; Lee, Vernon J; Tetteh, Kevin; Drakeley, Chris

2016-01-01

INTRODUCTION Although there have been several phylogenetic studies on Plasmodium knowlesi (P. knowlesi), only cytochrome c oxidase subunit 1 (COX1) gene analysis has shown some geographical differentiation between the isolates of different countries. METHODS Phylogenetic analysis of locally acquired P. knowlesi infections, based on circumsporozoite, small subunit ribosomal ribonucleic acid (SSU rRNA), merozoite surface protein 1 and COX1 gene targets, was performed. The results were compared with the published sequences of regional isolates from Malaysia and Thailand. RESULTS Phylogenetic analysis of the circumsporozoite, SSU rRNA and merozoite surface protein 1 gene sequences for regional P. knowlesi isolates showed no obvious differentiation that could be attributed to their geographical origin. However, COX1 gene analysis showed that it was possible to differentiate between Singapore-acquired P. knowlesi infections and P. knowlesi infections from Peninsular Malaysia and Sarawak, Borneo, Malaysia. CONCLUSION The ability to differentiate between locally acquired P. knowlesi infections and imported P. knowlesi infections has important utility for the monitoring of P. knowlesi malaria control programmes in Singapore. PMID:26805667

Utility of COX1 phylogenetics to differentiate between locally acquired and imported Plasmodium knowlesi infections in Singapore.

Science.gov (United States)

Loh, Jin Phang; Gao, Qiu Han Christine; Lee, Vernon J; Tetteh, Kevin; Drakeley, Chris

2016-12-01

Although there have been several phylogenetic studies on Plasmodium knowlesi (P. knowlesi), only cytochrome c oxidase subunit 1 (COX1) gene analysis has shown some geographical differentiation between the isolates of different countries. Phylogenetic analysis of locally acquired P. knowlesi infections, based on circumsporozoite, small subunit ribosomal ribonucleic acid (SSU rRNA), merozoite surface protein 1 and COX1 gene targets, was performed. The results were compared with the published sequences of regional isolates from Malaysia and Thailand. Phylogenetic analysis of the circumsporozoite, SSU rRNA and merozoite surface protein 1 gene sequences for regional P. knowlesi isolates showed no obvious differentiation that could be attributed to their geographical origin. However, COX1 gene analysis showed that it was possible to differentiate between Singapore-acquired P. knowlesi infections and P. knowlesi infections from Peninsular Malaysia and Sarawak, Borneo, Malaysia. The ability to differentiate between locally acquired P. knowlesi infections and imported P. knowlesi infections has important utility for the monitoring of P. knowlesi malaria control programmes in Singapore. Copyright: © Singapore Medical Association

On some aspects of the geometry of differential equations in physics

OpenAIRE

Gràcia, Xavier; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso

2004-01-01

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study...

effect of differentiated instructional strategies on students' retention

African Journals Online (AJOL)

PROF EKWUEME

show that retention ability was significantly higher in the experimental group ... Differentiated instruction, Lecture , Cognitive Achievement ,Retention ability, Geometry. ... thinking. Based on this knowledge, differentiated instruction applies an ...

Collecting and Analyzing Data from Smart Device Users with Local Differential Privacy

OpenAIRE

Nguyên, Thông T.; Xiao, Xiaokui; Yang, Yin; Hui, Siu Cheung; Shin, Hyejin; Shin, Junbum

2016-01-01

Organizations with a large user base, such as Samsung and Google, can potentially benefit from collecting and mining users' data. However, doing so raises privacy concerns, and risks accidental privacy breaches with serious consequences. Local differential privacy (LDP) techniques address this problem by only collecting randomized answers from each user, with guarantees of plausible deniability; meanwhile, the aggregator can still build accurate models and predictors by analyzing large amount...

KENO-IV/CG, the combinatorial geometry version of the KENO Monte Carlo criticality safety program

International Nuclear Information System (INIS)

West, J.T.; Petrie, L.M.; Fraley, S.K.

1979-09-01

KENO-IV/CG was developed to merge the simple geometry input description utilized by combinatorial geometry with the repeating lattice feature of the original KENO geometry package. The result is a criticality code with the ability to model a complex system of repeating rectangular lattices inside a complicated three-dimensional geometry system. Furthermore, combinatorial geometry was modified to differentiate between combinatorial zones describing a particular KENO BOX to be repeated in a KENO array and those combinatorial zones describing geometry external to an array. This allows the user to maintain a simple coordinate system without any geometric conflict due to spatial overlap. Several difficult criticality design problems have been solved with the new geometry package in KENO-IV/CG, thus illustrating the power of the code to model difficult geometries with a minimum of effort

Expository lectures on topology, geometry, and gauge theories

International Nuclear Information System (INIS)

Akyildiz, Y.

1983-01-01

The article provides an extremely useful and clear explanation of applications of topology and differential geometry in modern gauge theories. Basic concepts like invariants, manifolds, (co)homology, etc. are explained. The author has prepared this lecture with physicists in mind and the level of mathematical sophistication has been kept to a minimum. (S.J.P.)

Progression of Intravesical Condyloma Acuminata to Locally Advanced Poorly Differentiated Squamous Cell Carcinoma

Directory of Open Access Journals (Sweden)

A. Khambati

2016-07-01

Full Text Available Condyloma acuminata (CA is a common sexually transmitted disease caused by Human Papilloma Virus (HPV infection. CA of the bladder, however, is an exceedingly rare lesion. We present a rare case of poorly differentiated locally invasive squamous cell carcinoma (SCC arising from recurrent CA of the bladder in an immunocompetent patient and discuss pathophysiology and management of this unusual condition.

Interacting particle systems in time-dependent geometries

Science.gov (United States)

Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.

2013-09-01

Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.

Modeling tree crown dynamics with 3D partial differential equations.

Science.gov (United States)

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

Steady-state, local temperature fields with turbulent sodium flow in nominal and disturbed bundle geometries with spacer grids

International Nuclear Information System (INIS)

Moeller, R.; Tschoeke, H.; Kolodziej, M.

1980-12-01

The operating reliability of nuclear reactors calls for a reliable strength analysis of the highly loaded core elements, one of its prerequisites being the reliable determination of the three-dimensional velocity and temperature fields. To verify thermohydraulics computer programs, extensive local temperature measurements in the rod claddings of the critical bundle zone were performed on a heated 19-rod bundle model with sodium flow and provided with spacer grids (P/D = 1.30; W/D = 1.19). These are the essential results obtained: Outside the spacer grids the azimuthal temperature variations of the side and corner rods are greater by approximately the factor 10 in the bundle geometry under consideration as compared to rods in the central bundle zone. The spacer grids investigated give rise to great local temperature peaks and correspondingly great temperature gradients in the axial and azimuthal directions immediately around the support points. Continuous reduction of a subchannel by rod bowing results in substantial rises of temperature which, however, are limited to the adjacent cladding tube zones. (orig.) [de

Local environment but not genetic differentiation influences biparental care in ten plover populations.

Directory of Open Access Journals (Sweden)

Orsolya Vincze

Full Text Available Social behaviours are highly variable between species, populations and individuals. However, it is contentious whether behavioural variations are primarily moulded by the environment, caused by genetic differences, or a combination of both. Here we establish that biparental care, a complex social behaviour that involves rearing of young by both parents, differs between closely related populations, and then test two potential sources of variation in parental behaviour between populations: ambient environment and genetic differentiation. We use 2904 hours behavioural data from 10 geographically distinct Kentish (Charadrius alexandrinus and snowy plover (C. nivosus populations in America, Europe, the Middle East and North Africa to test these two sources of behavioural variation. We show that local ambient temperature has a significant influence on parental care: with extreme heat (above 40 °C total incubation (i.e. % of time the male or female incubated the nest increased, and female share (% female share of incubation decreased. By contrast, neither genetic differences between populations, nor geographic distances predicted total incubation or female's share of incubation. These results suggest that the local environment has a stronger influence on a social behaviour than genetic differentiation, at least between populations of closely related species.

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

On the geometry of fracture and frustration

NARCIS (Netherlands)

Koning, Vinzenz

2014-01-01

Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical,

Localization of DNA methyltransferase-1 during oocyte differentiation, in vitro maturation and early embryonic development in cow

Directory of Open Access Journals (Sweden)

A. M. Luciano

2009-12-01

Full Text Available DNA methyltransferase-1 (Dnmt1 is involved in the maintenance of DNA methylation patterns and is crucial for normal mammalian development. The aim of the present study was to assess the localization of Dnmt1 in cow, during the latest phases of oocyte differentiation and during the early stages of segmentation. Dnmt1 expression and localization were assessed in oocytes according to the chromatin configuration, which in turn provides an important epigenetic mechanism for the control of global gene expression and represents a morphological marker of oocyte differentiation.We found that the initial chromatin condensation was accompanied by a slight increase in the level of global DNA methylation, as assessed by 5-methyl-cytosine immunostaining followed by laser scanning confocal microscopy analysis (LSCM. RT-PCR confirmed the presence of Dnmt1 transcripts throughout this phase of oocyte differentiation. Analogously, Dnmt1 immunodetection and LSCM indicated that the protein was always present and localized in the cytoplasm, regardless the chromatin configuration and the level of global DNA methylation. Moreover, our data indicate that while Dnmt1 is retained in the cytoplasm in metaphase II stage oocytes and zygotes, it enters the nuclei of 8-16 cell stage embryos. As suggested in mouse, the functional meaning of the presence of Dnmt1 in the bovine embryo nuclei could be the maintainement of the methylation pattern of imprinted genes. In conclusion, the present work provides useful elements for the study of Dnmt1 function during the late stage of oocyte differentiation, maturation and early embryonic development in mammals.

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

An introduction to the geometry of singularities on general relativity

International Nuclear Information System (INIS)

Canarutto, D.

1988-01-01

The aim of this paper is the introduction of many ideas in differential geometry by adopting an abstract and general framework. Such a clearness permits to obtain a powerful and simple theory of connection on fibred manifolds allowing a clearer understanding and easier handling (C.P.)

The differential geometry of higher order jets and tangent bundles

International Nuclear Information System (INIS)

De Leon, M.; Rodrigues, P.R.

1985-01-01

This chapter is devoted to the study of basic geometrical notions required for the development of the main object of the text. Some facts about Jet theory are reviewed. A particular case of Jet manifolds is considered: the tangent bundle of higher order. It is shown that this jet bundle possesses in a canonical way a certain kind of geometric structure, the so called almost tangent structure of higher order, and which is a generalization of the almost tangent geometry of the tangent bundle. Another important fact examined is the extension of the notion of 'spray' to higher order tangent bundles. (Auth.)

Differential geometry of quasi-Sasakian manifolds

International Nuclear Information System (INIS)

Kirichenko, V F; Rustanov, A R

2002-01-01

The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind

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...

Covariant differential calculus on the quantum hyperplane

International Nuclear Information System (INIS)

Wess, J.

1991-01-01

We develop a differential calculus on the quantum hyperplane covariant with respect to the action of the quantum group GL q (n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane. (orig.)

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

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

2018-01-01

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

Analytical solution for the transport equation for neutral particles in cylindrical and Cartesian geometry

International Nuclear Information System (INIS)

Goncalves, Glenio Aguiar

2003-01-01

In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)

String theory considered as a local gauge theory of an extended object

International Nuclear Information System (INIS)

Chan Hongmo; Tsou Sheungtsun.

1986-11-01

In attempting to understand more about the physical origin of the so-called 'chordal gauge symmetry' in string field theory it is found that one can, at least formally, consider the theory as a generalised local gauge theory. However, the fundamental object is no longer a point, as in ordinary gauge theory, but a point with a tail, and it is the motion of this tail which represents the internal gauge degree of freedom. Moreover, the differential geometry is based on the non-abelian conformal group instead of the usual translation group. (author)

Methodology for wind turbine blade geometry optimization

Energy Technology Data Exchange (ETDEWEB)

Perfiliev, D.

2013-11-01

Nowadays, the upwind three bladed horizontal axis wind turbine is the leading player on the market. It has been found to be the best industrial compromise in the range of different turbine constructions. The current wind industry innovation is conducted in the development of individual turbine components. The blade constitutes 20-25% of the overall turbine budget. Its optimal operation in particular local economic and wind conditions is worth investigating. The blade geometry, namely the chord, twist and airfoil type distributions along the span, responds to the output measures of the blade performance. Therefore, the optimal wind blade geometry can improve the overall turbine performance. The objectives of the dissertation are focused on the development of a methodology and specific tool for the investigation of possible existing wind blade geometry adjustments. The novelty of the methodology presented in the thesis is the multiobjective perspective on wind blade geometry optimization, particularly taking simultaneously into account the local wind conditions and the issue of aerodynamic noise emissions. The presented optimization objective approach has not been investigated previously for the implementation in wind blade design. The possibilities to use different theories for the analysis and search procedures are investigated and sufficient arguments derived for the usage of proposed theories. The tool is used for the test optimization of a particular wind turbine blade. The sensitivity analysis shows the dependence of the outputs on the provided inputs, as well as its relative and absolute divergences and instabilities. The pros and cons of the proposed technique are seen from the practical implementation, which is documented in the results, analysis and conclusion sections. (orig.)

Euclidean distance geometry an introduction

CERN Document Server

Liberti, Leo

2017-01-01

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

Differential geometric methods in system theory.

Science.gov (United States)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

Conditional estimation of local pooled dispersion parameter in small-sample RNA-Seq data improves differential expression test.

