Discrete torsion in non-geometric orbifolds and their open-string descendants
International Nuclear Information System (INIS)
Bianchi, Massimo; Morales, Jose F.; Pradisi, Gianfranco
2000-01-01
We discuss some Z N L xZ N R orbifold compactifications of the type IIB superstring to D=4,6 dimensions and their type I descendants. Although the Z N L xZ N R generators act asymmetrically on the chiral string modes, they result into left-right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Moebius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z 2 L xZ 2 R orbifold gives rise to models with supersymmetry breaking in the open-string sector
International Nuclear Information System (INIS)
Bantay, P.
2002-01-01
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for fusion rule coefficients are presented, together with the relevant mathematical concepts, such as Λ-matrices and twisted dimensions. The arithmetic restrictions implied by the theory for the allowed modular representations in CFT are discussed. The simplest nonabelian example with twist group S 3 is described to illustrate the general theory
Permutation orbifolds and chaos
Belin, A.
2017-01-01
We study out-of-time-ordered correlation functions in permutation orbifolds at large central charge. We show that they do not decay at late times for arbitrary choices of low-dimension operators, indicating that permutation orbifolds are non-chaotic theories. This is in agreement with the fact they
Energy Technology Data Exchange (ETDEWEB)
Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard
2001-03-16
We discuss the form of the chiral anomaly on an S1/Z2 orbifold with chiral boundary conditions. We find that the 4-divergence of the higher-dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the chiral zero mode there. Nevertheless the anomaly, appropriately defined as the five dimensional divergence of the current, lives entirely on the orbifold fixed planes and is independent of the shape of the zero mode. Therefore long distance four dimensional anomaly cancellation ensures the consistency of the higher dimensional orbifold theory.
R-symmetries from the orbifolded heterotic string
International Nuclear Information System (INIS)
Schmitz, Matthias
2014-08-01
We examine the geometric origin of discrete R-symmetries in heterotic orbifold compactifications. By analysing the symmetries of the worldsheet instanton solutions and the underlying geometry, we obtain a scheme that allows us to systematically explore the R-symmetries arising in these compactifications. Applying this scheme to a classification of orbifold geometries, we are able to find all R-symmetries of heterotic orbifolds with Abelian point groups. We show that in the vast majority of cases, the R-symmetries found satisfy anomaly universality constraints, as required in heterotic orbifolds. Then we examine the implications of the presence of these R-symmetries on a class of phenomenologically attractive orbifold compactifications known as the heterotic mini-landscape. We use the technique of Hilbert bases in order to analyse the properties of a vacuum configuration. We find that phenomenologically viable models remain and the main attractive features of the mini-landscape are unaltered.
International Nuclear Information System (INIS)
Cvetic, M.
1987-05-01
A method to repair - ''blow-up'' - the singularities of the Abelian (2,2) orbifolds to obtain the corresponding (2,2) Calabi-Yau manifolds is presented. This approach makes use of the fact that with each orbifold singularity there are associated massless scalar fields - blowing-up modes - whose potential is flat to all orders in the string perturbation theory. The zero vacuum expectation values (VEV's) of the blowing-up modes correspond to the orbifold limit, while nonzero VEV's yield the corresponding Calabi-Yau manifold. One can then calculate explicitly, for such Calabi-Yau manifolds, the mass spectrum, Yukawa couplings, and all the other parameters of the effective Lagrangian by inserting successively all the background blowing-up modes with nonzero vacuum expectation value into the corresponding orbifold amplitudes. The results are exact at the string tree-level; however, they are perturbative in the blowing-up procedure. Mass spectra and Yukawa couplings for the blown-up Z 3 and Z 4 orbifolds are explicitly calculated. In particular all the E 6 singlets except the ones associated with the moduli-space of the blown-up orbifolds receive the mass; while the 27's and anti 27's do not pair up
T-duality orbifolds of heterotic Narain compactifications
Energy Technology Data Exchange (ETDEWEB)
Nibbelink, Stefan Groot [School of Engineering and Applied Sciences, Rotterdam University of Applied Sciences,G.J. de Jonghweg 4-6, 3015 GG Rotterdam (Netherlands); Vaudrevange, Patrick K.S. [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Physik Department T30, Technische Universität München,James-Franck-Straße, 85748 Garching (Germany)
2017-04-06
To obtain a unified framework for symmetric and asymmetric heterotic orbifold constructions we provide a systematic study of Narain compactifications orbifolded by finite order T-duality subgroups. We review the generalized vielbein that parametrizes the Narain moduli space (i.e. the metric, the B-field and the Wilson lines) and introduce a convenient basis of generators of the heterotic T-duality group. Using this we generalize the space group description of orbifolds to Narain orbifolds. This yields a unified, crystallographic description of the orbifold twists, shifts as well as Narain moduli. In particular, we derive a character formula that counts the number of unfixed Narain moduli after orbifolding. Moreover, we develop new machinery that may ultimately open up the possibility for a full classification of Narain orbifolds. This is done by generalizing the geometrical concepts of ℚ-, ℤ- and affine classes from the theory of crystallography to the Narain case. Finally, we give a variety of examples illustrating various aspects of Narain orbifolds, including novel T-folds.
Orbifold construction of the modes of the Poincare dodecahedral space
International Nuclear Information System (INIS)
Lachieze-Rey, Marc; Weeks, Jeffrey
2008-01-01
We provide a new construction of the modes of the Poincare dodecahedral space S 3 /I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S 3 /I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves
Orbifold construction of the modes of the Poincare dodecahedral space
Energy Technology Data Exchange (ETDEWEB)
Lachieze-Rey, Marc [Astroparticule et Cosmologie (APC), CNRS-UMR 7164 (France); Weeks, Jeffrey [15 Farmer Street, Canton, New York (United States)
2008-07-25
We provide a new construction of the modes of the Poincare dodecahedral space S{sup 3}/I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S{sup 3}/I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.
Discrete R-symmetries and anomaly universality in heterotic orbifolds
Energy Technology Data Exchange (ETDEWEB)
Bizet, Nana G. Cabo [Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear,Calle 30, esq.a 5ta Ave, Miramar, 6122 La Habana (Cuba); Kobayashi, Tatsuo [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Peña, Damián K. Mayorga [Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany); Parameswaran, Susha L. [Department of Mathematics and Physics, Leibniz Universität Hannover,Welfengarten 1, 30167 Hannover (Germany); Schmitz, Matthias [Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany); Zavala, Ivonne [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands)
2014-02-24
We study discrete R-symmetries, which appear in the 4D low energy effective field theory derived from heterotic orbifold models. We derive the R-symmetries directly from the geometrical symmetries of the orbifolds. In particular, we obtain the corresponding R-charges by requiring that the couplings be invariant under these symmetries. This allows for a more general treatment than the explicit computations of correlation functions made previously by the authors, including models with discrete Wilson lines, and orbifold symmetries beyond plane-by-plane rotational invariance. The R-charges obtained in this manner differ from those derived in earlier explicit computations. We study the anomalies associated with these R-symmetries, and comment on the results.
Natural inflation and moduli stabilization in heterotic orbifolds
International Nuclear Information System (INIS)
Ruehle, Fabian; Wieck, Clemens
2015-03-01
We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio r∼0.05. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedekind η function. We present two setups inspired by the mini-landscape models of the Z 6-II orbifold which realize aligned inflation and stabilization of the relevant moduli. One has a supersymmetric vacuum after inflation, while the other includes a gaugino condensate which breaks supersymmetry at a high scale.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Diagrams for symmetric product orbifolds
International Nuclear Information System (INIS)
Pakman, Ari; Rastelli, Leonardo; Razamat, Shlomo S.
2009-01-01
We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.
Heterotic non-Abelian orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ramos-Sanchez, Saul [UNAM, Mexico (Mexico). Dept. of Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non-Abelian orbifold geometries which yield N=1 supersymmetry for heterotic compactifications. Surprisingly, most Hodge numbers follow the empiric pattern h{sup (1,1)}-h{sup (2,1)}=0 mod 6, which might be related to the number of three standard model generations. Furthermore, we study the fundamental groups in order to identify the possibilities for non-local gauge symmetry breaking. Three examples are discussed in detail: the simplest non-Abelian orbifold S{sub 3} and two more elaborated examples, T{sub 7} and {Delta}(27), which have only one untwisted Kaehler and no untwisted complex structure modulus. Such models might be especially interesting in the context of no-scale supergravity. Finally, we briefly discuss the case of orbifolds with vanishing Euler numbers in the context of enhanced (spontaneously broken) supersymmetry.
Voisin-Borcea manifolds and heterotic orbifold models
Energy Technology Data Exchange (ETDEWEB)
Buchmuller, W.; Schmidt, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Louis, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Valandro, R. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2012-08-15
We study the relation between a heterotic T{sup 6}/Z{sub 6} orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a Z{sub 2} quotient of T{sup 4}/Z{sub 3} x T{sup 2}. We consider a two-step resolution, whose intermediate step is (K3 x T{sup 2})/Z{sub 2}. This allows us to identify the massless twisted states which correspond to the geometric Kaehler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after Higgsing does not even include the standard model gauge group. Moreover, after Higgsing, the massless spectrum is non-chiral under the surviving gauge group.