Science.gov (United States)

Gim, Jungsoo; Won, Sungho; Park, Taesung

2016-10-01

High throughput sequencing technology in transcriptomics studies contribute to the understanding of gene regulation mechanism and its cellular function, but also increases a need for accurate statistical methods to assess quantitative differences between experiments. Many methods have been developed to account for the specifics of count data: non-normality, a dependence of the variance on the mean, and small sample size. Among them, the small number of samples in typical experiments is still a challenge. Here we present a method for differential analysis of count data, using conditional estimation of local pooled dispersion parameters. A comprehensive evaluation of our proposed method in the aspect of differential gene expression analysis using both simulated and real data sets shows that the proposed method is more powerful than other existing methods while controlling the false discovery rates. By introducing conditional estimation of local pooled dispersion parameters, we successfully overcome the limitation of small power and enable a powerful quantitative analysis focused on differential expression test with the small number of samples.

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double Pn approximation

International Nuclear Information System (INIS)

Amouyal, A.; Tariel, H.

1966-01-01

Code name: January 1 st SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2 nd version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P n approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media [fr

Emergent Geometry from Entropy and Causality

Science.gov (United States)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

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

Evolution from the coplanar to the perpendicular plane geometry of helium (e,2e) differential cross sections symmetric in scattering angle and energy

International Nuclear Information System (INIS)

Murray, A.J.; Read, F.H.

1993-01-01

Experimentally determined differential cross sections are presented for the (e,2e) process in helium, in which the two outgoing electrons have the same energy and the same scattering angle with respect to the incident beam. At four incident energies from 20 to 50 eV above the ionization threshold the detection plane defined by the outgoing electrons was varied from being coplanar with the incident beam to being perpendicular to the beam. The differential cross section evolves from a two-peak structure in coplanar geometry to a three-peak structure in the perpendicular plane. At the lowest energy the forward-scattering coplanar peak is smaller than the backscatter peak, in contrast to the results at higher energies. A deep minimum is seen at an intermediate plane angle of 67.5 degree, this minimum being deepest at 40 eV above the ionization threshold. The results are normalized to an absolute scale using previous coplanar measurements as discussed in the text. The spectrometer used to collect these results is fully computer controlled and real-time computer optimized

Topology and geometry of six-dimensional (1, 0) supergravity black hole horizons

International Nuclear Information System (INIS)

Akyol, M; Papadopoulos, G

2012-01-01

We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS 3 x Σ 3 , where Σ 3 is a homology 3-sphere, or R 1,1 )xS 4 , where S 4 is a 4-manifold whose geometry depends on the hypermultiplet scalars. In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish. We also demonstrate that the AdS 3 x Σ 3 horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Σ 3 is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS 3 x S 3 or R 1, 1 x T 4 . Moreover, we show that the R 1,1 xS horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kaehler and hyper-Kaehler, respectively. (paper)

Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

International Nuclear Information System (INIS)

Hartong, Jelle; Obers, Niels A.

2015-01-01

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1local Galilean algebra that acts on the tangent space to TNC geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles,C.P. 231, 1050 Brussels (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)

2015-07-29

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1local Galilean algebra that acts on the tangent space to TNC geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

Real algebraic geometry

CERN Document Server

Bochnak, Jacek; Roy, Marie-Françoise

1998-01-01

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

Local transport method for hybrid diffusion-transport calculations in 2-D cylindrical (R, THETA) geometry

International Nuclear Information System (INIS)

Zhang, Dingkang; Rahnema, Farzad; Ougouag, Abderrfi M.

2011-01-01

A response-based local transport method has been developed in 2-D (r, θ) geometry for coupling to any coarse-mesh (nodal) diffusion method/code. Monte Carlo method is first used to generate a (pre-computed) the response function library for each unique coarse mesh in the transport domain (e.g., the outer reflector region of the Pebble Bed Reactor). The scalar flux and net current at the diffusion/transport interface provided by the diffusion method are used as an incoming surface source to the transport domain. A deterministic iterative sweeping method together with the response function library is utilized to compute the local transport solution within all transport coarse meshes. After the partial angular currents crossing the coarse mesh surfaces are converged, albedo coefficients are computed as boundary conditions for the diffusion methods. The iteration on the albedo boundary condition (for the diffusion method via transport) and the incoming angular flux boundary condition (for the transport via diffusion) is continued until convergence is achieved. The method was tested for in a simplified 2-D (r, θ) pebble bed reactor problem consisting of an inner reflector, an annular fuel region and a controlled outer reflector. The comparisons have shown that the results of the response-function-based transport method agree very well with a direct MCNP whole core solution. The agreement in coarse mesh averaged flux was found to be excellent: relative difference of about 0.18% and a maximum difference of about 0.55%. Note that the MCNP uncertainty was less than 0.1%. (author)

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...

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors.

Science.gov (United States)

Walcott, Sam

2014-10-01

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

Nonlinear poisson brackets geometry and quantization

CERN Document Server

Karasev, M V

2012-01-01

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Numerical optimization of laboratory combustor geometry for NO suppression

International Nuclear Information System (INIS)

Mazaheri, Karim; Shakeri, Alireza

2016-01-01

Highlights: • A five-step kinetics for NO and CO prediction is extracted from GRI-3.0 mechanism. • Accuracy and applicability of this kinetics for numerical optimization were shown. • Optimized geometry for a combustor was determined using the combined process. • NO emission from optimized geometry is found 10.3% lower than the basis geometry. - Abstract: In this article, geometry optimization of a jet stirred reactor (JSR) combustor has been carried out for minimum NO emissions in methane oxidation using a combined numerical algorithm based on computational fluid dynamics (CFD) and differential evolution (DE) optimization. The optimization algorithm is also used to find a fairly accurate reduced mechanism. The combustion kinetics is based on a five-step mechanism with 17 unknowns which is obtained using an optimization DE algorithm for a PSR–PFR reactor based on GRI-3.0 full mechanism. The optimization design variables are the unknowns of the five-step mechanism and the cost function is the concentration difference of pollutants obtained from the 5-step mechanism and the full mechanism. To validate the flow solver and the chemical kinetics, the computed NO at the outlet of the JSR is compared with experiments. To optimize the geometry of a combustor, the JSR combustor geometry is modeled using three parameters (i.e., design variables). An integrated approach using a flow solver and the DE optimization algorithm produces the lowest NO concentrations. Results show that the exhaust NO emission for the optimized geometry is 10.3% lower than the original geometry, while the inlet temperature of the working fluid and the concentration of O_2 are operating constraints. In addition, the concentration of CO pollutant is also much less than the original chamber.

Maximum and minimum entropy states yielding local continuity bounds

Science.gov (United States)

Hanson, Eric P.; Datta, Nilanjana

2018-04-01

Given an arbitrary quantum state (σ), we obtain an explicit construction of a state ρɛ * ( σ ) [respectively, ρ * , ɛ ( σ ) ] which has the maximum (respectively, minimum) entropy among all states which lie in a specified neighborhood (ɛ-ball) of σ. Computing the entropy of these states leads to a local strengthening of the continuity bound of the von Neumann entropy, i.e., the Audenaert-Fannes inequality. Our bound is local in the sense that it depends on the spectrum of σ. The states ρɛ * ( σ ) and ρ * , ɛ (σ) depend only on the geometry of the ɛ-ball and are in fact optimizers for a larger class of entropies. These include the Rényi entropy and the minimum- and maximum-entropies, providing explicit formulas for certain smoothed quantities. This allows us to obtain local continuity bounds for these quantities as well. In obtaining this bound, we first derive a more general result which may be of independent interest, namely, a necessary and sufficient condition under which a state maximizes a concave and Gâteaux-differentiable function in an ɛ-ball around a given state σ. Examples of such a function include the von Neumann entropy and the conditional entropy of bipartite states. Our proofs employ tools from the theory of convex optimization under non-differentiable constraints, in particular Fermat's rule, and majorization theory.

The SUSY oscillator from local geometry: Dynamics and coherent states

International Nuclear Information System (INIS)

Thienel, H.P.

1994-01-01

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

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

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

Entanglement entropy and differential entropy for massive flavors

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2015-01-01

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

Solvability conditions for non-local boundary value problems for two-dimensional half-linear differential systems

Czech Academy of Sciences Publication Activity Database

Kiguradze, I.; Šremr, Jiří

2011-01-01

Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573

Superbanana orbits in stellarator geometries

International Nuclear Information System (INIS)

Derr, J.A.; Shohet, J.L.

1979-04-01

The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron

Three theorems on near horizon extremal vanishing horizon geometries

Directory of Open Access Journals (Sweden)

S. Sadeghian

2016-02-01

Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.

Geometry

Indian Academy of Sciences (India)

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

Changes in localization of human discs large (hDlg) during keratinocyte differentiation is associated with expression of alternatively spliced hDlg variants

International Nuclear Information System (INIS)

Roberts, S.; Calautti, E.; Vanderweil, S.; Nguyen, H.O.; Foley, A.; Baden, H.P.; Viel, A.

2007-01-01

Alternative spliced variants of the human discs large (hDlg) tumour suppressor are characterized by combinations of insertions. Here, using insertions I2- and I3-specific antibodies, we show that I2 and I3 variants have distinct distributions in epidermal and cervical epithelia. In skin and cervix, I3 variants are found in the cytoplasm. Cytoplasmic localization of I3 variants decreases as cervical keratinocytes differentiate, concomitant with relocalization to the cell periphery. I2 variants are found at the cell periphery of differentiated epidermal and cervical keratinocytes. Nuclear localization of I2 variants was evident in both tissues, with concentration of nuclear I2 variants in basal and parabasal cervical keratinocytes. A prominent nuclear localization of hDlg in cells of hyperproliferative layers of psoriatic lesions, but not in mature differentiated keratinocytes, together with I2 redistribution in differentiating keratinocytes, suggests that nuclear hDlg functions may be pertinent to growth of undifferentiated cells. Supporting our findings in squamous tissues, a decrease of nuclear hDlg and an increase of membrane-bound and cytoplasmic hDlg upon calcium-induced keratinocyte differentiation were not concomitant processes. Furthermore, we confirm that the exit of I2 variants from the nucleus is linked to stimulation of epithelial differentiation. The dynamic redistribution of hDlg also correlated with a marked increase in the expression of I3 variants while the level of I2 variants showed only a moderate decrease. Because changes in the intracellular distribution of hDlg splice variants, and in their expression levels, correlate with changes in differentiation state we hypothesize that the different hDlg isoforms play distinct roles at various stages of epithelial differentiation

Parallel computation of electrostatic potentials and fields in technical geometries on SUPRENUM

International Nuclear Information System (INIS)

Alef, M.

1990-02-01

The programs EPOTZR und EFLDZR have been developed in order to compute electrostatic potentials and the corresponding fields in technical geometries (example: Diode geometry for optimum focussing of ion beams in pulsed high-current ion diodes). The Poisson equation is discretized in a two-dimensional boundary-fitted grid in the (r,z)-plane and solved using multigrid methods. The z- and r-components of the field are determined by numerical differentiation of the potential. This report contains the user's guide of the SUPRENUM versions EPOTZR-P and EFLDZR-P. (orig./HP) [de

A dissipative particle dynamics method for arbitrarily complex geometries

Science.gov (United States)

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

2018-02-01

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

Quantum Riemannian geometry of phase space and nonassociativity

Directory of Open Access Journals (Sweden)

Beggs Edwin J.

2017-04-01

Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.

Geometry of supersymmetric gauge theories

International Nuclear Information System (INIS)

Gieres, F.

1988-01-01

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

Clustering in Hilbert simplex geometry

KAUST Repository

Nielsen, Frank

2017-04-03

Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.

Systems of differential forms, including Kuranishi's theory of total prolongations. Technical report No. 2

Energy Technology Data Exchange (ETDEWEB)

Johnson, H.H.

1956-01-01

The theory of differential forms and their integral manifolds was created by E. Cartan in order to study the differential equations which occur in Lie groups and differential geometry. We present here a modern outline of this theory using refinements and notations taken from recent papers of Y. Matsushima and M. Kuranishi. Section III is devoted to an exposition of a paper of Kuranishi on total prolongations which was presented at the 1956 Summer Institute in Differential Geometry at the University of Washington.

Covariant differential calculus on quantum spheres of odd dimension

International Nuclear Information System (INIS)

Welk, M.

1998-01-01

Covariant differential calculus on the quantum spheres S q 2N-1 is studied. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including first and higher order calculi and a symmetry concept. (author)

Comparison of Microinstability Properties for Stellarator Magnetic Geometries

International Nuclear Information System (INIS)

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

2005-01-01

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

Needle decompositions in Riemannian geometry

CERN Document Server

Klartag, Bo'az

2017-01-01

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

Geometry Dependence of Stellarator Turbulence

International Nuclear Information System (INIS)

Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.

2009-01-01

Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes

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

Exact solutions to the time-fractional differential equations via local fractional derivatives

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Seedling traits, plasticity and local differentiation as strategies of invasive species of Impatiens in central Europe

Czech Academy of Sciences Publication Activity Database

Skálová, Hana; Havlíčková, Vendula; Pyšek, Petr

2012-01-01

Roč. 110, č. 7 (2012), s. 1429-1438 ISSN 0305-7364 R&D Projects: GA ČR GA206/07/0668; GA MŠk LC06073 Institutional research plan: CEZ:AV0Z60050516 Keywords : plant invasions * plasticity * local differentiation Subject RIV: EF - Botanics Impact factor: 3.449, year: 2012

Design of Tailored Non-Crimp Fabrics Based on Stitching Geometry

Science.gov (United States)

Krieger, Helga; Gries, Thomas; Stapleton, Scott E.