Integrability of orbifold ABJM theories
Energy Technology Data Exchange (ETDEWEB)
Bai, Nan; Chen, Hui-Huang [Institute of High Energy Physics and Theoretical Physics Center for Science Facilities,Chinese Academy of Sciences,19B Yuquan Road, Beijing 100049 (China); Ding, Xiao-Chen [School of Mathematical Sciences, Capital Normal University,105 North Road of West 3rd Ring, Beijing 100048 (China); Li, De-Sheng [Institute of High Energy Physics and Theoretical Physics Center for Science Facilities,Chinese Academy of Sciences,19B Yuquan Road, Beijing 100049 (China); Wu, Jun-Bao [Institute of High Energy Physics and Theoretical Physics Center for Science Facilities,Chinese Academy of Sciences,19B Yuquan Road, Beijing 100049 (China); School of Physics, Beihang University,37 Xueyuan Road, Beijing 100191 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); School of Physical Sciences, University of Chinese Academy of Sciences,19A Yuquan Road, Beijing 100049 (China)
2016-11-18
Integrable structure has played a very important role in the study of various non-perturbative aspects of planar Aharony-Bergman-Jafferis-Maldacena (ABJM) theories. In this paper, we showed that this remarkable structure survives after orbifold operation with discrete group Γ
Topological orbifold models and quantum cohomology rings
International Nuclear Information System (INIS)
Zaslow, E.
1993-01-01
We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of CP 1 by the dihedral group D 4 , how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral CP 1 orbifolds. We then consider CP 2 /D 4 , and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds. (orig.)
The superpotential in heterotic orbifold GUTs
Energy Technology Data Exchange (ETDEWEB)
Kappl, Rolf
2011-12-08
We study in this work the phenomenology of heterotic orbifold compactifications. Exact and approximate R symmetries of the superpotential in the context of supersymmetric field theories are discussed. We further study symmetries, phenomenological implications and Yukawa couplings from superpotential contributions in extra dimensional theories. We apply the developed methods to models, which base on heterotic orbifolds.
Quarks and leptons from orbifolded superstring
International Nuclear Information System (INIS)
Choi, K.S.; Kim, J.E.
2006-01-01
This book seeks to be a guidebook on the journey towards the minimal supersymmetric standard model down the orbifold road. It takes the viewpoint that the chirality of matter fermions is an essential aspect that orbifold compactification allows to derive from higher-dimensional string theories in a rather straight-forward manner. Halfway between a textbook and a tutorial review, ''Quarks and Leptons from Orbifolded Superstring'' is intended for the graduate student and particle phenomenologist wishing to get acquainted with this field. (orig.)
The orbifolder: A tool to study the low energy effective theory of heterotic orbifolds
International Nuclear Information System (INIS)
Nilles, H.P.; Wingerter, A.
2011-10-01
The orbifolder is a program developed in C ++ that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum-configurations. (orig.)
The orbifolder. A tool to study the low energy effective theory of heterotic orbifolds
Energy Technology Data Exchange (ETDEWEB)
Nilles, H P [Bonn Univ. (Germany). Bethe Center for Theoretical Physics and Physikalisches Institut; Ramos-Sanchez, S [Universidad Nacional Autonoma de Mexico (UNAM), Mexico City (Mexico). Dept. of Theoretical Physics; Vaudrevange, P K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Technische Univ. Muenchen, Garching (Germany). Physik-Department; Arnold-Sommerfeld-Center for Theoretical Physics, Muenchen (Germany); Wingerter, A [CNRS/IN2P3, INPG, Grenoble (France). Lab. de Physique Subatomique et de Cosmologie
2011-10-15
The orbifolder is a program developed in C{sup ++} that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum-configurations. (orig.)
Exact vacuum energy of orbifold lattice theories
International Nuclear Information System (INIS)
Matsuura, So
2007-01-01
We investigate the orbifold lattice theories constructed from supersymmetric Yang-Mills matrix theories (mother theories) with four and eight supercharges. We show that the vacuum energy of these theories does not receive any quantum correction perturbatively
Ice cream and orbifold Riemann-Roch
International Nuclear Information System (INIS)
Buckley, Anita; Reid, Miles; Zhou Shengtian
2013-01-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
ZNxZM orbifolds and discrete torsion
International Nuclear Information System (INIS)
Font, A.; Quevedo, F.
1989-01-01
We extend previous work on Z N -orbifolds to the general Z N xZ M abelian case for both (2, 2) and (0, 2) models. We classify the corresponding (2, 2) compactifications and show that a number of models obtained by tensoring minimal N = 2 superconformal theories can be constructed as Z N xZ M -orbifolds. Furthermore, Z N xZ M -orbifolds allow the addition of discrete torsion which leads to new (2, 2) compactifications not considered previously. Some of the latter have negative Euler characteristics and Betti numbers equal to those of some complete intersection Calabi-Yau (CICY) manifolds. This suggests the existence of a previously overlooked connection between CICY models and orbifolds. (orig.)
Ice cream and orbifold Riemann-Roch
Buckley, Anita; Reid, Miles; Zhou, Shengtian
2013-06-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
Orbifold matrix models and fuzzy extra dimensions
Chatzistavrakidis, Athanasios; Zoupanos, George
2011-01-01
We revisit an orbifold matrix model obtained as a restriction of the type IIB matrix model on a Z_3-invariant sector. An investigation of its moduli space of vacua is performed and issues related to chiral gauge theory and gravity are discussed. Modifications of the orbifolded model triggered by Chern-Simons or mass deformations are also analyzed. Certain vacua of the modified models exhibit higher-dimensional behaviour with internal geometries related to fuzzy spheres.
The structure of GUT breaking by orbifolding
International Nuclear Information System (INIS)
Hebecker, Arthur; March-Russell, John
2002-01-01
Recently, an attractive model of GUT breaking has been proposed in which a 5-dimensional supersymmetric SU(5) gauge theory on an S 1 /(Z 2 xZ 2 ') orbifold is broken down to the 4d MSSM by SU(5)-violating boundary conditions. Motivated by this construction and several related realistic models, we investigate the general structure of orbifolds in the effective field theory context, and of this orbifold symmetry breaking mechanism in particular. An analysis of the group theoretic structure of orbifold breaking is performed. This depends upon the existence of appropriate inner and outer automorphisms of the Lie algebra, and we show that a reduction of the rank of the GUT group is possible. Some aspects of larger GUT theories based on SO(10) and E 6 are discussed. We explore the possibilities of defining the theory directly on a space with boundaries and breaking the gauge symmetry by more general consistently chosen boundary conditions for the fields. Furthermore, we derive the relation of orbifold breaking with the familiar mechanism of Wilson line breaking, finding a one-to-one correspondence, both conceptually and technically. Finally, we analyse the consistency of orbifold models in the effective field theory context, emphasizing the necessity for self-adjoint extensions of the Hamiltonian and other conserved operators, and especially the highly restrictive anomaly cancellation conditions that apply if the bulk theory lives in more than 5 dimensions
Statistical sum of bosonic string, compactified on an orbifold
International Nuclear Information System (INIS)
Morozov, A.; Ol'shanetskij, M.
1986-01-01
Expression for statistical sum of bosonic string, compactified on a singular orbifold, is presented. All the information about the orbifold is encoded the specific combination of theta-functions, which the statistical sum is expressed through
Orbifolds, quantum cosmology, and nontrivial topology
International Nuclear Information System (INIS)
Fagundes, Helio V.; Vargas, Teofilo
2006-01-01
In order to include nontrivial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology into the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace. (author)
On orientifolds of c=1 orbifolds
Energy Technology Data Exchange (ETDEWEB)
Dijkstra, T.P.T. [NIKHEF, PO Box 41882, 1009 DB Amsterdam (Netherlands); Gato-Rivera, B. [NIKHEF, PO Box 41882, 1009 DB Amsterdam (Netherlands); Riccioni, F. [NIKHEF, PO Box 41882, 1009 DB Amsterdam (Netherlands)]. E-mail: f.riccioni@damtp.cam.ac.uk; Schellekens, A.N. [NIKHEF, PO Box 41882, 1009 DB Amsterdam (Netherlands)
2004-10-25
The aim of this paper is to study orientifolds of c=1 conformal field theories. A systematic analysis of the allowed orientifold projections for c=1 orbifold conformal field theories is given. We compare the Klein bottle amplitudes obtained at rational points with the orientifold projections that we claim to be consistent for any value of the orbifold radius. We show that the recently obtained Klein bottle amplitudes corresponding to exceptional modular invariants, describing bosonic string theories at fractional square radius, are also in agreement with those orientifold projections.
Orbifolded Konishi from the Mirror TBA
de Leeuw, M.; van Tongeren, S.J.
2011-01-01
Starting with a discussion of the general applicability of the simplified mirror thermodynamic Bethe ansatz (TBA) equations to simple deformations of the AdS5 × S5 superstring, we proceed to study a specific type of orbifold to which the undeformed simplified TBA equations directly apply. We then
Supersymmetric RG flows and Janus from type II orbifold compactification
Energy Technology Data Exchange (ETDEWEB)
Karndumri, Parinya; Upathambhakul, Khem [Chulalongkorn University, String Theory and Supergravity Group, Department of Physics, Faculty of Science, Bangkok (Thailand)
2017-07-15
We study holographic RG flow solutions within four-dimensional N = 4 gauged supergravity obtained from type IIA and IIB string theories compactified on T{sup 6}/Z{sub 2} x Z{sub 2} orbifold with gauge, geometric and non-geometric fluxes. In type IIB non-geometric compactifications, the resulting gauged supergravity has ISO(3) x ISO(3) gauge group and admits an N = 4 AdS{sub 4} vacuum dual to an N = 4 superconformal field theory (SCFT) in three dimensions. We study various supersymmetric RG flows from this N = 4 SCFT to N = 4 and N = 1 non-conformal field theories in the IR. The flows preserving N = 4 supersymmetry are driven by relevant operators of dimensions Δ = 1, 2 or alternatively by one of these relevant operators, dual to the dilaton, and irrelevant operators of dimensions Δ = 4 while the N = 1 flows in addition involve marginal deformations. Most of the flows can be obtained analytically. We also give examples of supersymmetric Janus solutions preserving N = 4 and N = 1 supersymmetries. These solutions should describe two-dimensional conformal defects within the dual N = 4 SCFT. Geometric compactifications of type IIA theory give rise to N = 4 gauged supergravity with ISO(3) x U(1){sup 6} gauge group. In this case, the resulting gauged supergravity admits an N = 1 AdS{sub 4} vacuum. We also numerically study possible N = 1 RG flows to non-conformal field theories in this case. (orig.)
The orbifolder: A tool to study the low-energy effective theory of heterotic orbifolds
Nilles, H. P.; Ramos-Sánchez, S.; Vaudrevange, P. K. S.; Wingerter, A.
2012-06-01
The orbifolder is a program developed in C++ that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum configurations. Program summaryProgram title: orbifolder Catalogue identifier: AELR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 145 572 No. of bytes in distributed program, including test data, etc.: 930 517 Distribution format: tar.gz Programming language:C++ Computer: Personal computer Operating system: Tested on Linux (Fedora 15, Ubuntu 11, SuSE 11) Word size: 32 bits or 64 bits Classification: 11.1 External routines: Boost (http://www.boost.org/), GSL (http://www.gnu.org/software/gsl/) Nature of problem: Calculating the low-energy spectrum of heterotic orbifold compactifications. Solution method: Quadratic equations on a lattice; representation theory; polynomial algebra. Running time: Less than a second per model.
D-branes, orbifolds, and Ext groups
International Nuclear Information System (INIS)
Katz, Sheldon; Pantev, Tony; Sharpe, Eric
2003-01-01
In this note we extend previous work on massless Ramond spectra of open strings connecting D-branes wrapped on complex manifolds, to consider D-branes wrapped on smooth complex orbifolds. Using standard methods, we calculate the massless boundary Ramond sector spectra directly in BCFT, and find that the states in the spectrum are counted by Ext groups on quotient stacks (which provide a notion of homological algebra relevant for orbifolds). Subtleties that cropped up in our previous work also appear here. We also use the McKay correspondence to relate Ext groups on quotient stacks to Ext groups on (large radius) resolutions of the quotients. As stacks are not commonly used in the physics community, we include pedagogical discussions of some basic relevant properties of stacks
2d orbifolds with exotic supersymmetry
Florakis, Ioannis; García-Etxebarria, Iñaki; Lüst, Dieter; Regalado, Diego
2018-02-01
We analyse various two dimensional theories arising from compactification of type II and heterotic string theory on asymmetric orbifolds. We find extra supersymmetry generators arising from twisted sectors, giving rise to exotic supersymmetry algebras. Among others we discover new cases with a large number of supercharges, such as N=(20,8), N=(24,8), N=(32,0), N=(24,24) and N=(48,0).
String Loop Threshold Corrections for N=1 Generalized Coxeter Orbifolds
Kokorelis, Christos
2000-01-01
We discuss the calculation of threshold corrections to gauge coupling constants for the, only, non-decomposable class of abelian (2, 2) symmetric N=1 four dimensional heterotic orbifold models, where the internal twist is realized as a generalized Coxeter automorphism. The latter orbifold was singled out in earlier work as the only N=1 heterotic $Z_N$ orbifold that satisfy the phenomenological criteria of correct minimal gauge coupling unification and cancellation of target space modular anom...
Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus
Berglund, P.; Henningson, M.
1994-01-01
We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirr...
Constructing 5d orbifold grand unified theories from heterotic strings
International Nuclear Information System (INIS)
Kobayashi, Tatsuo; Raby, Stuart; Zhang Renjie
2004-01-01
A three-generation Pati-Salam model is constructed by compactifying the heterotic string on a particular T 6 /Z 6 Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice G 2 -bar SU(3)-bar SO(4). When one dimension of the SO(4) lattice is large compared to the string scale, this model reproduces many features of a 5d SO(10) grand unified theory compactified on an S 1 /Z 2 orbifold. (Of course, with two large extra dimensions we can obtain a 6d SO(10) grand unified theory.) We identify the orbifold parities and other ingredients of the orbifold grand unified theories in the string model. Our construction provides a UV completion of orbifold grand unified theories, and gives new insights into both field theoretical and string theoretical constructions
Local gauge coupling running in supersymmetric gauge theories on orbifolds
International Nuclear Information System (INIS)
Hillenbach, M.
2007-01-01
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
Schoen manifold with line bundles as resolved magnetized orbifolds
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Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.
Local gauge coupling running in supersymmetric gauge theories on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Hillenbach, M.
2007-11-21
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
Neutral Naturalness from Orbifold Higgs Models
Craig, Nathaniel; Knapen, Simon; Longhi, Pietro
2015-02-01
We present a general class of natural theories in which the Higgs boson is a pseudo-Goldstone boson in an orbifolded gauge theory. The symmetry protecting the Higgs boson at low energies is an accidental global symmetry of the quadratic action, rather than a full continuous symmetry. The lightest degrees of freedom protecting the weak scale carry no standard model (SM) quantum numbers and interact with visible matter principally through the Higgs portal. This opens the door to the systematic study of "neutral naturalness": natural theories with SM-neutral states that are as yet untested by the LHC.
Hadronic EDM constraints on orbifold GUTs
International Nuclear Information System (INIS)
Hisano, Junji; Kakizaki, Mitsuru; Nagai, Minoru
2005-01-01
We point out that the null results of the hadronic electric dipole moment (EDM) searches constrain orbifold grand unified theories (GUTs), where the GUT symmetry and supersymmetry (SUSY) are both broken by boundary conditions in extra dimensions and it leads to rich fermion and sfermion flavor structures. A marginal chromoelectric dipole moment (CEDM) of the up quark is induced by the misalignment between the CP violating left- and right-handed up-type squark mixings, in contrast to the conventional four-dimensional SUSY GUTs. The up quark CEDM constraint is found to be as strong as those from charged lepton flavor violation (LFV) searches. The interplay between future EDM and LFV experiments will probe the structures of the GUTs and the SUSY breaking mediation mechanism
Kinetic Mixing of U(1)s in Heterotic Orbifolds
Goodsell, Mark; Ringwald, Andreas
2012-01-01
We study kinetic mixing between massless U(1) gauge symmetries in the bosonic formulation of heterotic orbifold compactifications. For non-prime Z_N factorisable orbifolds, we find a simple expression of the mixing in terms of the properties of the N=2 subsectors, which helps understand under what conditions mixing can occur. With this tool, we analyse Z_6-II heterotic orbifolds and find non-vanishing mixing even without including Wilson lines. We show that some semi-realistic models of the Mini-Landscape admit supersymmetric vacua with mixing between the hypercharge and an additional U(1), which can be broken at low energies. We finally discuss some phenomenologically appealing possibilities that hidden photons in heterotic orbifolds allow.
Dynamical supersymmetry breaking on magnetized tori and orbifolds
Directory of Open Access Journals (Sweden)
Hiroyuki Abe
2016-10-01
Full Text Available We construct several dynamical supersymmetry breaking (DSB models within a single ten-dimensional supersymmetric Yang–Mills (SYM theory, compactified on magnetized tori with or without orbifolding. We study the case that the supersymmetry breaking is triggered by a strong dynamics of SU(NC SYM theory with NF flavors contained in the four-dimensional effective theory. We show several configurations of magnetic fluxes and orbifolds, those potentially yield, below the compactification scale, the field contents and couplings required for triggering DSB. We especially find a class of self-complete DSB models on orbifolds, where all the extra fields are eliminated by the orbifold projection and DSB successfully occurs within the given framework. Comments on some perspectives for associating the obtained DSB models with the other sectors, such as the visible sector and another hidden sector for, e.g., stabilizing moduli, are also given.
Kinetic mixing of U(1)s in heterotic orbifolds
Energy Technology Data Exchange (ETDEWEB)
Goodsell, Mark [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Ramos-Sanchez, Saul [UNAM, Mexico (Mexico). Dept. of Theoretical Physics; Ringwald, Andreas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-10-15
We study kinetic mixing between massless U(1) gauge symmetries in the bosonic formulation of heterotic orbifold compactifications. For non-prime Z{sub N} factorisable orbifolds, we find a simple expression of the mixing in terms of the properties of the N=2 subsectors, which helps understand under what conditions mixing can occur. With this tool, we analyse Z{sub 6}-II heterotic orbifolds and find non-vanishing mixing even without including Wilson lines. We show that some semi-realistic models of the Mini-Landscape admit supersymmetric vacua with mixing between the hypercharge and an additional U(1), which can be broken at low energies. We finally discuss some phenomenologically appealing possibilities that hidden photons in heterotic orbifolds allow. (orig.)
Heterotic free fermionic and symmetric toroidal orbifold models
Energy Technology Data Exchange (ETDEWEB)
Athanasopoulos, P.; Faraggi, A.E. [Department of Mathematical Sciences, University of Liverpool,Liverpool L69 7ZL (United Kingdom); Nibbelink, S. Groot [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München,80333 München (Germany); Mehta, V.M. [Institute for Theoretical Physics, University of Heidelberg,69120 Heidelberg (Germany)
2016-04-07
Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for ℤ{sub 2}×ℤ{sub 2} orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all ℤ{sub 2}×ℤ{sub 2} orbifold geometries in six dimensions.