2018-02-01

Automation of the preforming process brings up two opposing requirements for the used engineering fabric. On the one hand, the fabric requires a sufficient drapeability, or low shear stiffness, for forming into double-curved geometries; but on the other hand, the fabric requires a high form stability, or high shear stiffness, for automated handling. To meet both requirements tailored non-crimp fabrics (TNCFs) are proposed. While the stitching has little structural influence on the final part, it virtually dictates the TNCFs local capability to shear and drape over a mold during preforming. The shear stiffness of TNCFs is designed by defining the local stitching geometry. NCFs with chain stitch have a comparatively high shear stiffness and NCFs with a stitch angle close to the symmetry stitch angle have a very low shear stiffness. A method to design the component specific local stitching parameters of TNCFs is discussed. For validation of the method, NCFs with designed tailored stitching parameters were manufactured and compared to benchmark NCFs with uniform stitching parameters. The designed TNCFs showed both, generally a high form stability and in locally required zones a good drapeability, in drape experiments over an elongated hemisphere.

The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

International Nuclear Information System (INIS)

Pfeifer, Christian

2013-11-01

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

Energy Technology Data Exchange (ETDEWEB)

Pfeifer, Christian

2013-11-15

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

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 ...

Local linearization methods for the numerical integration of ordinary differential equations: An overview

International Nuclear Information System (INIS)

Jimenez, J.C.

2009-06-01

Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)

Plateau's problem an invitation to varifold geometry

CERN Document Server

Frederick J Almgren, Jr

2001-01-01

There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book--or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encour...

Differential geometry and topology with a view to dynamical systems

CERN Document Server

Burns, Keith

2005-01-01

MANIFOLDSIntroductionReview of topological conceptsSmooth manifoldsSmooth mapsTangent vectors and the tangent bundleTangent vectors as derivationsThe derivative of a smooth mapOrientationImmersions, embeddings and submersionsRegular and critical points and valuesManifolds with boundarySard's theoremTransversalityStabilityExercisesVECTOR FIELDS AND DYNAMICAL SYSTEMSIntroductionVector fieldsSmooth dynamical systemsLie derivative, Lie bracketDiscrete dynamical systemsHyperbolic fixed points and periodic orbitsExercisesRIEMANNIAN METRICSIntroductionRiemannian metricsStandard geometries on surfacesExercisesRIEMANNIAN CONNECTIONS AND GEODESICSIntroductionAffine connectionsRiemannian connectionsGeodesicsThe exponential mapMinimizing properties of geodesicsThe Riemannian distanceExercisesCURVATUREIntroductionThe curvature tensorThe second fundamental formSectional and Ricci curvaturesJacobi fieldsManifolds of constant curvatureConjugate pointsHorizontal and vertical sub-bundlesThe geodesic flowExercisesTENSORS AND DI...

Effect of interior geometry on local climate inside an electronic device enclosure

DEFF Research Database (Denmark)

Joshy, Salil; Jellesen, Morten Stendahl; Ambat, Rajan

2017-01-01

Electronic enclosure design and the internal arrangement of PCBs and components influence microclimate inside the enclosure. This work features a general electronic unit with parallel PCBs. One of the PCB is considered to have heat generating components on it. The humidity and temperature profiles...... geometry of the device and related enclosure design parameters on the humidity and temperature profiles inside the electronic device enclosure....

Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System

Directory of Open Access Journals (Sweden)

Wenyu Yang

2014-01-01

Full Text Available Particle swarm optimization (PSO is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE. In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems.

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

Partial differential equation-based localization of a monopole source from a circular array.

Science.gov (United States)

Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

2013-10-01

Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.

Local and global eulerian gyrokinetic simulations of microturbulence in realistic geometry with applications to the TCV Tokamak

International Nuclear Information System (INIS)

Lapillonne, X.

2010-04-01

In magnetically confined fusion devices, the energy and particle transport is significantly larger than expected from purely collisional processes. This degraded confinement mostly results from small-scale turbulence and prevents from reaching self-sustained burning plasma conditions in present day experiments. A better understanding of these nonlinear phenomena is therefore of key importance on the way towards controlled fusion. The small-scale microinstabilities and associated turbulence are investigated for Tokamak plasmas by means of numerical simulations in the frame of the gyrokinetic theory. This model describes the evolution of the particle distribution functions in phase space together with self-consistent electromagnetic fields, while neglecting the fast motion associated with the Larmor orbit of particles around the magnetic field lines. In the course of this thesis work, substantial modifications to the existing Eulerian gyrokinetic code GENE have been carried out in collaboration with the Max-Planck- Institute f¨ur Plasmaphysik in Garching, Germany. The code has been extended from a local approximation, which only considers a reduced volume of a fusion plasma, to a global version which fully includes radial temperature and density profiles as well as radial magnetic equilibrium variations. To this end, the gyrokinetic equations have been formulated for general magnetic geometry, keeping radial variations of equilibrium quantities, and considering field aligned coordinates, suitable for their numerical implementation. The numerical treatment of the radial direction has been modified from a Fourier representation in the local approach to real space in the global code. This has in particular required to adapt the radial derivatives, the field solver, and to implement a real space dealiasing scheme for the treatment of the nonlinearity. A heat source was in addition introduced to allow for steady state global nonlinear simulations. An important part of

Methods for acquiring data on terrain geomorphology, course geometry and kinematics of competitors' runs in alpine skiing: a historical review.

Science.gov (United States)

Erdmann, Włodzimierz S; Giovanis, Vassilis; Aschenbrenner, Piotr; Kiriakis, Vaios; Suchanowski, Andrzej

2017-01-01

This paper aims at the description and comparison of methods of topographic analysis of racing courses at all disciplines of alpine skiing sports for the purposes of obtaining: terrain geomorphology (snowless and with snow), course geometry, and competitors' runs. The review presents specific methods and instruments according to the order of their historical appearance as follows: (1) azimuth method with the use of a compass, tape and goniometer instruments; (2) optical method with geodetic theodolite, laser and photocells; (3) triangulation method with the aid of a tape and goniometer; (4) image method with the use of video cameras; (5) differential global positioning system and carrier phase global positioning system methods. Described methods were used at homologation procedure, at training sessions, during competitions of local level and during International Ski Federation World Championships or World Cups. Some methods were used together. In order to provide detailed data on course setting and skiers' running it is recommended to analyse course geometry and kinematics data of competitors' running for all important competitions.

PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

Science.gov (United States)

Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

2009-10-01

-component dispersionless Boussinesq-type system. T E Kouloukas and V G Papageorgiou introduce a family of nonparametric Yang-Baxter maps obtained by re-factorization of matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket, and their degenerations are connected to known integrable systems on quad-graphs. S V Manakov and P M Santini apply a novel version of the inverse scattering transform based on Lax pairs in multidimensional commuting vector fields to the heavenly and Pavlov equations, establishing that their localized solutions evolve without breaking, and constructing the long-time behaviour of the corresponding Cauchy problems. Discretizations of integrable geometric models depend heavily on the coordinates used. M Nieszporski and A Sym show how to discretize Bianchi surfaces (associated with an elliptic version of the Ernst equation) in arbitrary parametrization. C Rogers and A Szereszewski study the Bäcklund transformation for L-isothermic surfaces in the original Bianchi formulation. They establish a connection between this transformation and a nonhomogeneous linear Schrödinger equation and construct a class of generalized Dupin cyclides. W K Schief, A Szereszewski and C Rogers study a classical system of equilibrium equations for shell membranes. Various examples of viable membrane geometries lead to remarkable geometric configurations such as generalized Dupin cyclides and L-minimal surfaces. A Sergyeyev constructs infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using the spectral problem. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz for the WDVV equations. J Shiraishi and Y Tutiya study an integro-differential equation which generalizes the periodic intermediate long wave equation. The kernel of the singular integral involved is a second order difference of the Weierstrass ζ-function. Using Sato's formulation, the authors

Higher dimensional uniformisation and W-geometry

International Nuclear Information System (INIS)

Govindarajan, S.

1995-01-01

We formulate the uniformisation problem underlying the geometry of W n -gravity using the differential equation approach to W-algebras. We construct W n -space (analogous to superspace in supersymmetry) as an (n-1)-dimensional complex manifold using isomonodromic deformations of linear differential equations. The W n -manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in bfCP n-1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W n -manifold. We discuss how the Teichmueller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W n -manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ''generic'' W-algebras. (orig.)

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

Science.gov (United States)

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

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

Stages as models of scene geometry.

Science.gov (United States)

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

2010-09-01

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

Geometry of physical dispersion relations

International Nuclear Information System (INIS)

Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.

2011-01-01

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.

Re-visioning local biologies: HIV-2 and the pattern of differential valuation in biomedical research.

Science.gov (United States)

Gilbert, Hannah

2013-01-01

The discovery of HIV-2, a distinctly West African variant of HIV, is often portrayed as the result of a straightforward, if serendipitous, error. This article reframes the history of how HIV-2 came to be a knowable scientific identity. Relying on narratives from an African laboratory and clinic, it suggests that the rise and fall of HIV-2 as a viable research entity is indicative of a differential visibility and valuation of both human bodies and viruses. Understanding how HIV-2 emerged as a local biology reveals the complex set of relations that contemporary African scientists face in navigating local moral economies and the mercurial politics of the contemporary global health industry.

Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

International Nuclear Information System (INIS)

Rivera Hernandez, Sergio

2012-01-01

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all

Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

Energy Technology Data Exchange (ETDEWEB)

Rivera Hernandez, Sergio

2012-02-15

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all

Sums over geometries and improvements on the mean field approximation

International Nuclear Information System (INIS)

Sacksteder, Vincent E. IV

2007-01-01

The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

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

Exotic smoothness and physics differential topology and spacetime models

CERN Document Server

Asselmeyer-Maluga, T

2007-01-01

The recent revolution in differential topology related to the discovery of non-standard ("exotic") smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further app...

Geometry and Gâteaux smoothness in separable Banach spaces

Czech Academy of Sciences Publication Activity Database

Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav

2012-01-01

Roč. 6, č. 2 (2012), s. 201-232 ISSN 1846-3886 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux differentiable norms * extreme points * Radon -Nikodým property Subject RIV: BA - General Mathematics Impact factor: 0.529, year: 2012 http://oam.ele-math.com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces

Numerical investigation of laminar forced convection heat transfer in rectangular channels with different block geometries using nano-fluids

Directory of Open Access Journals (Sweden)

Foroutani Saeed

2017-01-01

Full Text Available This research investigates the laminar steady-forced convection heat transfer of a Cu-water nanofluid in a 2-D horizontal channel with different block geometries attached to the bottom wall. The block geometries assumed in this research are triangular and curve blocks. The governing equations associated with the required boundary conditions are solved using finite volume method based on the SIMPLE technique and the effects of Reynolds number, nanofluid volume fraction, block geometry, and the numbers of blocks on the local and average Nusselt numbers are explored. The obtained results show that nanoparticles can effectively enhance the heat transfer in a channel. Furthermore, the local and average Nusselt number distribution is strongly dependent on the block geometry. As observed, the heat transfer augments with the increase in the Reynolds number and nanofluid volume fraction for both block geometries. It is also concluded that the average Nusselt number of the curve block is higher than that of the triangular block for different Reynolds numbers which declares the importance of the block geometry in the heat transfer enhancement.

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

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

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

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

Geometry of the Universe

International Nuclear Information System (INIS)

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

1978-01-01

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

Early local differentiation of the cell wall matrix defines the contact sites in lobed mesophyll cells of Zea mays.

Science.gov (United States)

Giannoutsou, E; Sotiriou, P; Apostolakos, P; Galatis, B

2013-10-01

The morphogenesis of lobed mesophyll cells (MCs) is highly controlled and coupled with intercellular space formation. Cortical microtubule rings define the number and the position of MC isthmi. This work investigated early events of MC morphogenesis, especially the mechanism defining the position of contacts between MCs. The distributions of plasmodesmata, the hemicelluloses callose and (1 → 3,1 → 4)-β-d-glucans (MLGs) and the pectin epitopes recognized by the 2F4, JIM5, JIM7 and LM6 antibodies were studied in the cell walls of Zea mays MCs. Matrix cell wall polysaccharides were immunolocalized in hand-made sections and in sections of material embedded in LR White resin. Callose was also localized using aniline blue in hand-made sections. Plasmodesmata distribution was examined by transmission electron microscopy. Before reorganization of the dispersed cortical microtubules into microtubule rings, particular bands of the longitudinal MC walls, where the MC contacts will form, locally differentiate by selective (1) deposition of callose and the pectin epitopes recognized by the 2F4, LM6, JIM5 and JIM7 antibodies, (2) degradation of MLGs and (3) formation of secondary plasmodesmata clusterings. This cell wall matrix differentiation persists in cell contacts of mature MCs. Simultaneously, the wall bands between those of future cell contacts differentiate with (1) deposition of local cell wall thickenings including cellulose microfibrils, (2) preferential presence of MLGs, (3) absence of callose and (4) transient presence of the pectins identified by the JIM5 and JIM7 antibodies. The wall areas between cell contacts expand determinately to form the cell isthmi and the cell lobes. The morphogenesis of lobed MCs is characterized by the early patterned differentiation of two distinct cell wall subdomains, defining the sites of the future MC contacts and of the future MC isthmi respectively. This patterned cell wall differentiation precedes cortical microtubule

Gaussian process regression for geometry optimization

Science.gov (United States)

Denzel, Alexander; Kästner, Johannes

2018-03-01

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

2008-01-01

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

Analytic, Algebraic and Geometric Aspects of Differential Equations

CERN Document Server

Haraoka, Yoshishige; Michalik, Sławomir

2017-01-01

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of i...

Differential influences of local subpopulations on regional diversity and differentiation for greater sage-grouse (Centrocercus urophasianus)

Science.gov (United States)

Row, Jeffery R.; Oyler-McCance, Sara J.; Fedy, Brad C.