Orbifold line topology and the cosmic microwave background
Energy Technology Data Exchange (ETDEWEB)
Rathaus, Ben; Ben-David, Assaf; Itzhaki, Nissan, E-mail: ben.rathaus@gmail.com, E-mail: bd.assaf@gmail.com, E-mail: nitzhaki@post.tau.ac.il [Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)
2013-10-01
We extend our study of a universe with a non-classical stringy topology, and consider an orbifold line topology, R × R{sup 2}/Z{sub p}. This topology has a fixed line and identifies each point in space with p−1 other points. An observable imprint of an orbifold line on the CMB is the appearance of up to (p−1)/2 pairs of matching circles. Searching the WMAP data for matching circles, we can rule out an orbifold line topology with p up to 10, except for p = 8. While the significance of the peak at p = 8 varies between data releases of WMAP, it does not appear in Planck data, enabling us to rule out p = 8 as well.
Simple currents versus orbifolds with discrete torsion -- a complete classification
Kreuzer, M
1994-01-01
We give a complete classification of all simple current modular invariants, extending previous results for $(\\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with discrete torsion is complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.
Simple currents versus orbifolds with discrete torsion - a complete classification
International Nuclear Information System (INIS)
Kreuzer, M.; Schellekens, A.N.
1993-01-01
We give a complete classification of all simple current modular invariants, extending previous results for (Z p ) k to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with discrete torsion is complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility. (orig.)
One-Loop Effective Action in Orbifold Compactifications
Von Gersdorff, Gero
2008-01-01
We employ the covariant background formalism to derive generic expressions for the one-loop effective action in field theoretic orbifold compactifications. The contribution of each orbifold sector is given by the effective action of its fixed torus with a shifted mass matrix. We thus study in detail the computation of the heat kernel on tori. Our formalism manifestly separates UV sensitive (local) from UV-insensitive (nonlocal) renormalization. To exemplify our methods, we study the effective potential of 6d gauge theory as well as kinetic terms for gravitational moduli in 11d supergravity.
Gauge origin of discrete flavor symmetries in heterotic orbifolds
Directory of Open Access Journals (Sweden)
Florian Beye
2014-09-01
Full Text Available We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus T. Using this mechanism it is shown that the Δ(54 non-Abelian discrete symmetry group originates from a SU(3 gauge symmetry, whereas the D4 symmetry group is obtained from a SU(2 gauge symmetry.
String flipped SO(10) model from Z4 orbifold
International Nuclear Information System (INIS)
Sato, H.; Shimojo, M.
1993-01-01
We search all possible string grand-unified-theory models obtained from heterotic superstrings compactified on a Z 4 orbifold with one Wilson line. It is shown that there is an essentially unique anomaly-free flipped SO(10) model with three generations plus one mirror conjugate generation of matter fields. We derive effective Yukawa interactions and examine the structure of mass matrices as well as a possible scenario of string coupling unification. The four-generation Z 4 orbifold model is a phenomenologically viable model beyond the minimal supersymmetric standard one
D-instantons on orbifolds and gauge/gravity correspondence
International Nuclear Information System (INIS)
Tanzini, Alessandro
2002-01-01
D-instantons are used to probe the near-horizon geometry of D3-branes systems on orbifold spaces. For fractional D3-branes, D-instanton calculus correctly reproduces the gauge β-function and U(1) R anomaly of the corresponding N=2 non-conformal Super Yang-Mills theories. For D3-branes wrapping the orbifold singularity, D-instantons can be identified with gauge instantons on ALE space, providing evidence of AdS/CFT duality for gauge theories on curved spaces. (Abstract Copyright[2002], Wiley Periodicals, Inc.)
Orbifolds of M-theory and type II string theories in two dimensions
International Nuclear Information System (INIS)
Roy, S.
1997-01-01
We consider several orbifold compactifications of M-theory and theircorresponding type II duals in two space-time dimensions. In particular, we show that while the orbifold compactification of M-theory on T 9 /J 9 is dual to the orbifold compactification of type IIB string theory on T 8 /I 8 , the same orbifold T 8 /I 8 of type IIA string theory is dual to M-theory compactified on a smooth product manifold K3 x T 5 . Similarly, while the orbifold compactification of M-theory on (K3 x T 5 )/σ. J 5 is dual to the orbifold compactification of type IIB string theory on (K3 x T 4 )/σ.I 4 , the same orbifold of type IIA string theory is dual to the orbifold T 4 x (K3 x S 1 )/σ.J 1 of M-theory. The spectrum of various orbifold compactifications of M-theory and type II string theories on both sides are compared giving evidence in favor of these duality conjectures. We also comment on a connection between the Dasgupta-Mukhi-Witten conjecture and the Dabholkar-Park-Sen conjecture for the six-dimensional orbifold models of type IIB string theory and M-theory. (orig.)
Three-generation flipped SU(5) string models on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Burwick, T.T. (Zurich Univ. (Switzerland). Inst. fuer Theoretische Physik); Kaiser, R.K.; Mueller, H.F. (ETH-Hoenggerberg, Zurich (Switzerland). Inst. fuer Theoretische Physik)
1991-09-16
We construct four-dimensional twisted string models on non-prime orbifolds which have as gauge group flipped SU(5) with a phenomenologically interesting matter spectrum of k generations plus (k-3) antigenerations. Using generalized selection rules for Yukawa couplings on non-prime orbifolds, we analyse one model in greater detail and obtain the following phenomenologically promising features: We find one pair of H and anti H GUT Higgs fields which break the GUT gauge group into the standard model, and in addition generate large mass terms for the unwanted triplet parts of the standard model Higgs fields, plus one pair of standard model Higgs fields. Moreover, we obtain couplings of the standard model Higgs to quark and lepton fields in all families. (orig.).
Phenomenological viability of orbifold models with three Higgs families
International Nuclear Information System (INIS)
Escudero, Nicolas; Munoz, Carlos; Teixeira, Ana M.
2006-01-01
We discuss the phenomenological viability of string multi-Higgs doublet models, namely a scenario of heterotic Z 3 orbifolds with two Wilson lines, which naturally predicts three supersymmetric families of matter and Higgs fields. We study the orbifold parameter space, and discuss the compatibility of the predicted Yukawa couplings with current experimental data. We address the implications of tree-level flavour changing neutral processes in constraining the Higgs sector of the model, finding that viable scenarios can be obtained for a reasonably light Higgs spectrum. We also take into account the tree-level contributions to indirect CP violation, showing that the experimental value of ε K can be accommodated in the present framework
Reducing the rank of gauge groups in orbifold compactification
International Nuclear Information System (INIS)
Sato, H.
1989-01-01
The Wilson-line mechanism in orbifold compactification is investigated for both Abelian and non-Abelian embedding of the Z 3 group in the E 8 x E 8 . The authors give general argument in the fermionic formulation for the gauge degrees of freedom and show that the rank of the gauge group is reduced by introducing nondiagonal Wilson-line matrix in the fermionic boundary conditions
Supertwistor orbifolds: gauge theory amplitudes and topological strings
International Nuclear Information System (INIS)
Park, Jaemo; Rey, Soojong
2004-01-01
Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space CP 3verticalbar4 . We extend Witten's correspondence to gauge theories with lower supersymmetries, product gauge groups, and fermions and scalars in complex representations. Such gauge theories arise in high-energy limit of the Standard Model of strong and electroweak interactions. We construct such theories by orbifolding prescription. Much like gauge and string theories, such prescription is applicable equally well to topological string theories on supertwistor space. We work out several examples of orbifolds of CP 3verticalbar4 that are dual to N=2,1,0 quiver gauge theories. We study gauged sigma model describing topological B-model on the superorbifolds, and explore mirror pairs with particular attention to the parity symmetry. We check the orbifold construction by studying multiparton amplitudes in these theories with particular attention to those involving fermions in bifundamental representations and interactions involving U(1) subgroups. (author)
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
International Nuclear Information System (INIS)
Groot Nibbelink, Stefan; Hillenbach, Mark
2005-01-01
We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S 1 /Z 2 . This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T 2 /Z N orbifolds using supergraph techniques in six dimensions. On general Z N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z 2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.
Softening the supersymmetric flavor problem in orbifold grand unified theories
International Nuclear Information System (INIS)
Kajiyama, Yuji; Terao, Haruhiko; Kubo, Jisuke
2004-01-01
The infrared attractive force of the bulk gauge interactions is applied to soften the supersymmetric flavor problem in the orbifold SU(5) grand unified theory of Kawamura. Then this force aligns in the infrared regime the soft supersymmetry breaking terms out of their anarchical disorder at a fundamental scale, in such a way that flavor-changing neutral currents as well as dangerous CP-violating phases are suppressed at low energies. It is found that this dynamical alignment is sufficiently good compared with the current experimental bounds, as long as the diagonalization matrices of the Yukawa couplings are CKM-like
Rankin-Selberg methods for closed strings on orbifolds
Angelantonj, Carlo; Pioline, Boris
2013-01-01
In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent. In the present paper, we generalise this procedure to the case of Abelian Z_N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup {\\Gamma}_0(N). As a result, the original modular integral reduces to an integral over the fundamental domain of {\\Gamma}_0(N), which we then evaluate by extending our previous techniques. Our method is applicable, for instance, to the evaluation of one-loop corrections to BPS-saturated couplings in the low energy effective action of closed string mo...
M(atrix) theory on an orbifold and twisted membrane
International Nuclear Information System (INIS)
Kim, N.