2016-01-01

The distribution of spatial genetic variation across a region can shape evolutionary dynamics and impact population persistence. Local population dynamics and among-population dispersal rates are strong drivers of this spatial genetic variation, yet for many species we lack a clear understanding of how these population processes interact in space to shape within-species genetic variation. Here, we used extensive genetic and demographic data from 10 subpopulations of greater sage-grouse to parameterize a simulated approximate Bayesian computation (ABC) model and (i) test for regional differences in population density and dispersal rates for greater sage-grouse subpopulations in Wyoming, and (ii) quantify how these differences impact subpopulation regional influence on genetic variation. We found a close match between observed and simulated data under our parameterized model and strong variation in density and dispersal rates across Wyoming. Sensitivity analyses suggested that changes in dispersal (via landscape resistance) had a greater influence on regional differentiation, whereas changes in density had a greater influence on mean diversity across all subpopulations. Local subpopulations, however, varied in their regional influence on genetic variation. Decreases in the size and dispersal rates of central populations with low overall and net immigration (i.e. population sources) had the greatest negative impact on genetic variation. Overall, our results provide insight into the interactions among demography, dispersal and genetic variation and highlight the potential of ABC to disentangle the complexity of regional population dynamics and project the genetic impact of changing conditions.

Eps homology domain endosomal transport proteins differentially localize to the neuromuscular junction

Directory of Open Access Journals (Sweden)

Mate Suzanne E

2012-09-01

Full Text Available Abstract Background Recycling of endosomes is important for trafficking and maintenance of proteins at the neuromuscular junction (NMJ. We have previously shown high expression of the endocytic recycling regulator Eps15 homology domain-containing (EHD1 proteinin the Torpedo californica electric organ, a model tissue for investigating a cholinergic synapse. In this study, we investigated the localization of EHD1 and its paralogs EHD2, EHD3, and EHD4 in mouse skeletal muscle, and assessed the morphological changes in EHD1−/− NMJs. Methods Localization of the candidate NMJ protein EHD1 was assessed by confocal microscopy analysis of whole-mount mouse skeletal muscle fibers after direct gene transfer and immunolabeling. The potential function of EHD1 was assessed by specific force measurement and α-bungarotoxin-based endplate morphology mapping in EHD1−/− mouse skeletal muscle. Results Endogenous EHD1 localized to primary synaptic clefts of murine NMJ, and this localization was confirmed by expression of recombinant green fluorescent protein labeled-EHD1 in murine skeletal muscle in vivo. EHD1−/− mouse skeletal muscle had normal histology and NMJ morphology, and normal specific force generation during muscle contraction. The EHD 1–4 proteins showed differential localization in skeletal muscle: EHD2 to muscle vasculature, EHD3 to perisynaptic regions, and EHD4 to perinuclear regions and to primary synaptic clefts, but at lower levels than EHD1. Additionally, specific antibodies raised against mammalian EHD1-4 recognized proteins of the expected mass in the T. californica electric organ. Finally, we found that EHD4 expression was more abundant in EHD1−/− mouse skeletal muscle than in wild-type skeletal muscle. Conclusion EHD1 and EHD4 localize to the primary synaptic clefts of the NMJ. Lack of obvious defects in NMJ structure and muscle function in EHD1−/− muscle may be due to functional compensation by other EHD paralogs.

CIME school “Fully Nonlinear PDEs in Real and Complex Geometry and Optics”

CERN Document Server

Capogna, Luca; Gutiérrez, Cristian E; Montanari, Annamaria

2014-01-01

The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.

New geometries for black hole horizons

Energy Technology Data Exchange (ETDEWEB)

Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)

2015-07-10

We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.

Non-Abelian bubbles in microstate geometries

Energy Technology Data Exchange (ETDEWEB)

Ramírez, Pedro F. [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera, 13-15, C.University Cantoblanco, E-28049 Madrid (Spain); Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers bâtiment 774, F-91191 Gif-sur-Yvette (France)

2016-11-24

We find the first smooth bubbling microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of N=1, d=5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.

Near horizon geometry of rotating black holes in five dimensions

International Nuclear Information System (INIS)

Cvetic, M.; Larsen, F.

1998-01-01

We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near-horizon limit the geometry is locally AdS 3 x S 3 , as in the non-rotating case. However, the global structure couples the AdS 3 and the S 3 , giving angular velocity to the S 3 . The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein-Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory. (orig.)

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...

Complementary effect of natural and sexual selection against immigrants maintains differentiation between locally adapted fish

Science.gov (United States)

Plath, Martin; Riesch, Rüdiger; Oranth, Alexandra; Dzienko, Justina; Karau, Nora; Schießl, Angela; Stadler, Stefan; Wigh, Adriana; Zimmer, Claudia; Arias-Rodriguez, Lenin; Schlupp, Ingo; Tobler, Michael

2010-08-01

Adaptation to ecologically heterogeneous environments can drive speciation. But what mechanisms maintain reproductive isolation among locally adapted populations? Using poeciliid fishes in a system with naturally occurring toxic hydrogen sulfide, we show that (a) fish from non-sulfidic sites ( Poecilia mexicana) show high mortality (95 %) after 24 h when exposed to the toxicant, while locally adapted fish from sulfidic sites ( Poecilia sulphuraria) experience low mortality (13 %) when transferred to non-sulfidic water. (b) Mate choice tests revealed that P. mexicana females exhibit a preference for conspecific males in non-sulfidic water, but not in sulfidic water, whereas P. sulphuraria females never showed a preference. Increased costs of mate choice in sulfidic, hypoxic water, and the lack of selection for reinforcement due to the low survival of P. mexicana may explain the absence of a preference in P. sulphuraria females. Taken together, our study may be the first to demonstrate independent—but complementary—effects of natural and sexual selection against immigrants maintaining differentiation between locally adapted fish populations.

Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry

Energy Technology Data Exchange (ETDEWEB)

Volkov, Victor [Bereozovaya 2A, Konstantinovo, Moscow Region 140207 (Russian Federation)

2014-10-07

The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.

Experimental validation on the effect of material geometries and processing methodology of Polyoxymethylene (POM)

Science.gov (United States)

Hafizzal, Y.; Nurulhuda, A.; Izman, S.; Khadir, AZA

2017-08-01

POM-copolymer bond breaking leads to change depending with respect to processing methodology and material geometries. This paper present the oversights effect on the material integrity due to different geometries and processing methodology. Thermo-analytical methods with reference were used to examine the degradation of thermomechanical while Thermogravimetric Analysis (TGA) was used to judge the thermal stability of sample from its major decomposition temperature. Differential Scanning Calorimetry (DSC) investigation performed to identify the thermal behaviour and thermal properties of materials. The result shown that plastic gear geometries with injection molding at higher tonnage machine more stable thermally rather than resin geometries. Injection plastic gear geometries at low tonnage machine faced major decomposition temperatures at 313.61°C, 305.76 °C and 307.91 °C while higher tonnage processing method are fully decomposed at 890°C, significantly higher compared to low tonnage condition and resin geometries specimen at 398°C. Chemical composition of plastic gear geometries with injection molding at higher and lower tonnage are compare based on their moisture and Volatile Organic Compound (VOC) content, polymeric material content and the absence of filler. Results of higher moisture and Volatile Organic Compound (VOC) content are report in resin geometries (0.120%) compared to higher tonnage of injection plastic gear geometries which is 1.264%. The higher tonnage of injection plastic gear geometry are less sensitive to thermo-mechanical degradation due to polymer chain length and molecular weight of material properties such as tensile strength, flexural strength, fatigue strength and creep resistance.

Steady three-fluid coronal expansion for nonspherical geometries

International Nuclear Information System (INIS)

Joselyn, J.; Holzer, T.E.

1978-01-01

A steady three-fluid model of the solar coronal expansionk in which 4 He ++ ions (alphas) are treated as a nonminor species, is developed for nonspherically symmetric flow geometries of the general sort thought to be characteristic of coronal holes. It is found that the very high mass fluxes in the low corona, which are associated with rapidly diverging flow geometries, lead to a locally enhanced frictional coupling between protons and alphas and consequently to a significant reduction of the He/H abundance ratio in the lower corona from that normally predicted by multifluid models. In the models considered, the frictional drag on the protons by the alphas (a process neglected in most studies) is found to play an important role near the sun. Heavy ions, other than alphas, are treated as minor species and are seen to exhibit varying responses to the rapidly diverging flow geometries, depending on the ion mass and charge. As for the protons, the frictional effect of the alphas on the heavier ions is found to be significant in the models considered

Esclerodermia localizada: Diagnósticos diferenciales Localized scleroderma: Differential diagnosis

Directory of Open Access Journals (Sweden)

MB Leroux

2011-09-01

Full Text Available La esclerodermia localizada constituye un desorden autoinmune órgano específico, que compromete sobre todo la piel. Se caracteriza por inflamación seguida de esclerosis e incluye distintas formas clínicas. La etiología de la esclerodermia localizada no ha sido establecida. El diagnóstico diferencial incluye cuadros esclerodermiformes, desencadenados por factores intrínsecos y extrínsecos que están siendo estudiados. Entre ellos se incluyen: exposición a radiaciones o tóxicos, consumo de medicamentos, infecciones y enfermedades de origen endocrino-metabólico, genético e inflamatorio. En primer lugar, se debe descartar la esclerodermia sistémica. En segundo lugar, se clasifican las entidades con predominio de esclerosis o atrofia. Por último, se incluyen algunas enfermedades en un cuadro comparativo.Localized scleroderma is an autoimmune organ specific disorder with an important skin compromise. It is an inflammatory process with several distinct clinical characteristics. The etiology of localized scleroderma has not been established yet. Differential diagnosis includes sclerodermiform onset unchained by intrinsic and extrinsic factors that are presently studied. Among them must be taking into account: exposure to radiation or toxic agents, therapeutic drugs, infections and diseases of endocrine, metabolic, genetic or inflammatory etiology. Firstly, it must be point out that systemic scleroderma must be ruled out. Secondly, disorders predominantly with sclerosis and atrophy must be classified and lastly, some other diseases are included in a comparative table.

Differential invariants of generic parabolic Monge–Ampère equations

International Nuclear Information System (INIS)

Ferraioli, D Catalano; Vinogradov, A M

2012-01-01

Some new results on the geometry of classical parabolic Monge–Ampère equations (PMAs) are presented. PMAs are either integrable, or non-integrable according to the integrability of its characteristic distribution. All integrable PMAs are locally equivalent to the equation u xx = 0. We study non-integrable PMAs by associating with each of them a one-dimensional distribution on the corresponding first-order jet manifold, called the directing distribution. According to some property of this distribution, non-integrable PMAs are subdivided into three classes, one generic and two special. Generic PMAs are completely characterized by their directing distributions, and we study canonical models of the latter, projective curve bundles (PCB). A PCB is a one-dimensional sub-bundle of the projectivized cotangent bundle of a four-dimensional manifold. Differential invariants of projective curves composing such a bundle are used to construct a series of contact differential invariants for corresponding PMAs. These give a solution of the equivalence problem for generic PMAs with respect to contact transformations. The introduced invariants measure the nonlinearity of PMAs in an exact manner. (paper)

Jet-Based Local Image Descriptors

DEFF Research Database (Denmark)

Larsen, Anders Boesen Lindbo; Darkner, Sune; Dahl, Anders Lindbjerg

2012-01-01

We present a general novel image descriptor based on higherorder differential geometry and investigate the effect of common descriptor choices. Our investigation is twofold in that we develop a jet-based descriptor and perform a comparative evaluation with current state-of-the-art descriptors on ...

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

An introduction to differential manifolds

CERN Document Server

Lafontaine, Jacques

2015-01-01

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...

Differential formalism aspects of the gauge classical theories

International Nuclear Information System (INIS)

Stedile, E.

1982-01-01

The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.) [pt

Hyper-fast interstellar travel via a modification of spacetime geometry

Energy Technology Data Exchange (ETDEWEB)

Kheyfets, A. [Department of Mathematics, North Carolina State University, Raleigh, NC (United States); Miller, W.A. [Los Alamos National Lab., NM (United States)

1997-08-01

We analyze difficulties with proposals for hyper-fast interstellar travel via modifying the spacetime geometry, using as illustrations the Alcubierre warp drive and the Krasnikov tube. As it is easy to see, no violations of local causality or any other known physical principles are involved as far as motion of spacecrafts is concerned. However, the generation and support of the appropriate spacetime geometry configurations does create problems, the most significant of which are a violation of the weak energy condition, a violation of local causality, and a violation of the global causality protection. The violation of the chronology protection is the most serious of them as it opens a possibility of time travel. We trace the origin of the difficulties to the classical nature of the gravity field. This strongly indicates that hyper-fast interstellar travel should be transferred to the realm of a fully quantized gravitational theory. We outline an approach to further the research in this direction.

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

Product Differentiation in Local Television News.

Science.gov (United States)

Atwater, Tony

A study was conducted to investigate the extent to which local television stations exhibited diversity in newscast content within three midwest broadcast markets. A second objective was to describe the nature of the news content characteristic of local news stories that were broadcast by only one station within a market (or unique news stories). A…

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…

Local density approach to surfaces and adsorbed layers

International Nuclear Information System (INIS)

Wimmer, E.; Freeman, A.J.; Weinert, M.

1986-01-01

The authors show that the local density problem for the thin film geometry can be solved with high accuracy by employing the all-electron full-potential linearized augmented-plane-wave method. This is achieved by removing all shape approximations in the charge density and the potential and by using a highly flexible variational basis set. Also demonstrated is the fact that for a graphite monolayer, local density total energies give excellent descriptions of equilibrium geometries and discuss the overestimation of local-density cohesive energies due to an incomplete treatment of correlation effects in the free atom

Quantitative fluorescence spectroscopy in turbid media using fluorescence differential path length spectroscopy

NARCIS (Netherlands)

Amelink, Arjen; Kruijt, Bastiaan; Robinson, Dominic J.; Sterenborg, Henricus J. C. M.