1997-01-01
M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis on heterotic M(atrix) theory on S 1 / Z 2 relevant to strongly coupled heterotic and dual type IA string theories. By analyzing the orbifold condition on Chan-Paton factors, we show that three choices of gauge group are possible for heterotic M(atrix) theory: SO(2N), SO(2N+1) or USp(2N). By examining the area-preserving diffeomorphism that underlies the M(atrix) theory, we find that each choice of gauge group restricts the possible topologies of two-branes. The result suggests that only the choice of SO(2N) or SO(2N+1) allows open two-branes, and hence, is relevant to heterotic M(atrix) theory. We show that the requirement of both local vacuum energy cancellation and of world-sheet anomaly cancellation of the resulting heterotic string identifies supersymmetric twisted sector spectra with sixteen fundamental representation spinors from each of the two fixed points. Twisted open and closed two-brane configurations are obtained in the large N limit. (orig.)
The construction of ``realistic'' four-dimensional strings through orbifolds
Font, A.; Ibáñez, L. E.; Quevedo, F.; Sierra, A.
1990-02-01
We discuss the construction of "realistic" lower rank 4-dimensional strings, through symmetric orbifolds with background fields. We present Z 3 three-generation SU(3) × SU(2) × U(1) models as well as models incorporating a left-right SU(2) L × SU(2) R × U(1) B-L symmetry in which proton stability is automatically guaranteed. Conformal field theory selection rules are used to find the flat directions to all orders which lead to these low-rank models and to study the relevant Yukawa couplings. A hierarchical structure of quark-lepton masses appears naturally in some models. We also present a detailed study of the structure of the Z 3 × Z 3 orbifold including the generalized GSO projection, the effect of discrete torsion and the conformal field theory Yukawa coupling selection rules. All these points are illustrated with a three-generation Z 3 × Z 3 model. We have made an effort to write a self-contained presentation in order to make this material available to non-string experts interested in the phenomenological aspects of this theory.
The construction of 'realistic' four-dimensional strings through orbifolds
International Nuclear Information System (INIS)
Font, A.; Quevedo, F.; Sierra, A.
1990-01-01
We discuss the construction of 'realistic' lower rank 4-dimensional strings, through symmetric orbifolds with background fields. We present Z 3 three-generation SU(3)xSU(2)xU(1) models as well as models incorporating a left-right SU(2) L xSU(2) R xU(1) B-L symmetry in which proton stability is automatically guaranteed. Conformal field theory selection rules are used to find the flat directions to all orders which lead to these low-rank models and to study the relevant Yukawa couplings. A hierarchical structure of quark-lepton masses appears naturally in some models. We also present a detailed study of the structure of the Z 3 xZ 3 orbifold including the generalized GSO projection, the effect of discrete torsion and the conformal field theory Yukawa coupling selection rules. All these points are illustrated with a three-generation Z 3 xZ 3 model. We have made an effort to write a self-contained presentation in order to make this material available to non-string experts interested in the phenomenological aspects of this theory. (orig.)
Superpartner mass spectrum and cosmological implications from orbifolds
Energy Technology Data Exchange (ETDEWEB)
Schmidt-Hoberg, K.
2007-06-15
This thesis is devoted to orbifolded quantum field theories in six spacetime dimensions. Within the framework of T{sup 2}/Z{sub 2} and T{sup 2}/(Z{sub 2} x Z{sub 2}{sup PS} x Z{sub 2}{sup GG}) we calculate the Casimir energy, which yields an essential contribution to the modulus potential. Turning to more phenomenological aspects, we study gaugino-mediated supersymmetry breaking in a six-dimensional SO(10) orbifold GUT model where quarks and leptons are mixtures of brane and bulk fields. We derived bounds on the soft supersymmetry breaking parameters and calculate the superparticle mass spectrum. Higgs fields are bulk fields, and in general their masses differ from those of squarks and sleptons at the unification scale. As a consequence, at different points in parameter space, the gravitino, a neutralino or a scalar lepton can be the lightest or next-to-lightest superparticle. We investigate the constraints from primordial nucleosynthesis on the different scenarios. While neutralino dark matter and gravitino dark matter with a {nu} next-to-lightest superparticle are consistent for a wide range of parameters, gravitino dark matter with a {tau} next-to-lightest superparticle is strongly constrained.
Superpartner mass spectrum and cosmological implications from orbifolds
International Nuclear Information System (INIS)
Schmidt-Hoberg, K.
2007-06-01
This thesis is devoted to orbifolded quantum field theories in six spacetime dimensions. Within the framework of T 2 /Z 2 and T 2 /(Z 2 x Z 2 PS x Z 2 GG ) we calculate the Casimir energy, which yields an essential contribution to the modulus potential. Turning to more phenomenological aspects, we study gaugino-mediated supersymmetry breaking in a six-dimensional SO(10) orbifold GUT model where quarks and leptons are mixtures of brane and bulk fields. We derived bounds on the soft supersymmetry breaking parameters and calculate the superparticle mass spectrum. Higgs fields are bulk fields, and in general their masses differ from those of squarks and sleptons at the unification scale. As a consequence, at different points in parameter space, the gravitino, a neutralino or a scalar lepton can be the lightest or next-to-lightest superparticle. We investigate the constraints from primordial nucleosynthesis on the different scenarios. While neutralino dark matter and gravitino dark matter with a ν next-to-lightest superparticle are consistent for a wide range of parameters, gravitino dark matter with a τ next-to-lightest superparticle is strongly constrained
Chern-Simons gauge theory on orbifolds: Open strings from three dimensions
Hořava, Petr
1996-12-01
Chern-Simons gauge theory is formulated on three-dimensional Z2 orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known to be related to two-dimensional (2D) conformal field theory (CFT) on closed-string surfaces; here it is shown that the theory on orbifolds is related to 2D CFT of unoriented closed- and open-string models, i.e. to worldsheet orbifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open-string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group Z2 as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories.
Lepton masses and mixings in orbifold models with three Higgs families
International Nuclear Information System (INIS)
Escudero, N.; Munoz, C.; Teixeira, A.M.
2007-01-01
We analyse the phenomenological viability of heterotic Z 3 orbifolds with two Wilson lines, which naturally predict three supersymmetric families of matter and Higgs fields. Given that these models can accommodate realistic scenarios for the quark sector avoiding potentially dangerous flavour-changing neutral currents, we now address the leptonic sector, finding that viable orbifold configurations can in principle be obtained. In particular, it is possible to accomodate present data on charged lepton masses, while avoiding conflict with lepton flavour-violating decays. Concerning the generation of neutrino masses and mixings, we find that Z 3 orbifolds offer several interesting possibilities
Geometry of (0,2) Landau-Ginzburg orbifolds
International Nuclear Information System (INIS)
Kawai, Toshiya; Mohri, Kenji
1994-01-01
Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma models. Our formalism gives an easy way to calculate the generation numbers for lots of Distler-Kachru models even if they are based on singular Calabi-Yau spaces. We also make some general remarks on the Born-Oppenheimer calculation of the ground states elucidating its mathematical meaning in the untwisted sector. For Distler-Kachru models based on non-singular Calabi-Yau spaces we show that there exist ''residue'' type formulas of the elliptic genera as well. ((orig.))
Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
Córdova, Clay; Heidenreich, Ben; Popolitov, Alexandr; Shakirov, Shamil
2018-02-01
We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarithmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.
Dark matter and localised fermions from spherical orbifolds?
Energy Technology Data Exchange (ETDEWEB)
Cacciapaglia, Giacomo; Deandrea, Aldo [Université de Lyon,Lyon (France); Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France); Deutschmann, Nicolas [Université de Lyon,Lyon (France); Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France); Centre for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)
2016-04-14
We study a class of six-dimensional models based on positive curvature surfaces (spherical 2-orbifolds) as extra-spaces. Using the Newman-Penrose formalism, we discuss the particle spectrum in this class of models. The fermion spectrum problem, which has been addressed with flux compactifications in the past, can be avoided using localised fermions. In this framework, we find that there are four types of geometry compatible with the existence of a stable dark matter candidate and we study the simplest case in detail. Using the complementarity between collider resonance searches and relic density constraints, we show that this class of models is under tension, unless the model lies in a funnel region characterised by a resonant Higgs s-channel in the dark matter annihilation.
Phenomenological aspects of heterotic orbifold models at one loop
International Nuclear Information System (INIS)
Birkedal-Hansen, A.; Binetruy, P.; Mambrini, Y.; Nelson, B.
2003-01-01
We provide a detailed study of the phenomenology of orbifold compactifications of the heterotic string within the context of supergravity effective theories. Our investigation focuses on those models where the soft Lagrangian is dominated by loop contributions to the various soft supersymmetry breaking parameters. Such models typically predict non-universal soft masses and are thus significantly different from minimal supergravity and other universal models. We consider the pattern of masses that are governed by these soft terms and investigate the implications of certain indirect constraints on supersymmetric models, such as flavor-changing neutral currents, the anomalous magnetic moment of the muon and the density of thermal relic neutralinos. These string-motivated models show novel behavior that interpolates between the phenomenology of unified supergravity models and models dominated by the superconformal anomaly
More on non-supersymmetric asymmetric orbifolds with vanishing cosmological constant
International Nuclear Information System (INIS)
Sugawara, Yuji; Wada, Taiki
2016-01-01
We explore various non-supersymmetric type II string vacua constructed based on asymmetric orbifolds of tori with vanishing cosmological constant at the one loop. The string vacua we present are modifications of the models studied in http://dx.doi.org/10.1007/JHEP02(2016)184, of which orbifold group is just generated by a single element. We especially focus on two types of modifications: (i) the orbifold twists include different types of chiral reflections not necessarily removing massless Rarita-Schwinger fields in the 4-dimensional space-time, (ii) the orbifold twists do not include the shift operator. We further discuss the unitarity and stability of constructed non-supersymmetric string vacua, with emphasizing the common features of them.
Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem
International Nuclear Information System (INIS)
Gato, B.; Massachusetts Inst. of Tech., Cambridge
1990-01-01
We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)
Landau-Ginzburg orbifolds and symmetries of K3 CFTs
International Nuclear Information System (INIS)
Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; Paquette, Natalie M.
2017-01-01
Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K 3 string theory. To test and clarify these proposed K 3 -moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K 3 sigma models. We compute K 3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 c 2.M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Finally, our results provide strong evidence for the relevance of umbral moonshine for K 3 symmetries, as well as new hints for its eventual explanation.
Landau-Ginzburg orbifolds and symmetries of K3 CFTs
Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; Paquette, Natalie M.
2017-01-01
Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K3 string theory. To test and clarify these proposed K3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K3 sigma models. We compute K3ellipticgeneratwinedbydiscretesymmetriesthataremanifestintheUVdescription, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 ⊂ 2 .M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Our results provide strong evidence for the relevance of umbral moonshine for K3 symmetries, as well as new hints for its eventual explanation.
Resolutions of Cn/Zn orbifolds, their U(1) bundles, and applications to string model building
International Nuclear Information System (INIS)
Nibbelink, Stefan Groot; Trapletti, Michele; Walter, Martin G.A.
2007-01-01
We describe blowups of C n /Z n orbifolds as complex line bundles over CP n-1 . We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic C 2 /Z 2 and C 3 /Z 3 orbifold models. (Only the Z 3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T 6 /Z 3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down
Reducing the rank of gauge groups in orbifold compactification
International Nuclear Information System (INIS)
Sato, Hikaru
1989-01-01
The report introduces general twisted boundary conditions on fermionic string variables and shows that a non-Abelian embedding is possible when background gauge field is introduced on orbifold. This leads to reduction of the rank of the gauge group. The report presents a procedure to obtain the lower-rank gauge groups by the use of non-Abelian Wilson lines. The unbroken gauge group is essentially determined by the eigen vector which should obey the level-matching conditions. The gauge symmetry is determined by certain conditions. In a particular application, it is not necessary to introduce explicit form of the non-Abelian Wilson lines. The procedure starts with introduction of desired eigen vectors which are supposed to be obtained by diagonalization of the boundary conditions with the appropriate transformation matrix. The rank is reduced by one by using the Wilson lines which transform as 3 of SU(2) R or SU(2) in SU(4). A possible way of reducing the rank by two is to use the Wilson lines from SU(2) R x SU(2) or SU(3) in SU(4). The rank is reduced by three by means of the Wilson lines which transform as SU(4) or SU(2) R SU(3). Finally the rank is reduced by four when the Wilson lines with full symmetry of SU(2) R x SU(4) are used. The report tabulates the possible lower-rank gauge groups obtained by the proposed method. Massless fermions corresponding to the eigen vectors are also listed. (N.K.)
R-charge Conservation and More in Factorizable and Non-Factorizable Orbifolds
Bizet, Nana Geraldine Cabo; Pena, Damian Kaloni Mayorga; Parameswaran, Susha L; Schmitz, Matthias; Zavala, Ivonne
2013-01-01
We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the Gamma-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the 'torus lattice selection rule'. Moreover, we identify a new string selection rule, that we call Rule 6 or the 'coset vector selection rule'.
String flipped SO(10) model from [ital Z][sub 4] orbifold
Energy Technology Data Exchange (ETDEWEB)
Sato, H. (Department of Physics, Hyogo University of Education, Yashiro-cho, Hyogo 673-14 (Japan)); Shimojo, M. (Department of Electronics and Information Engineering, Fukui National College of Technology, Sabae, Fukui 916 (Japan))
1993-12-15
We search all possible string grand-unified-theory models obtained from heterotic superstrings compactified on a [ital Z][sub 4] orbifold with one Wilson line. It is shown that there is an essentially unique anomaly-free flipped SO(10) model with three generations plus one mirror conjugate generation of matter fields. We derive effective Yukawa interactions and examine the structure of mass matrices as well as a possible scenario of string coupling unification. The four-generation [ital Z][sub 4] orbifold model is a phenomenologically viable model beyond the minimal supersymmetric standard one.
A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
Lebedev, O; Raby, S; Ramos-Sánchez, S; Ratz, M; Vaudrevange, P K S; Wingerter, A; Lebedev, Oleg; Nilles, Hans Peter; Raby, Stuart; Ramos-Sanchez, Saul; Ratz, Michael; Vaudrevange, Patrick K.S.; Wingerter, Akin
2007-01-01
We explore a "fertile patch" of the heterotic landscape based on a Z_6-II orbifold with SO(10) and E_6 local GUT structures. We search for models allowing for the exact MSSM spectrum. Our result is that of order 100 out of a total 3\\times 10^4 inequivalent models satisfy this requirement.
Bosonisation of four dimensional real fermionic string models and asymmetric orbifolds
International Nuclear Information System (INIS)
Bailin, D.; Dunbar, D.C.; Love, A.
1990-01-01
Models of four dimensional strings based on internal world-sheet fermions are bosonised and the partition functions are compared with the partition functions of asymmetric Z 2 M orbifold models. Selection rules and couplings are also compared between the two formations. (orig.)
International Nuclear Information System (INIS)
Kovtun, Pave; Uensal, Mithat; Yaffe, Laurence G.
2005-01-01
Large N coherent state methods are used to study the relation between U(N c ) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N c limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N c dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N c dynamics of the daughter theory, restricted to the untwisted sector invariant under 'theory space' permutations, coincide. This implies equality, in the large N c limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N c equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N c equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling
International Nuclear Information System (INIS)
Walter, M.G.A.
2004-02-01
We consider several examples of a special class of heterotic compactifications, i.e. heterotic E 8 x E 8 orbifolds with Wilson line backgrounds. By developing a local perspective we show that a brane world like picture emerges. As an important result we prove that the local massless spectrum at such a brane can always be traced back to the global spectrum of a (different) orbifold without Wilson lines. One particular implication of this result is that the use of (discrete) Wilson lines for the construction of phenomenologically interesting models has to be rethought. We show that stringy constraints render the brane spectra consistent. Using our local picture we are able to compute the local anomalies appearing at the different branes for our examples and show that they can all be cancelled by a local version of the Green-Schwarz mechanism at the same time. (orig.)
An example of higher weight superpotential interaction in the heterotic string on orbifolds
International Nuclear Information System (INIS)
Erdenebayar, D.
1994-11-01
An explicit orbifold example of the non-zero correlation functions related to the additional contribution to the induced mass term for Higgs particles at low energies is given. We verify that they form finite dimensional representations of the target space modular transformation SL 2 (Z). This action of the modular group is shown to be consistent with its action on the fixed points set defining the twisted fields. (author). 11 refs
N=2 heterotic string compactifications on orbifolds of K3×T{sup 2}
Energy Technology Data Exchange (ETDEWEB)
Chattopadhyaya, Aradhita; David, Justin R. [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India)
2017-01-10
We study N=2 compactifications of E{sub 8}×E{sub 8} heterotic string theory on orbifolds of K3×T{sup 2} by g{sup ′} which acts as an ℤ{sub N} automorphism of K3 together with a 1/N shift on a circle of T{sup 2}. The orbifold action g{sup ′} corresponds to the 26 conjugacy classes of the Mathieu group M{sub 24}. We show that for the standard embedding the new supersymmetric index for these compactifications can always be decomposed into the elliptic genus of K3 twisted by g{sup ′}. The difference in one-loop corrections to the gauge couplings are captured by automorphic forms obtained by the theta lifts of the elliptic genus of K3 twisted by g{sup ′}. We work out in detail the case for which g{sup ′} belongs to the equivalence class 2B. We then investigate all the non-standard embeddings for K3 realized as a T{sup 4}/ℤ{sub ν} orbifold with ν=2,4 and g{sup ′} the 2A involution. We show that for non-standard embeddings the new supersymmetric index as well as the difference in one-loop corrections to the gauge couplings are completely characterized by the instanton numbers of the embeddings together with the difference in number of hypermultiplets and vector multiplets in the spectrum.
Closed string tachyons on AdS orbifolds and dual Yang-Mills instantons
Energy Technology Data Exchange (ETDEWEB)
Hikida, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Iizuka, N. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2007-06-15
We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS{sub 5}/Z{sub k} to AdS{sub 3}/Z{sub k} case, and we proposed that the AdS{sub 3}/Z{sub k} decays into AdS{sub 3}/Z{sub k'} with k{sup '} < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in different parameter regimes of 't Hooft coupling. We also consider AdS{sub 5} orbifold. The decay of AdS{sub 5}/Z{sub k} is dual to the transition between the vacua of dual gauge theory on R{sub t} x S{sup 3}/Z{sub k}. We constructed the instanton solutions describing the transitions by making use of instanton solutions on R{sub t} x S{sup 2}. (orig.)
Orbifold constructions and the classification of self-dual c=24 conformal field theories
International Nuclear Information System (INIS)
Montague, P.S.