2008-01-01

We have developed a new technique, fluorescence differential path length spectroscopy (FDPS), that enables the quantitative investigation of fluorophores in turbid media. FDPS measurements are made with the same probe geometry as differential path length spectroscopy (DPS) measurements. Phantom

Information geometry

CERN Document Server

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

2017-01-01

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

Algebraic methods in random matrices and enumerative geometry

CERN Document Server

Eynard, Bertrand

2008-01-01

We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms, and a sequence of complex numbers Fg . We recall the definition of the invariants Fg, and we explain their main properties, in particular symplectic invariance, integrability, modularity,... Then, we give several example of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, non-intersecting brownian motions,...

Geometries inherent to N=1 supergravities

International Nuclear Information System (INIS)

Galperin, A.S.; Ogievetsky, V.I.; Sokatchev, E.S.

1981-01-01

The first part of the talk is devoted to a consideration of linearized N=1 supergravities. The second main part deals with complex geometries inherent to different N=1 supergravities. A special attention is paid to a new version with local symmetry. It is connected to the special nonminimal case (n=0) having a remarkable property of supervolume preservation in Csup(4.4) superspace. Therefore the superdeterminant of change of variables from left to right-handed Rsup(4.4) parametrization is a dimensionless scalar. This geometric invariant has to be constrained to obtain an action. Solving such a constraint on vector and spinor prepotentials in Wess-Zumino gauge one obtains the new supergravity with 12+12 fields and local symmetry. A possible relaxation of this constraint is briefly considered (16+16 fields version) [ru

Differential topology

CERN Document Server

Margalef-Roig, J

1992-01-01

...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

Analysis of the effect of pore geometry in the physical properties of rocks

Directory of Open Access Journals (Sweden)

Luiz Alberto Oliveira Lima Roque

2012-12-01

Full Text Available Pore geometry is one of the main factors influencing the flow of reservoir fluids under pressure. Pores with narrower formats are more easily compressed when subject to pressure. Pressure modifies pore geometry by opening or closing cracks, causing increase or decrease in the elastic modulus, porosity, permeability, and other parameters. Rock physical properties depend on the size and shape of pores. Thus, in order to analyze changes on the physical properties behavior according to the pores geometry, it is necessary to study and improve mathematical models of the porous media by taking into account the pore shape factor for estimating rock elastic properties. Differential effective medium model (DEM, Hertz-Mindlin theory and coherent potential approximation (CPA are some of the theoretical paradigms that take into account pore geometry in changes in elastic moduli. Given the importance of the pore structure effect on the behavior of physical parameters, this article proposes an analysis of some mathematical models that consider the influence of pore shapes in the physical properties of rocks.

Scattering forms and the positive geometry of kinematics, color and the worldsheet

Science.gov (United States)

Arkani-Hamed, Nima; Bai, Yuntao; He, Song; Yan, Gongwang

2018-05-01

The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint ϕ 3 scalar theory, we establish a direct connection between its "scattering form" and a classic polytope — the associahedron — known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the "canonical form" associated with this "positive geometry". Fundamental physical properties such as locality and unitarity, as well as novel "soft" limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—"Color is Kinematics"— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi

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

Analog geometry in an expanding fluid from AdS/CFT perspective

Science.gov (United States)

Bilić, Neven; Domazet, Silvije; Tolić, Dijana

2015-04-01

The dynamics of an expanding hadron fluid at temperatures below the chiral transition is studied in the framework of AdS/CFT correspondence. We establish a correspondence between the asymptotic AdS geometry in the 4 + 1 dimensional bulk with the analog spacetime geometry on its 3 + 1 dimensional boundary with the background fluid undergoing a spherical Bjorken type expansion. The analog metric tensor on the boundary depends locally on the soft pion dispersion relation and the four-velocity of the fluid. The AdS/CFT correspondence provides a relation between the pion velocity and the critical temperature of the chiral phase transition.

Gauge symmetry, T-duality and doubled geometry

International Nuclear Information System (INIS)

Hull, C.M.

2007-11-01

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)

The BTZ black hole as a Lorentz-flat geometry

Energy Technology Data Exchange (ETDEWEB)

Alvarez, Pedro D., E-mail: alvarez@physics.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, University of Oxford (United Kingdom); Pais, Pablo, E-mail: pais@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile); Rodríguez, Eduardo, E-mail: eduarodriguezsal@unal.edu.co [Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción (Chile); Salgado-Rebolledo, Patricio, E-mail: pasalgado@udec.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Zanelli, Jorge, E-mail: z@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile)

2014-11-10

It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.

Seesaw mechanism in warped geometry

International Nuclear Information System (INIS)

Huber, Stephan J.; Shafi, Qaisar

2004-01-01

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 M Pl 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

Differential memory in the Earth's magnetotail

International Nuclear Information System (INIS)

Burkhart, G.R.; Chen, J.

1991-01-01

The process of differential memory is quantitatively studied in the modified Harris magnetotail geometry. This process arises as a consequence of nonlinear particle dynamics in the magnetotail which gives rise to partitioning of phase space into disjoint regions. Different regions are occupied by distinct classes of orbits and have widely separated time scales. This paper gives the first study of the time scales and potentially observable signatures in plasma distribution functions associated with the process of differential memory. It is foudn that the effective trapping time of stochastic orbits plays a critical role in differential memory and that in the magnetotail geometry, this time has resonances at certain values of the parameter H. A scaling law H 1/4 has been found for this previously unknown resonance effect. This scaling is directly related to the phase space structures of this stochastic system and leads to signatures in the distribution functions, and their velocity moments (density, velocity components, and kinetic temperatures) are computed following a prescribed change in the boundary conditions. The relationships between the initial changes and the time-asymptotic distribution functions are discussed. The results depend only on the large-scale phase space structures and not on individual chaotic orbits

4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

International Nuclear Information System (INIS)

Han, Muxin

2016-01-01

A class of 3d N=2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction http://dx.doi.org/10.1007/s00220-013-1863-2 in 3d-3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in http://dx.doi.org/10.1007/JHEP12(2014)177 from the 3d N=2 gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

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

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00211497; The ATLAS collaboration; Boudreau, Joseph; Vukotic, Ilija

2017-01-01

The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the-fly on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS software framework "Athena", which provides the online services and the tools to retrieve the data from the database. This operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geometry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. The new mechanism is composed by a new file format and the modules to make use of it. The new file format allows to store the whole detector description locally in a flat file, and it is e...

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.)

Interplay between geometry and temperature in the Casimir effect

International Nuclear Information System (INIS)

Weber, Alexej

2010-01-01

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.)

submitter On Roebel Cable Geometry for Accelerator Magnet

CERN Document Server

Fleiter, J; Ballarino, A

2016-01-01

Roebel-type cables made of a ReBCO conductor are potential candidates for high-field accelerator magnets. The necessity to promote a large effective transverse section in a Roebel cable to avoid local overstress leading to degradation in electrical performance has been recently addressed. In this paper, a new geometry of meander tapes for a Roebel cable that enhances both the transverse effective section and the current margin at crossing segments is discussed. As Roebel cables are bent at the coil ends, the modulation of the bending radius of strands along the cable pitch leads to a shift of the strands with respect to each other. The shift magnitude is analytically investigated in this paper as a function of both cable features and coil geometry. Finally, the minimum transposition pitch of Roebel cables is determined on the basis of coil characteristics.

Laminar simulation of intersubchannel mixing in a triangular nuclear fuel bundle geometry

International Nuclear Information System (INIS)

Zaretsky, A.; Lightstone, M.F.; Tullis, S.

2015-01-01

Highlights: • Quasi-periodic flow was observed through rod-to-wall gaps. • Triangular subchannel flows were fundamentally irregular. • Cross-gap flow was influenced both by local and adjacent cross-gap intensity. • Phase-linking between gaps induced cross-plane peripheral circulation through rod–wall gaps. • Cross-gap flow structure was dependent on subchannel geometry. - Abstract: Predicting temperature distributions in fuel rod bundles is an important component of nuclear reactor safety analysis. Intersubchannel mixing acts to homogenize coolant temperatures thus reducing the likelihood of localized regions of high fuel temperature. Previous research has shown that intersubchannel mixing in nuclear fuel rod bundles is enhanced by a large-scale quasi-periodic energetic fluid motion, which transports fluid on the cross-plane between the narrow gaps connecting subchannels. This phenomenon has also been observed in laminar flows. Unsteady laminar flow simulations were performed in a simplified bundle of three rods with a pipe. Three similar geometries of varying gap width were examined, and a thermal trace was implemented on the first geometry. Thermal mixing was driven by the advection of energy between subchannels by the cross-plane flow. Flow through the rod-to-wall gaps in the wall subchannels alternated with a dominant frequency, particularly when rod-to-wall gaps were smaller than rod-to-rod gaps. Significant phase-linking between rod-to-wall gaps was also observed such that a peripheral circulation occurred through each gap simultaneously. Cross-plane flow through the rod-to-rod gaps in the triangular subchannel was irregular in each case. This was due to the fundamental irregularity of the triangular subchannel geometry. Vortices were continually broken up by cross-plane flow from other gaps due to the odd number of fluid pathways within the central subchannel. Cross-plane flow in subchannel geometries is highly interconnected between gaps. The

Assessment of Constraint Effects based on Local Approach

International Nuclear Information System (INIS)

Lee, Tae Rin; Chang, Yoon Suk; Choi, Jae Boong; Seok, Chang Sung; Kim, Young Jin

2005-01-01

Traditional fracture mechanics has been used to ensure a structural integrity, in which the geometry independence is assumed in crack tip deformation and fracture toughness. However, the assumption is applicable only within limited conditions. To address fracture covering a broad range of loading and crack geometries, two-parameter global approach and local approach have been proposed. The two-parameter global approach can quantify the load and crack geometry effects by adopting T-stress or Q-parameter but time-consuming and expensive since lots of experiments and finite element (FE) analyses are necessary. On the other hand, the local approach evaluates the load and crack geometry effects based on damage model. Once material specific fitting constants are determined from a few experiments and FE analyses, the fracture resistance characteristics can be obtained by numerical simulation. The purpose of this paper is to investigate constraint effects for compact tension (CT) specimens with different in-plane or out-of-plane size using local approach. Both modified GTN model and Rousselier model are adopted to examine the ductile fracture behavior of SA515 Gr.60 carbon steel at high temperature. The fracture resistance (J-R) curves are estimated through numerical analysis, compared with corresponding experimental results and, then, crack length, thickness and side-groove effects are evaluated

Local adaptation and pronounced genetic differentiation in an extremophile fish, Poecilia mexicana, inhabiting a Mexican cave with toxic hydrogen sulphide.

Science.gov (United States)

Plath, M; Hauswaldt, J S; Moll, K; Tobler, M; García De León, F J; Schlupp, I; Tiedemann, R

2007-03-01

We investigated genetic differentiation and migration patterns in a small livebearing fish, Poecilia mexicana, inhabiting a sulfidic Mexican limestone cave (Cueva del Azufre). We examined fish from three different cave chambers, the sulfidic surface creek draining the cave (El Azufre) and a nearby surface creek without the toxic hydrogen sulphide (Arroyo Cristal). Using microsatellite analysis of 10 unlinked loci, we found pronounced genetic differentiation among the three major habitats: Arroyo Cristal, El Azufre and the cave. Genetic differentiation was also found within the cave between different pools. An estimation of first-generation migrants suggests that (i) migration is unidirectional, out of the cave, and (ii) migration among different cave chambers occurs to some extent. We investigated if the pattern of genetic differentiation is also reflected in a morphological trait, eye size. Relatively large eyes were found in surface habitats, small eyes in the anterior cave chambers, and the smallest eyes were detected in the innermost cave chamber (XIII). This pattern shows some congruence with a previously proposed morphocline in eye size. However, our data do not support the proposed mechanism for this morphocline, namely that it would be maintained by migration from both directions into the middle cave chambers. This would have led to an increased variance in eye size in the middle cave chambers, which we did not find. Restricted gene flow between the cave and the surface can be explained by local adaptations to extreme environmental conditions, namely H2S and absence of light. Within the cave system, habitat properties are patchy, and genetic differentiation between cave chambers despite migration could indicate local adaptation at an even smaller scale.

Kinematic Localization for Global Navigation Satellite Systems: A Kalman Filtering Approach

Science.gov (United States)

Tabatabaee, Mohammad Hadi

Use of the Global Positioning System (GNSS) has expanded significantly in the past decade, especially with advances in embedded systems and the emergence of smartphones and the Internet of Things (IoT). The growing demand has stimulated research on development of GNSS techniques and programming tools. The focus of much of the research efforts have been on high-level algorithms and augmentations. This dissertation focuses on the low-level methods at the heart of GNSS systems and proposes a new methods for GNSS positioning problems based on concepts of distance geometry and the use of Kalman filters. The methods presented in this dissertation provide algebraic solutions to problems that have predominantly been solved using iterative methods. The proposed methods are highly efficient, provide accurate estimates, and exhibit a degree of robustness in the presence of unfavorable satellite geometry. The algorithm operates in two stages; an estimation of the receiver clock bias and removal of the bias from the pseudorange observables, followed by the localization of the GNSS receiver. The use of a Kalman filter in between the two stages allows for an improvement of the clock bias estimate with a noticeable impact on the position estimates. The receiver localization step has also been formulated in a linear manner allowing for the direct application of a Kalman filter without any need for linearization. The methodology has also been extended to double differential observables for high accuracy pseudorange and carrier phase position estimates.

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

Locally adapted fish populations maintain small-scale genetic differentiation despite perturbation by a catastrophic flood event.

Science.gov (United States)

Plath, Martin; Hermann, Bernd; Schröder, Christiane; Riesch, Rüdiger; Tobler, Michael; García de León, Francisco J; Schlupp, Ingo; Tiedemann, Ralph

2010-08-23

Local adaptation to divergent environmental conditions can promote population genetic differentiation even in the absence of geographic barriers and hence, lead to speciation. Perturbations by catastrophic events, however, can distort such parapatric ecological speciation processes. Here, we asked whether an exceptionally strong flood led to homogenization of gene pools among locally adapted populations of the Atlantic molly (Poecilia mexicana, Poeciliidae) in the Cueva del Azufre system in southern Mexico, where two strong environmental selection factors (darkness within caves and/or presence of toxic H2S in sulfidic springs) drive the diversification of P. mexicana. Nine nuclear microsatellites as well as heritable female life history traits (both as a proxy for quantitative genetics and for trait divergence) were used as markers to compare genetic differentiation, genetic diversity, and especially population mixing (immigration and emigration) before and after the flood. Habitat type (i.e., non-sulfidic surface, sulfidic surface, or sulfidic cave), but not geographic distance was the major predictor of genetic differentiation. Before and after the flood, each habitat type harbored a genetically distinct population. Only a weak signal of individual dislocation among ecologically divergent habitat types was uncovered (with the exception of slightly increased dislocation from the Cueva del Azufre into the sulfidic creek, El Azufre). By contrast, several lines of evidence are indicative of increased flood-induced dislocation within the same habitat type, e.g., between different cave chambers of the Cueva del Azufre. The virtual absence of individual dislocation among ecologically different habitat types indicates strong natural selection against migrants. Thus, our current study exemplifies that ecological speciation in this and other systems, in which extreme environmental factors drive speciation, may be little affected by temporary perturbations, as adaptations

Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy

OpenAIRE

Neagu, Mircea

2007-01-01

The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.

State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory

Directory of Open Access Journals (Sweden)

Stefano Bellucci

2014-01-01

Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

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

CMS geometry through 2020

International Nuclear Information System (INIS)

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

2014-01-01

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

Quantum Entanglement of Matter and Geometry in Large Systems

Energy Technology Data Exchange (ETDEWEB)

Hogan, Craig J.

2014-12-04

Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard quantum field theory with general relativity on macroscopic scales can be reconciled by nonstandard, nonlocal entanglement of field states with quantum states of geometry. Wave functions of particle world lines are used to estimate scales of geometrical entanglement and emergent locality. Simple models of entanglement predict coherent fluctuations in position of massive bodies, of Planck scale origin, measurable on a laboratory scale, and may account for the fact that the information density of long lived position states in Standard Model fields, which is determined by the strong interactions, is the same as that determined holographically by the cosmological constant.

Gauge symmetry, T-duality and doubled geometry

Energy Technology Data Exchange (ETDEWEB)

Hull, C.M. [Imperial College London (United Kingdom). Inst. for Mathematical Sciences]|[Imperial College London (United Kingdom). Blackett Laboratory; Reid-Edwards, R.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2007-11-15

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)

Topology, Geometry, and Mechanics of Z -Plasty

Science.gov (United States)

Matsumoto, Elisabetta A.; Liang, Haiyi; Mahadevan, L.

2018-02-01

Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z -plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z -plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z -plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.

Introduction to localization in quantum field theory

International Nuclear Information System (INIS)

Pestun, Vasily; Zabzine, Maxim

2017-01-01

This is the introductory chapter to this issue. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present issue. (topical review)

Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

International Nuclear Information System (INIS)

Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.

2011-01-01

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2)

Energy Technology Data Exchange (ETDEWEB)

Schütz, Martin, E-mail: martin.schuetz@chemie.uni-regensburg.de [Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg (Germany)

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

Science.gov (United States)

Schütz, Martin

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2)

International Nuclear Information System (INIS)

Schütz, Martin

2015-01-01

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a

Knots, braids and Möbius strips particle physics and the geometry of elementarity : an alternative view

CERN Document Server

Avrin, Jack

2015-01-01

Elementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself. As such they are characterized by their geometry, that is their topology and configuration which lead directly to their physical attributes and behavior as well as to a simplification and reduction of assumptions and the importation of parameter values. The emphasis of the book is thus on that geometry, the algebraic geometry associated with taxonomical issues and the differential geometry that determines the physics as well as on simplifying the results. In itself, however, the process of assembling and developing what eventually went into the book has been a singularly rewarding journey. Along the way some fascinating insights and connections to known physical attributes and theories emerge, some predictable but others unbidden and even unanticipated. The book is intended to summarize that journey in a way that, readers with a range of backgrounds will find interesting and provocative. Connections to other physical...

Vertebral hemangioma: an important differential in the evaluation of locally aggressive spinal lesions.

Science.gov (United States)

Alexander, Justin; Meir, Adam; Vrodos, Nikitas; Yau, Yun-Hom

2010-08-15

A case report and a discussion of recent published data. To highlight the importance of vertebral hemangioma (VH) as a differential diagnosis in the evaluation of locally aggressive spinal lesions. VH commonly occur as incidental findings, however, locally aggressive VH have been described. Difficulties in diagnosing these lesions are well reported and relate to changes in fat content causing uncharacteristic appearances on imaging. The management options for these lesions include a combination of observation, embolization, sclerotherapy, surgical decompression, or stabilization and radiotherapy. A 45-year-old patient who was previously well presented with back pain and rapidly progressive paraparesis. Imaging confirmed the presence of an extensive lesion centered within the right T3 vertebral pedicle with intrusion into the spinal canal. Urgent surgical decompression was undertaken and was complicated by extensive intraoperative hemorrhage requiring massive transfusion. Histologically, the lesion was shown to be a cavernous VH with no evidence of malignancy. Following radiation oncology review, he was offered adjuvant radiotherapy to minimize the risks of recurrence. He achieved a near full neurologic recovery within 2 weeks and had a full recovery by 12 months. VH should be considered in the evaluation of locally aggressive spinal lesions. Angiography is a useful adjunct in the evaluation of these lesions, both as a diagnostic and therapeutic tool. After diagnosed correctly a wide range of treatment options exist that may prevent the patient from undergoing major surgical resection and reconstruction procedures, which may be associated with high rates of morbidity.

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

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

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

Seesaw mechanism in warped geometry

International Nuclear Information System (INIS)

Huber, S.J.; Shafi, Q.

2003-09-01

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 M P1 .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.)

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

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

Adaptive differentiation coincides with local bioclimatic conditions along an elevational cline in populations of a lichen-forming fungus.

Science.gov (United States)

Dal Grande, Francesco; Sharma, Rahul; Meiser, Anjuli; Rolshausen, Gregor; Büdel, Burkhard; Mishra, Bagdevi; Thines, Marco; Otte, Jürgen; Pfenninger, Markus; Schmitt, Imke

2017-03-31

Many fungal species occur across a variety of habitats. Particularly lichens, fungi forming symbioses with photosynthetic partners, have evolved remarkable tolerances for environmental extremes. Despite their ecological importance and ubiquity, little is known about the genetic basis of adaption in lichen populations. Here we studied patterns of genome-wide differentiation in the lichen-forming fungus Lasallia pustulata along an altitudinal gradient in the Mediterranean region. We resequenced six populations as pools and identified highly differentiated genomic regions. We then detected gene-environment correlations while controlling for shared population history and pooled sequencing bias, and performed ecophysiological experiments to assess fitness differences of individuals from different environments. We detected two strongly differentiated genetic clusters linked to Mediterranean and temperate-oceanic climate, and an admixture zone, which coincided with the transition between the two bioclimates. High altitude individuals showed ecophysiological adaptations to wetter and more shaded conditions. Highly differentiated genome regions contained a number of genes associated with stress response, local environmental adaptation, and sexual reproduction. Taken together our results provide evidence for a complex interplay between demographic history and spatially varying selection acting on a number of key biological processes, suggesting a scenario of ecological speciation.

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

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

Water modelling studies of blockage with discrete permeabilities in an 11 pin geometry

International Nuclear Information System (INIS)

Robinson, D.P.

1977-06-01

A linear array of 11 pins, representing a radial section through a 325 pin bundle, has been used to investigate the effect of discrete permeabilities on the wake geometry behind a local blockage in water. Three series of experiments were performed in each of which a different position of the permeability was considered. The complex wake geometries, visualised by the injection of air, are shown to be controlled by the position of, and flowrate through the permeability. Good agreement is shown between the experimental flow patterns and predictions by SABRE 1. (author)

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

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

Combined Effects of Surface Morphology and Mechanical Straining Magnitudes on the Differentiation of Mesenchymal Stem Cells without Using Biochemical Reagents

Directory of Open Access Journals (Sweden)

Ji-Yeon Jang

2011-01-01

Full Text Available Existing studies examining the control of mesenchymal stem cell (MSC differentiation into desired cell types have used a variety of biochemical reagents such as growth factors despite possible side effects. Recently, the roles of biomimetic microphysical environments have drawn much attention in this field. We studied MSC differentiation and changes in gene expression in relation to osteoblast-like cell and smooth muscle-like cell type resulting from various microphysical environments, including differing magnitudes of tensile strain and substrate geometries for 8 days. In addition, we also investigated the residual effects of those selected microphysical environment factors on the differentiation by ceasing those factors for 3 days. The results of this study showed the effects of the strain magnitudes and surface geometries. However, the genes which are related to the same cell type showed different responses depending on the changes in strain magnitude and surface geometry. Also, different responses were observed three days after the straining was stopped. These data confirm that controlling microenvironments so that they mimic those in vivo contributes to the differentiation of MSCs into specific cell types. And duration of straining engagement was also found to play important roles along with surface geometry.

Mechanisms involved in the differential recovery of CD4 and CD8 T-lymphocytes after local irradiation in mice

International Nuclear Information System (INIS)

De Ruysscher, D; Waer, M.; Vandeputte, M.; Van der Schueren, E.

1990-01-01

The mechanisms involved in the differential recovery of CD4 (helper/inducer phenotype) and CD8 (Cytotoxic/suppressor phenotype) T-lymphocytes after fractionated local irradiation were investigated. In mice, a better recovery of CD4 cells than of CD8 cells was found, while the reverse has been described in humans. Differences in radiosensivitity between CD4 and CD8 mouse splenocytes could not be found. No sequestration of CD8 cells in irradiated tissues could be demonstrated. Irradiation of the thymus did not influence the observed immune changes. Altered thymic production of CD4 and CD8 cells could be excluded by intrathymic injection of FITC (fluorescein isothiocyanate). Hindlimb and tail irradiation did suggest that the differential recovery of CD4 and CD8 T-lymphocytes after local irradiation is determined by extrathymic factors in man and mice, and that the observed differences in immune recovery between man and mice are due to defective thymic function in the former and normal function in the latter. (author). 12 refs.; 5 figs.; 2 tabs

The geometry of higher-order Lagrange spaces applications to mechanics and physics

CERN Document Server

Miron, Radu

1997-01-01

This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1 A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with Applications to higher-order analytical mechanics and theoretical physics are included as well Audience This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology

Examples of the Application of Nonparametric Information Geometry to Statistical Physics

Directory of Open Access Journals (Sweden)

Giovanni Pistone

2013-09-01

Full Text Available We review a nonparametric version of Amari’s information geometry in which the set of positive probability densities on a given sample space is endowed with an atlas of charts to form a differentiable manifold modeled on Orlicz Banach spaces. This nonparametric setting is used to discuss the setting of typical problems in machine learning and statistical physics, such as black-box optimization, Kullback-Leibler divergence, Boltzmann-Gibbs entropy and the Boltzmann equation.

Localized magnetic polaritons in thin flims

International Nuclear Information System (INIS)

Lima, N.P.

1985-01-01

In this thesis we study the localized retarted modes (polaritons) in a ferromagnetic slab. For this we used the linear response theory to obtain the dispersion relations of the bulk, surface and guided modes, for a geometry more general than the Voigt's one. We got both the Green functions in the Voight geometry and the power spectra of these modes. Finally, we show that these Green functions fulfill the correct general symmetry requirements. (author) [pt

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double P{sub n} approximation; Janvier: programme de resolution sur IBM 7094 des problemes de cellules en geometrie plane, spherique et cylindrique dans l'approximation double P{sub n}

Energy Technology Data Exchange (ETDEWEB)

Amouyal, A; Tariel, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1966-07-01

Code name: January 1{sup st} SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2{sup nd} version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P{sub n} approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media < 100, number of geometrical regions < 100, number of points < 1000. 6) Physical approximations: limiting conditions for reflection, black body or grey body (restrictions for spherical and cylindrical geometries). The diffusion can include an isotropy term in cylindrical geometry, 2 terms in the other geometries. Taking into account of macroscopic data. 7) Duration: calculation time for a network of 100 points: planar and spherical geometry: double P 1 1 second, D P 3 = 4 seconds; cylindrical geometry: double P 1 2 seconds, D P 2 = 4 seconds. To these times should be added the 3 seconds required for the output. 8) State of the programme under production. (authors) [French] 1) Nom du Code: Janvier 1 SCEA 011S. 2) Calculateur: IBM 7094; Systeme de programmation: Fortran II version-2. 3) Nature du probleme: resolution des problemes de cellule a une variable d'espace (geometries plane, spherique et cylindrique) et un groupe d'energie, avec sources isotropes, dans l'approxirnation double P{sub n} (Approximations DP 1 et DP 3 en geometrie plane et spherique, approximations DP 1 et DP 2 en geometrie cylindrique). Methode employee: les equations differentielles avec conditions aux limites sont transformees en systemes differentiels avec conditions initiales que l'on integre par une methode a pas separes. 5) Restrictions: nombre de

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

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

Partial differential equations

CERN Document Server

Agranovich, M S

2002-01-01

Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

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.