1994-01-01
We discuss questions arising from the work of Schellekens [A.N. Schellekens, Phys. Lett. B 277 (1992) 277; Meromorphic c=24 conformal field theories, CERN-TH.6478/92, 1992.] After introducing the concept of complementary representations, we examine Z 2 -orbifold constructions in general, and propose a technique for identifying the orbifold theory without knowledge of its explicit construction. This technique is then generalised to twists of order 3, 5 and 7, and we proceed to apply our considerations to the FKS constructions H (Λ) (Λ an even self-dual lattice) and the reflection-twisted orbifold theories and H ;(Λ), which together remain the only c=24 theories which have so far been proven to exist [L. Dolan, P. Goddard and P. Montague, Nucl. Phys. B 338 (1990) 529.] We also make, in the course of our arguments, some comments on the automorphism groups of the theories H (Λ) and and H ;(Λ), and of meromorphic theories in general, introducing the concept of deterministic theories. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Ebata, T [Tohoku Univ., Sendai (Japan). Coll. of General Education
1976-06-01
The geometrical distribution inferred from the inelastic cross section is assumed to be proportional to the partial waves. The precocious scaling and the Q/sup 2/-dependence of various quantities are treated from the geometrical point of view. It is shown that the approximate conservation of the orbital angular momentum may be a very practical rule to understand the helicity structure of various hadronic and electromagnetic reactions. The rule can be applied to inclusive reactions as well. The model is also applied to large angle processes. Through the discussion, it is suggested that many peculiar properties of the quark-parton can be ascribed to the geometrical effects.
International Nuclear Information System (INIS)
Bagnoud, Maxime; Carlevaro, Luca
2006-01-01
We study T 11-D-q x T q /Z n orbifold compactifications of eleven-dimensional supergravity and M-theory using a purely algebraic method. Given the description of maximal supergravities reduced on square tori as non-linear coset σ-models, we exploit the mapping between scalar fields of the reduced theory and directions in the tangent space over the coset to construct the orbifold action as a non-Cartan preserving finite order inner automorphism of the complexified U-duality algebra. Focusing on the exceptional serie of Cremmer-Julia groups, we compute the residual U-duality symmetry after orbifold projection and determine the reality properties of their corresponding Lie algebras. We carry out this analysis as far as the hyperbolic e 10 algebra, conjectured to be a symmetry of M-theory. In this case the residual subalgebras are shown to be described by a special class of Borcherds and Kac-Moody algebras, modded out by their centres and derivations. Furthermore, we construct an alternative description of the orbifold action in terms of equivalence classes of shift vectors, and, in D 1, we show that a root of e 10 can always be chosen as the class representative. Then, in the framework of the E 10/10 /K(E 10/10 ) effective σ-model approach to M-theory near a spacelike singularity, we identify these roots with brane configurations stabilizing the corresponding orbifolds. In the particular case of Z 2 orbifolds of M-theory descending to type 0' orientifolds, we argue that these roots can be interpreted as pairs of magnetized D9- and D9'-branes, carrying the lower-dimensional brane charges required for tadpole cancellation. More generally, we provide a classification of all such roots generating Z n product orbifolds for n≤6, and hint at their possible interpretation
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R
2011-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.
A flipped SO(10) model from Z{sub 6}-I orbifold
Energy Technology Data Exchange (ETDEWEB)
Shimojo, Masafumi [Fukui National Coll. of Technology, Sabae (Japan)
1994-08-01
We look for flipped SO(10) and flipped SU(5) models obtained from heterotic superstrings compactified on Z{sub 6}-I orbifold with one Wilson line. We obtain twelve/fifteen independent Wilson lines which give SO(10)/SU(5) models. While we cannot construct an SU(5) model whose sum of X-charge vanishes, we find only one chiral and modular anomaly-free spectrum with three generations of sixteen dimensional representations of SU(10) which may be matter fields. For the SO(10) model, we derive effective Yukawa couplings and examine the structure of mass matrices. We also comment on the breaking mechanism of the gauge group SO(10).
Operator analysis of physical states on magnetized T{sup 2}/Z{sub N} orbifolds
Energy Technology Data Exchange (ETDEWEB)
Abe, Tomo-hiro, E-mail: t-abe@scphys.kyoto-u.ac.jp [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Fujimoto, Yukihiro, E-mail: Fujimoto@het.phys.sci.osaka-u.ac.jp [Department of Physics, Osaka University, Toyonaka 560-0043 (Japan); Kobayashi, Tatsuo, E-mail: kobayashi@particle.sci.hokudai.ac.jp [Department of Physics, Hokkaido University, Sapporo 060-0810 (Japan); Miura, Takashi, E-mail: takashi.miura@people.kobe-u.ac.jp [Department of Physics, Kobe University, Kobe 657-8501 (Japan); Nishiwaki, Kenji, E-mail: nishiken@kias.re.kr [Regional Centre for Accelerator-based Particle Physics, Harish-Chandra Research Institute, Allahabad 211 019 (India); School of Physics, Korea Institute for Advanced Study, Seoul 130 722 (Korea, Republic of); Sakamoto, Makoto, E-mail: dragon@kobe-u.ac.jp [Department of Physics, Kobe University, Kobe 657-8501 (Japan)
2015-01-15
We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases T{sup 2}/Z{sub 3}, T{sup 2}/Z{sub 4} and T{sup 2}/Z{sub 6}. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds T{sup 2}/Z{sub 3}, T{sup 2}/Z{sub 4}, T{sup 2}/Z{sub 6} (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries. (Note: This article is registered under preprint number: (arXiv:1409.5421).)
The construction of 'realistic' four-dimensional strings through orbifolds
Energy Technology Data Exchange (ETDEWEB)
Font, A. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules); Ibanez, L.E. (Geneva Univ. (Switzerland)); Quevedo, F. (McGill Univ., Montreal, Quebec (Canada)); Sierra, A. (Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica)
1990-02-12
We discuss the construction of 'realistic' lower rank 4-dimensional strings, through symmetric orbifolds with background fields. We present Z{sub 3} three-generation SU(3)xSU(2)xU(1) models as well as models incorporating a left-right SU(2){sub L}xSU(2){sub R}xU(1){sub B-L} symmetry in which proton stability is automatically guaranteed. Conformal field theory selection rules are used to find the flat directions to all orders which lead to these low-rank models and to study the relevant Yukawa couplings. A hierarchical structure of quark-lepton masses appears naturally in some models. We also present a detailed study of the structure of the Z{sub 3}xZ{sub 3} orbifold including the generalized GSO projection, the effect of discrete torsion and the conformal field theory Yukawa coupling selection rules. All these points are illustrated with a three-generation Z{sub 3}xZ{sub 3} model. We have made an effort to write a self-contained presentation in order to make this material available to non-string experts interested in the phenomenological aspects of this theory. (orig.).
ADHM and D-instantons in orbifold AdS/CFT duality
International Nuclear Information System (INIS)
Hollowood, Timothy J.; Khoze, Valentin V.
2000-01-01
We consider ADHM instantons in product group gauge theories that arise from D3-branes located at points in the orbifold R 6 /Z p . At finite N we argue that the ADHM construction and collective coordinate integration measure can be deduced from the dynamics of D-instantons in the D3-brane background. For the large-N conformal field theories of this type, we compute a saddle-point approximation of the ADHM integration measure and show that it is proportional to the partition function of D-instantons in the dual AdS 5 xS 5 /Z p background, in agreement with the orbifold AdS/CFT correspondence. Matching the expected behaviour of D-instantons, we find that when S 5 /Z p is smooth a saddle-point solution only exists in the sector where the instanton charges in each gauge group factor are the same. However, when S 5 /Z p is singular, the instanton charges at large N need not be the same and the space of saddle-point solutions has a number of distinct branches which represent the possible fractionations of D-instantons at the singularity. For the theories with a type 0B dual the saddle-point solutions manifest two types of D-instantons
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
Orbifold compactification and solutions of M-theory from Milne spaces
International Nuclear Information System (INIS)
Bytsenko, A.A.; Guimaraes, M.E.X.; Kerner, R.
2005-01-01
In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications SL(2,Z+iZ)/{±Id}, where Id is the identity matrix, is analyzed in detail. The spectrum of an eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed. (orig.)
On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds
Energy Technology Data Exchange (ETDEWEB)
Parameswaran, Susha L. [Uppsala Univ. (Sweden). Dept. of Physics and Astronomy; Ramos-Sanchez, Saul [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Zavala, Ivonne [Bonn Univ. (Germany). Bethe Center for Theoretical Physics and Physikalisches Inst.
2010-09-15
We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only ''generic'' features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but so far, they all turn out to be unstable. (orig.)
The soft supersymmetry breaking in D=5 supergravity compactified on S_1/Z_2 orbifolds
Diamandis, G A; Kouroumalou, P; Lahanas, A B
2010-01-01
We study the origin of the supersymmetry breaking induced by the mediation of gravity and the radion multiplet from the hidden to the visible brane in the context of the N=2, D=5 supergravity compactified on S_1/Z_2 orbifolds. The soft supersymmetry breaking terms for scalar masses, trilinear scalar couplings and gaugino masses are calculated to leading order in the five dimensional Newton's constant k_5^2 and the gravitino mass m_{3/2}. These are finite and non-vanishing, with the scalar soft masses be non-tachyonic, and are all expressed in terms of the gravitino mass and the length scale R of the fifth dimension. The soft supersymmetry breaking parameters are thus correlated and the phenomenological implications are discussed.
Energy Technology Data Exchange (ETDEWEB)
Walter, M.G.A.
2004-02-01
We consider several examples of a special class of heterotic compactifications, i.e. heterotic E{sub 8} x E{sub 8} orbifolds with Wilson line backgrounds. By developing a local perspective we show that a brane world like picture emerges. As an important result we prove that the local massless spectrum at such a brane can always be traced back to the global spectrum of a (different) orbifold without Wilson lines. One particular implication of this result is that the use of (discrete) Wilson lines for the construction of phenomenologically interesting models has to be rethought. We show that stringy constraints render the brane spectra consistent. Using our local picture we are able to compute the local anomalies appearing at the different branes for our examples and show that they can all be cancelled by a local version of the Green-Schwarz mechanism at the same time. (orig.)