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…

Solution of the neutron transport equation by the collision probability for 3D geometries; Resolution de l`equation du transport pour les neutrons par la methode des probabilites de collision dans le geometries 3D

Energy Technology Data Exchange (ETDEWEB)

Oujidi, B.

1996-09-19

The TDT code solves the multigroup transport equation by the interface current method for unstructured 2D geometries. This works presents the extension of TDT to the treatment of 3D geometries obtained by axial displacement of unstructured 2D geometries. Three-dimensional trajectories are obtained by lifting the 2D trajectories. The code allows for the definition of macro-domains in the axial direction to be used in the interface-current method. Specular and isotropic reflection or translations boundary conditions can be applied to the horizontal boundaries of the domain. Numerical studies have shown the need for longer trajectory cutoffs for trajectories intersecting horizontal boundaries. Numerical applications to the calculation of local power peaks are given in a second part for: the local destruction of a Pyrex absorbent and inter-assembly (UO{sub 2}-MOX) power distortion due to pellet collapsing at the top of the core. Calculations with 16 groups were performed by coupling TDT to the spectral code APOLLO2. One-group comparisons with the Monte Carlo code TRIMARAN2 are also given. (author). 30 refs.

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

KAUST Repository

Pani, Amiya K.

2010-06-06

In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

KAUST Repository

Pani, Amiya K.; Yadav, Sangita

2010-01-01

In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

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

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).

Effect of differentiated instructional strategies on students' retention ...

African Journals Online (AJOL)

The effect of differentiated instructional strategies on students' retention in geometry in senior secondary schools was examined. The study employed experimental research design of pretest, posttest control group. The area of this study is Abuja Municipal Area Council, the Federal Capital Territory. The target population ...

Phase change heat transfer and bubble behavior observed on twisted wire heater geometries in microgravity

International Nuclear Information System (INIS)

Munro, Troy R.; Koeln, Justin P.; Fassmann, Andrew W.; Barnett, Robert J.; Ban, Heng

2014-01-01

Highlights: • Subcooled water boiled in microgravity on twists of thin wires. • Wire twisting creates heat transfer enhancements because of high local temperatures. • A preliminary version of a new bubble dynamics method is discussed. • A critical distance that fluid must be superheated for boiling onset is presented. - Abstract: Phase change is an effective method of transferring heat, yet its application in microgravity thermal management systems requires greater understanding of bubble behavior. To further this knowledge base, a microgravity boiling experiment was performed (floating) onboard an aircraft flying in a parabolic trajectory to study the effect of surface geometry and heat flux on phase change heat transfer in a pool of subcooled water. A special emphasis was the investigation of heat transfer enhancement caused by modifying the surface geometry through the use of a twist of three wires and a twist of four wires. A new method for bubble behavior analysis was developed to quantify bubble growth characteristics, which allows a quantitative comparison of bubble dynamics between different data sets. It was found that the surface geometry of the three-wire twist enhanced heat transfer by reducing the heat flux needed for bubble incipience and the average wire temperature in microgravity. Simulation results indicated that increased local superheating in wire crevices may be responsible for the change of bubble behavior seen as the wire geometry configuration was varied. The convective heat transfer rate, in comparison to ground experiments, was lower for microgravity at low heating rates, and higher at high heating rates. This study provides insights into the role of surface geometry on superheating behavior and presents an initial version of a new bubble behavior analysis method. Further research on these topics could lead to new designs of heater surface geometries using phase change heat transfer in microgravity applications

Transpressional folding and associated cross-fold jointing controlling the geometry of post-orogenic vein-type W-Sn mineralization: examples from Minas da Panasqueira, Portugal

Science.gov (United States)

Jacques, Dominique; Vieira, Romeu; Muchez, Philippe; Sintubin, Manuel

2018-02-01

The world-class W-Sn Panasqueira deposit consists of an extensive, subhorizontal vein swarm, peripheral to a late-orogenic greisen cupola. The vein swarm consists of hundreds of co-planar quartz veins that are overlapping and connected laterally over large distances. Various segmentation structures, a local zigzag geometry, and the occurrence of straight propagation paths indicate that they exploited a regional joint system. A detailed orientation analysis of the systematic joints reveals a geometrical relationship with the subvertical F2 fold generation, reflecting late-Variscan transpression. The joints are consistently orthogonal to the steeply plunging S0-S2 intersection lineation, both on the regional and the outcrop scale, and are thus defined as cross-fold or ac-joints. The joint system developed during the waning stages of the Variscan orogeny, when already uplifted to an upper-crustal level. Veining reactivated these cross-fold joints under the conditions of hydraulic overpressures and low differential stress. The consistent subperpendicular orientation of the veins relative to the non-cylindrical F2 hinge lines, also when having an inclined attitude, demonstrates that veining did not occur during far-field horizontal compression. Vein orientation is determined by local stress states variable on a meter-scale but with the minimum principal stress consistently subparallel to fold hinge lines. The conspicuous subhorizontal attitude of the Panasqueira vein swarm is thus dictated by the geometry of late-orogenic folds, which developed synchronous with oroclinal buckling of the Ibero-Armorican arc.

Women in numbers Europe II contributions to number theory and arithmetic geometry

CERN Document Server

Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel

2018-01-01

Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...

Yardang geometries in the Qaidam Basin and their controlling factors

Science.gov (United States)

Hu, Chengqing; Chen, Ninghua; Kapp, Paul; Chen, Jianyu; Xiao, Ancheng; Zhao, Yanhui

2017-12-01

The hyperarid Qaidam Basin features extensive fields of yardangs (covering an area of 40,000km2) sculpted in tectonically folded sedimentary rocks. We extracted the geometries of 16,749 yardangs, such as length-to-width ratio (L/W), spatial density, and spacing, from multi-source remote sensing data provided by Google Earth™. We classified the yardangs into four types based on their L/W: short-axis (1-2), whale-back (2-6), hogsback (6-10) and long-ridge (10 - 210). We interpreted the yardang geometries in the context of their geologic setting (bedding orientation, location along anticline crests or syncline troughs, and lithologic heterogeneity). Our results show that the yardang geometries in the Qaidam Basin are mainly controlled by the structural geology and rheology of the sedimentary rocks (e.g., strike and dip of bedding, the presence or absence of interbedded soft and hard beds, and structural position with folds), the angle between geomorphically-effective wind directions and the strike of bedding, and the relative cumulative wind shear force where two geomorphically-effective wind directions are present. Our analysis revealed the following: 1) nearly 69% of the yardangs with long-ridge and hogsback geometries are distributed in syncline areas whereas 73% of the yardangs with short-axis geometries are distributed in anticline areas; 2) the L/W ratio of yardangs exposed along the windward limbs of anticlines is lower than that of yardangs exposed along the leeward limbs; and 3) in the westernmost parts of the basin, yardangs are locally sculpted into mounds by two geomorphically-effective wind directions.

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

OpenAIRE

Fujita, Taro; Jones, Keith

2002-01-01

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

Solution of the neutron transport equation by the collision probability method for 3D geometries; Resolution de l`equation du transport par les neutrons par la methode des probabilites de collision dans les geometries 3D

Energy Technology Data Exchange (ETDEWEB)

Oujidi, B

1996-09-19

The TDT code solves the multigroup transport equation by the interface-current method for unstructured 2D geometries. This works presents the extension of TDT to the treatment of 3D geometries obtained by axial displacement of unstructured 2D geometries. Three-dimensional trajectories are obtained by lifting the 2D trajectories. The code allows for the definition of macro-domains in the axial direction to be used in interface-current method. Specular and isotropic reflection or translations boundary conditions can be applied to the horizontal boundaries of the domain. Numerical studies have shown the need for longer trajectory cutoffs for trajectories intersecting horizontal boundaries. Numerical applications to the calculation of local power peaks are given in a second part for: the local destruction of a Pyrex absorbent, inter-assembly (U02-MOX) power distortion due to pellet collapsing at the top of the core. Calculations with 16 groups were performed by coupling TDT to the spectral code APOLLO2. One-group comparisons with the Monte Carlo code TRIMARAN2 are also given. (author) 30 refs.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.

Science.gov (United States)

Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

2015-09-16

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.

Sources of hyperbolic geometry

CERN Document Server

Stillwell, John

1996-01-01

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

Triply differential cross sections for ionization of helium by electrons

International Nuclear Information System (INIS)

Brauner, M.; Briggs, J.S.; Broad, J.T.

1991-01-01

A correlated three-body continuum wavefunction, already successfully employed to describe hydrogen atom impact ionization, is used to calculate the triply-differential cross section for electron impact ionization of helium. A good description is obtained of all the major structure in the differential cross sections in both symmetric and asymmetric geometries. It is demonstrated how interference between the various projectile-target interactions is necessary to reproduce the experimentally observed structure. (author)

Beam geometry, alignment, and wavefront aberration effects on interferometric differential wavefront sensing

International Nuclear Information System (INIS)

Yu, Xiangzhi; Gillmer, S R; Ellis, J D

2015-01-01

Heterodyne interferometry is a widely accepted methodology with high resolution in many metrology applications. As a functionality enhancement, differential wavefront sensing (DWS) enables simultaneous measurement of displacement, pitch, and yaw using a displacement interferometry system and a single beam incident on a plane mirror target. The angular change is measured using a weighted phase average between symmetrically adjacent quadrant photodiode pairs. In this paper, we present an analytical model to predict the scaling of differential phase signals based on fundamental Gaussian beams. Several numerical models are presented to discuss the effects of physical beam parameters, detector size, system alignment errors, and beam wavefront aberrations on the DWS technique. The results of our modeling predict rotational scaling factors and a usable linear range. Furthermore, experimental results show the analytically predicted scaling factor is in good agreement with empirical calibration. Our three degree-of-freedom interferometer can achieve a resolution of 0.4 nm in displacement and 0.2 μrad in pitch and yaw simultaneously. (paper)

Local symplectic operators and structures related to them

International Nuclear Information System (INIS)

Dorfman, I.Y.; Mokhov, O.I.

1991-01-01

Matrices with entries being differential operators, that endow the phase space of an evolution system with a (pre)symplectic structure are considered. Special types of such structures are explicitly described. Links with integrability, geometry of loop spaces, and Baecklund transformations are traces

Geometry effects on magnetization dynamics in circular cross-section wires

Energy Technology Data Exchange (ETDEWEB)

Sturma, M. [Univ. Grenoble Alpes, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France); Univ. Grenoble Alpes, I. Neel, F-38000 Grenoble (France); CNRS, I. Neel, F-38000 Grenoble (France); Toussaint, J.-C., E-mail: jean-christophe.toussaint@neel.cnrs.fr, E-mail: daria.gusakova@cea.fr [Univ. Grenoble Alpes, I. Neel, F-38000 Grenoble (France); CNRS, I. Neel, F-38000 Grenoble (France); Gusakova, D., E-mail: jean-christophe.toussaint@neel.cnrs.fr, E-mail: daria.gusakova@cea.fr [Univ. Grenoble Alpes, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France)

2015-06-28

Three-dimensional magnetic memory design based on circular-cross section nanowires with modulated diameter is the emerging field of spintronics. The consequences of the mutual interaction between electron spins and local magnetic moments in such non-trivial geometries are still open to debate. This paper describes the theoretical study of domain wall dynamics within such wires subjected to spin polarized current. We used our home-made finite element software to characterize the variety of domain wall dynamical regimes observed for different constriction to wire diameter ratios d/D. Also, we studied how sizeable geometry irregularities modify the internal micromagnetic configuration and the electron spin spatial distribution in the system, the geometrical reasons underlying the additional contribution to the system's nonadiabaticity, and the specific domain wall width oscillations inherent to fully three-dimensional systems.

The geometry description markup language

International Nuclear Information System (INIS)

Chytracek, R.

2001-01-01

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

Global aspects of complex geometry

CERN Document Server

Catanese, Fabrizio; Huckleberry, Alan T

2006-01-01

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

Risk stratification of patients with locally aggressive differentiated thyroid cancer. Results of the MSDS trial

International Nuclear Information System (INIS)

Riemann, B.; Kraemer, J.A.; Schober, O.; Schmid, K.W.; Dralle, H.; Dietlein, M.; Schicha, H.; Sauerland, C.; Frankewitsch, T.

2010-01-01

The Multicentre Study Differentiated Thyroid Cancer (MSDS) collective represents a well defined group of patients with locally aggressive thyroid carcinomas (pT4; AJCC/UICC 1997). The aim of the present study was to compare the survival of patients with minimum and extensive extrathyroidal growth according to the new AJCC/UICC TNM staging system 2009. Patients, methods: The follow-up data of 347 patients were analysed. Patients were reclassified according to the current AJCC/UICC 2009 classification. The event-free and overall survival was evaluated using Kaplan-Meier analysis. In addition, postoperative complications and status of disease were documented. Results: 327 patients were assigned to stage pT3 and 20 patients to stage pT4a, respectively. Median follow-up was 6.1 years (range 0.04-9.8 years). 92.5% of patients reached complete remission. There were 7.8% recurrences in the thyroid bed, in locoregional lymph nodes and/or in distant sites. The overall survival was >98% both in pT3 and pT4a patients (p = n. s.). In contrast, the event-free survival was significantly less favourable in pT4a patients (p < 0.001). Using multivariate analysis the following parameters were significant predictors of event-free survival: histological tumour type, degree of extrathyroidal extension and nodal metastasis (p < 0.05). Conclusions: The MSDS patients with locally aggressive differentiated thyroid cancer showed an excellent overall survival during a median follow-up of 6.1 years. According to the current AJCC/UICC 2009 classification, pT3 patients with minimal extrathyroidal extension revealed a significantly better event-free survival than pT4a patients with extensive extrathyroidal growth. (orig.)

Geometry of Quantum States

International Nuclear Information System (INIS)

Hook, D W

2008-01-01

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

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Science.gov (United States)

Clark, S. E.; Oishi, Jeffrey S.

2017-05-01

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Energy Technology Data Exchange (ETDEWEB)

Clark, S. E. [Department of Astronomy, Columbia University, New York, NY 10027 (United States); Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu [Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

Sarcomere lattice geometry influences cooperative myosin binding in muscle.

Directory of Open Access Journals (Sweden)

Bertrand C W Tanner

2007-07-01

Full Text Available In muscle, force emerges from myosin binding with actin (forming a cross-bridge. This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca(2+ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca(2+ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model, while the other comprises only one thick and one thin filament (two-filament model. Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments.

Analytic geometry

CERN Document Server

Burdette, A C

1971-01-01

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

Vector geometry

CERN Document Server

Robinson, Gilbert de B

2011-01-01

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

Hyperunified field theory and gravitational gauge-geometry duality

International Nuclear Information System (INIS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Energy Technology Data Exchange (ETDEWEB)

Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

2018-01-15

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Science.gov (United States)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

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

OpenAIRE

Li, Dong

2012-01-01

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

Geometry as an aspect of dynamics

International Nuclear Information System (INIS)

Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

1982-07-01

Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a free particle endowed with the fundamental property of momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the free particle (its kynetic energy), in the latter case, it has to resort, perhaps not unexpectedly, to the two dynamical entities mass and energy, separately. (Author) [pt

Geometry as an aspect of dynamics

International Nuclear Information System (INIS)

Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

1983-12-01

Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a particle endowed with the fundamental property of covariant momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the particle (its energy), in the latter case, one have to resort, perhaps not unexpectedly, to the two dynamical entities mass energy, separately. (Author) [pt

Distributed and localized horizontal tectonic deformation as inferred from drainage network geometry and topology: A case study from Lebanon

Science.gov (United States)

Goren, Liran; Castelltort, Sébastien; Klinger, Yann

2016-04-01

Partitioning of horizontal deformation between localized and distributed modes in regions of oblique tectonic convergence is, in many cases, hard to quantify. As a case study, we consider the Dead Sea Fault System that changes its orientation across Lebanon and forms a restraining bend. The oblique deformation along the Lebanese restraining bend is characterized by a complex suite of tectonic structures, among which, the Yammouneh fault, is believed to be the main strand that relays deformation from the southern section to the northern section of the Dead Sea Fault System. However, uncertainties regarding slip rates along the Yammouneh fault and strain partitioning in Lebanon still prevail. In the current work we use the geometry and topology of river basins together with numerical modeling to evaluate modes and rates of the horizontal deformation in Mount Lebanon that is associated with the Arabia-Sinai relative plate motion. We focus on river basins that drain Mount Lebanon to the Mediterranean and originate close to the Yammouneh fault. We quantify a systematic counterclockwise rotation of these basins and evaluate drainage area disequilibrium using an application of the χ mapping technique, which aims at estimating the degree of geometrical and topological disequilibrium in river networks. The analysis indicates a systematic spatial pattern whereby tributaries of the rotated basins appear to experience drainage area loss or gain with respect to channel length. A kinematic model that is informed by river basin geometry reveals that since the late Miocene, about a quarter of the relative plate motion parallel to the plate boundary has been distributed along a wide band of deformation to the west of the Yammouneh fault. Taken together with previous, shorter-term estimates, the model indicates little variation of slip rate along the Yammouneh fault since the late Miocene. Kinematic model results are compatible with late Miocene paleomagnetic rotations in western

Superfocusing modes of surface plasmon polaritons in conical geometry based on the quasi-separation of variables approach

International Nuclear Information System (INIS)

Kurihara, Kazuyoshi; Otomo, Akira; Syouji, Atsushi; Takahara, Junichi; Suzuki, Koji; Yokoyama, Shiyoshi

2007-01-01

Analytic solutions to the superfocusing modes of surface plasmon polaritons in a conical geometry are theoretically studied using an ingenious method called the quasi-separation of variables. This method can be used to look for fundamental solutions to the wave equation for a field that must satisfy boundary conditions at all points on the continuous surface of tapered geometries. The set of differential equations exclusively separated from the wave equation can be consistently solved in combination with perturbation methods. This paper presents the zeroth-order perturbation solution of conical superfocusing modes with azimuthal symmetry and graphically represents them in electric field-line patterns

Akurasi Kriteria Voltase Elektrokardiografi Hipertrofi Ventrikel Kiri untuk Membedakan Jenis Geometri Hipertrofi Ventrikel Kiri

Directory of Open Access Journals (Sweden)

Octo Tumbur

2017-08-01

The different types of left ventricular hypertrophy geometry is associated with different risk of cardiovascular disease. Echocardiography is the gold standard for diagnosis of left ventricular hypertrophy. Electrocardiographic (ECGleft ventricular hypertrophy voltage criteria can distinguish the type of geometry of left ventricular hypertrophy. The purpose of this study to find out the role of various voltage ECG criteria to distinguish the type of geometry of left ventricle hypertrophy. A cross-sectional study doing from June to November 2015 on 100 patients in cardiology clinic and inpatient at Adam Malik Hospital, Medan, through anamnesis, body mass index  measurement, ECG and echocardiography examinations. If the Sokolow-Lyon ECG criteria for left ventricular hypertrophy did not met, normal left ventricular geometry was diagnosed with 60% sensitivity, 72.22% specificity and 71% accuracy. The eccentric left ventricular hypertrophy geometry was diagnosed if Cornel voltage was not fulfilled, with 25% sensitivity, 71.88% specificity and 55% accuracy. The concentric hypertrophy geometry was diagnosed if the RV6/V5 ratio >1, with 55.56% sensitivity, 56.36% specificity and 56% accuracy. If the RV6/V5 ratio >1 are not met, concentric hypertrophic remodeling geometry was diagnosed with a sensitivity of 55.56%, a specificity of 49.45% and an accuracy of 50%. This study also found the sensitivity and specificity for left ventricular hypertrophy in echocardiography of Sokolow-Lyon criteria were 72.22% and 60.00%, the Cornel voltage criteria with a sensitivity of 77.78% and a specificity of 70.00%, and RV6/V5 ratio criteria with a sensitivity of 51.11% and a specificity of 70.00%. The overall sensitivity and specificity was low. In conclusion, various criteria of  ECG left ventricular geometry voltage can differentiate left ventricular hypertrophy geometry types. Sokolow-Lyon and Cornell voltage criteria are more sensitive and specific than the RV6/V5 ratio.

KAMPUNG SENI ISLAM DI MAKASSAR DENGAN PENDEKATAN ARSITEKTUR ISLAM GEOMETRI

Directory of Open Access Journals (Sweden)

Yaumil Maghfirah Asaf

2015-06-01

work produced. So it can be recognized by both local and international. The approach used in the building of Islamic Art Village is Islamic architecture geometry. Geometry is a branch of mathematics that studies of point, line, plane and space objects along with their properties, the measurements, and the relationship between each other. Islamic architectural design more use patterns in the form of lines, circles and other geometric patterns arranged to form a unity which implies spiritual and aesthetic value or beauty of a high level. Islamic art looks association complex geometry, between forms, ornaments, and façade Key Word: Village Islamic Art, Islamic architecture geometry

Conference on Algebraic Geometry for Coding Theory and Cryptography

CERN Document Server

Lauter, Kristin; Walker, Judy

2017-01-01

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this vo...

Local supertwistors

International Nuclear Information System (INIS)

Merkulov, S.A.

1987-01-01

Geometry of local supertwistors is investigated. It is proved that the Yang-Mills equations for the introduced ansatz for supertwistor connection are equivalent to free bach equations, describing the dynamics of N=1 conformal supergravity. Analogous interpretation of the dynamics of N=1 conformal supergravity coupled to a vector superfield is proposed. It is proved that any complex conformally right or left flat superspace automatically satisfies the Bach equations

Study Paths, Riemann Surfaces, and Strebel Differentials

Science.gov (United States)

Buser, Peter; Semmler, Klaus-Dieter

2017-01-01

These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…

Dispersion relation for localized magnetic polaritons propagating at ...

Indian Academy of Sciences (India)

Abstract. Localized magnetic polaritons are investigated in the systems consisting of two magnetic superlattices, coupled by a ferromagnetic contact layer. The general dis- persion relation for localized magnetic polaritons are derived in the framework of the electromagnetic wave theory in the Voigt geometry by the 'transfer' ...

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

Science.gov (United States)

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

Science.gov (United States)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

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

Spinorial Geometry and Branes

International Nuclear Information System (INIS)

Sloane, Peter

2007-01-01

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

Solution of the kinetic equation in the P3-approximation in a plane geometry

International Nuclear Information System (INIS)

Vlasov, Yu.A.

1975-01-01

A method and a program are described for solving single-velocity kinetic equations of neutron transfer for the plane geometry in the finite-difference approximation. A difference high-accuracy scheme and a matrix factorization method are used for the differential-difference equation systems. The program is written in the ALGOL-60 language and is adapted for M-20, M-220, M-222 and BESM-4 computers

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

An introduction to incidence geometry

CERN Document Server

De Bruyn, Bart

2016-01-01

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

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

Science.gov (United States)

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

2017-10-01

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

Performance of a liquid argon electromagnetic calorimeter with a cylindrical accordion geometry

International Nuclear Information System (INIS)

Aubert, B.; Bazan, A.; Beaugiraud, B.; Colas, J.; Leflour, T.; Maire, M.; Vialle, J.P.; Wingerter-Seez, I.; Zolnierowski, Y.P.; Gordon, H.A.; Radeka, V.; Rahm, D.; Stephani, D.; Bulgakov, N.; Chevalley, J.L.; Fabjan, C.W.; Fournier, D.; Gildemeister, O.; Jenni, P.; Nessi, M.; Nessi-Tedaldi, F.; Pepe, M.; Richter, W.; Soderqvist, J.; Vuillemin, V.; Baze, J.M.; Gosset, L.; Lavocat, P.; Lottin, J.P.; Mansoulie, B.; Meyer, J.P.; Renardy, J.R.; Teiger, J.; Zaccone, H.; Battistoni, G.; Camin, D.V.; Cavalli, D.; Costa, G.; Cravero, A.; Ferrari, A.; Gianotti, F.; Mandelli, L.; Mazzanti, M.; Perini, L.; Sciamanna, M.; Auge, E.; Chase, R.; Chollet, J.C.; La Taille, C. de; Fayard, L.; Hrisoho, A.; Jean, P.; Iconomidou-Fayard, L.; Le Meur, G.; Merkel, B.; Noppe, J.M.; Parrour, G.; Petroff, P.; Repellin, J.P.; Schaffer, A.; Seguin, N.; Unal, G.; Fuglesang, C.; Lefebvre, M.

1993-01-01

A prototype of a lead liquid argon accordion calorimeter with two types of cylindrical geometry was constructed and equipped with high speed readout electronics. The energy resolution for electrons is 10%/√E (GeV) with a local constant term of 0.65%. The resolutions obtained for position and angular measurements are given. (orig.)

Supertwistor connection and conformal supergravity

International Nuclear Information System (INIS)

Merkulov, S.A.

1985-01-01

Supersymmetry expansion of the geometry of local twistors is suggested. Definition of the space of local supertwistors is given and its differential geometry is formulated. Variational principles are discussed, and it is shown that corresponding Euler-Lagrange equations also coincide and result in superzero equations of N=1 conformal supergravitation, which generalize Bach equations

Experimental investigations of structure and dynamics of drift-wave turbulence in stellarator geometry

International Nuclear Information System (INIS)

Birkenmeier, Gregor

2012-01-01

For more than 60 years, fusion scientists try to confine a plasma by means of external magnetic fields in order to achieve appropriately high densities and temperatures for the ignition of nuclear fusion. Despite of great progress in the design of confinement concepts, which are considered for the confinement of burning plasmas in the near future, theoretical plasma physics promises further confinement improvements using novel magnetic field geometries. Therefor, the key is the minimization of turbulent transport by choosing appropiate magnetic field geometries, which necessitates a fundamental understanding of the influence of magnetic field geometry on plasma turbulence. There are several theoretical works on turbulent plasma dynamics in three-dimensional geometries, but only a few experimental studies for validation of the theoretical results exist. Hence, the present work aims at providing experimental data for comparison with theory and to gain insights into the interplay between drift-wave turbulence and magnetic field geometry. By means of two multi-probe arrays, local density and potential fluctuations are measured in low-temperature plasmas at 128 positions on a single flux surface of the stellarator TJ-K with high temporal resolution. Using methods of statistical timeseries analysis structure sizes and dynamic properties of the drift-wave turbulence in TJ-K are determined. Thereby, it is shown that the size of turbulent structures perpendicular to the magnetic field is reduced in regions of high absolute local magnetic shear. In addition, a poloidal displacement with respect to the magnetic field lines and a complex propagation pattern of parallelly extended turbulent structures is found. Also, poloidal profiles of turbulent transport are calculated from the probe data. The maximum transport is found to be poloidally localized in a region of negative normal curvature (unfavourable curvature). In addition, the results point to an influence of geodesic

Spinorial Geometry and Branes

Energy Technology Data Exchange (ETDEWEB)

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

2007-09-15

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

Introduction to non-Euclidean geometry

CERN Document Server

Wolfe, Harold E

2012-01-01

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