Flipped SU(5) from Z{sub 12-I} orbifold with Wilson line
Energy Technology Data Exchange (ETDEWEB)
Kim, Jihn E. [Department of Physics and Astronomy, and Center for Theoretical Physics, Seoul National University, Seoul 151-747 (Korea, Republic of)]. E-mail: jekim@phyp.snu.ac.kr; Kyae, Bumseok [School of Physics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)]. E-mail: bkyae@kias.re.kr
2007-05-14
We construct a three family flipped SU(5) model from the heterotic string theory compactified on the Z{sub 12-I} orbifold with one Wilson line. The gauge group is SU(5)xU(1){sub X}xU(1){sup 3}x[SU(2)xSO(10)xU(1){sup 2}]{sup '}. This model does not derive any non-Abelian group except SU(5) from E{sub 8}, which is possible only for two cases in case of one shift V, one in Z{sub 12-I} and the other in Z{sub 12-II}. We present all possible Yukawa couplings. We place the third quark family in the twisted sectors and two light quark families in the untwisted sector. From the Yukawa couplings, the model provides the R-parity, the doublet-triplet splitting, and one pair of Higgs doublets. It is also shown that quark and lepton mixings are possible. So far we have not encountered a serious phenomenological problem. There exist vector-like flavor SU(5) exotics (including Q{sub em}=+/-16 color exotics and Q{sub em}=+/-12 electromagnetic exotics) and SU(5) vector-like singlet exotics with Q{sub em}=+/-12 which can be removed near the GUT scale. In this model, sin{sup 2}{theta}{sub W}{sup 0}=38 at the full unification scale.
International Nuclear Information System (INIS)
Kovtun, Pavel; Uensal, Mithat; Yaffe, Laurence G.
2005-01-01
In previous work, we found that necessary and sufficient conditions for large N c equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N c ) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z k projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z k projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N c equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z 2 projections, we show that previous assertions of large N c inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter
On bivariate geometric distribution
Directory of Open Access Journals (Sweden)
K. Jayakumar
2013-05-01
Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
Visualizing the Geometric Series.
Bennett, Albert B., Jr.
1989-01-01
Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)
Energy Technology Data Exchange (ETDEWEB)
Kersten, J.
2006-05-15
We study gaugino-mediated supersymmetry breaking in a six-dimensional SO(10) orbifold GUT model where quarks and leptons are mixtures of brane and bulk fields. The couplings of bulk matter fields to the supersymmetry breaking brane field have to be suppressed in order to avoid large FCNCs. We derive bounds on the soft supersymmetry breaking parameters and calculate the superparticle mass spectrum. If the gravitino is the LSP, the {tau}{sub 1} or the {nu}{sub {tau}}{sub L} turns out to be the NLSP, with characteristic signatures at future colliders and in cosmology. (Orig.)
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
Druţu, Cornelia
2018-01-01
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Geometric ghosts and unitarity
International Nuclear Information System (INIS)
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold
Asymptotic and geometrical quantization
International Nuclear Information System (INIS)
Karasev, M.V.; Maslov, V.P.
1984-01-01
The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered
On geometrized gravitation theories
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
Elevating the Free-Fermion $Z_{2} \\times Z_{2}$ Orbifold Model to a Compactification of $F$-Theory
Berglund, P; Faraggi, A E; Nanopoulos, Dimitri V; Qiu, Z; Berglund, Per; Ellis, John; Faraggi, Alon E.; Qiu, Zongan
2000-01-01
We study the elliptic fibrations of some Calabi-Yau three-folds, including the $Z_2\\times Z_2$ orbifold with $(h_{1,1},h_{2,1})=(27,3)$, which is equivalent to the common framework of realistic free-fermion models, as well as related models with $(h_{1,1},h_{2,1})=(51,3)$ and $(31,7)$. Two related puzzles arise when one considers the $(h_{1,1},h_{2,1})=(27,3)$ model as an F-theory compactification to six dimensions. One is that the condition for the vanishing of the gravitational anomaly is not satisfied. This suggests that either a new feature must appear in the F-theory limit of the corresponding four-dimensional type-IIA vacuum, or that the F-theory compactification does not make sense. However, the elliptic fibration is well defined everywhere except at four singular points in the base. We speculate on the possible existence of N=1 tensor and hypermultiplets at these points which would cancel the gravitational anomaly.
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
International Nuclear Information System (INIS)
La, H.
1992-01-01
A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint
A Geometric Dissection Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 7. A Geometric Dissection Problem. M N Deshpande. Think It Over Volume 7 Issue 7 July 2002 pp 91-91. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/07/0091-0091. Author Affiliations.
Geometric statistical inference
International Nuclear Information System (INIS)
Periwal, Vipul
1999-01-01
A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined
Geometric Series via Probability
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Lectures in geometric combinatorics
Thomas, Rekha R
2006-01-01
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gr�bner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational as...
Geometric information provider platform
Directory of Open Access Journals (Sweden)
Meisam Yousefzadeh
2015-07-01
Full Text Available Renovation of existing buildings is known as an essential stage in reduction of the energy loss. Considerable part of renovation process depends on geometric reconstruction of building based on semantic parameters. Following many research projects which were focused on parameterizing the energy usage, various energy modelling methods were developed during the last decade. On the other hand, by developing accurate measuring tools such as laser scanners, the interests of having accurate 3D building models are rapidly growing. But the automation of 3D building generation from laser point cloud or detection of specific objects in that is still a challenge. The goal is designing a platform through which required geometric information can be efficiently produced to support energy simulation software. Developing a reliable procedure which extracts required information from measured data and delivers them to a standard energy modelling system is the main purpose of the project.
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Ruffino, Fabio Ferrari
2013-01-01
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification wi...
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Developing geometrical reasoning
Brown, Margaret; Jones, Keith; Taylor, Ron; Hirst, Ann
2004-01-01
This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current requirements of the UK National Curriculum and the Key Stage 3 strategy, and to consider the whole atta...
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Geometric leaf placement strategies
International Nuclear Information System (INIS)
Fenwick, J D; Temple, S W P; Clements, R W; Lawrence, G P; Mayles, H M O; Mayles, W P M
2004-01-01
Geometric leaf placement strategies for multileaf collimators (MLCs) typically involve the expansion of the beam's-eye-view contour of a target by a uniform MLC margin, followed by movement of the leaves until some point on each leaf end touches the expanded contour. Film-based dose-distribution measurements have been made to determine appropriate MLC margins-characterized through an index d 90 -for multileaves set using one particular strategy to straight lines lying at various angles to the direction of leaf travel. Simple trigonometric relationships exist between different geometric leaf placement strategies and are used to generalize the results of the film work into d 90 values for several different strategies. Measured d 90 values vary both with angle and leaf placement strategy. A model has been derived that explains and describes quite well the observed variations of d 90 with angle. The d 90 angular variations of the strategies studied differ substantially, and geometric and dosimetric reasoning suggests that the best strategy is the one with the least angular variation. Using this criterion, the best straightforwardly implementable strategy studied is a 'touch circle' approach for which semicircles are imagined to be inscribed within leaf ends, the leaves being moved until the semicircles just touch the expanded target outline
Studies in geometric quantization
International Nuclear Information System (INIS)
Tuynman, G.M.
1988-01-01
This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs
Geometrical model of multiple production
International Nuclear Information System (INIS)
Chikovani, Z.E.; Jenkovszky, L.L.; Kvaratshelia, T.M.; Struminskij, B.V.
1988-01-01
The relation between geometrical and KNO-scaling and their violation is studied in a geometrical model of multiple production of hadrons. Predictions concerning the behaviour of correlation coefficients at future accelerators are given
Geometric Computing for Freeform Architecture
Wallner, J.; Pottmann, Helmut
2011-01-01
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area
Geometric Constructions with the Computer.
Chuan, Jen-chung
The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…
On the equivalence of N=1 brane worlds and geometric singularities with flux
International Nuclear Information System (INIS)
Kaste, Peter; Partouche, Herve
2004-01-01
We consider Kaluza Klein reductions of M-theory on the Z N orbifold of the spin bundle over S 3 along two different U(1) isometries. The first one gives rise to the familiar 'large-N duality' of the N=1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S 3 , whereas the IR involves N units of RR flux through an S 2 . The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of a P 1 of A N-1 singularities, with one unit of RR flux through the P 1 . The IR is reached via a geometric transition and involves a single D6 brane on a lens space S 3 /Z N or, alternatively, a singular background (S 2 xR 4 )/Z N , with one unit of RR flux through S 2 and, localized at the singularities, an action of their stabilizer group in the U(1) RR gauge bundle, so that no massless twisted states occur. We also consider linear s-model descriptions of these backgrounds. (author)
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Geometric multipartite entanglement measures
International Nuclear Information System (INIS)
Paz-Silva, Gerardo A.; Reina, John H.
2007-01-01
Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive
Geometric correlations and multifractals
International Nuclear Information System (INIS)
Amritkar, R.E.
1991-07-01
There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs
International Nuclear Information System (INIS)
Noga, M.T.
1984-01-01
This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry
Geometrization of quantum physics
International Nuclear Information System (INIS)
Ol'khov, O.A.
2009-01-01
It is shown that the Dirac equation for a free particle can be considered as a description of specific distortion of the space Euclidean geometry (space topological defect). This approach is based on the possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such a concept explains all so-called 'strange' properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of the suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There are no any particles a priory, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device
Geometrization of quantum physics
Ol'Khov, O. A.
2009-12-01
It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.
Havelka, Jan
2008-01-01
Tato diplomová práce se zabývá akcelerací geometrických transformací obrazu s využitím GPU a architektury NVIDIA (R) CUDA TM. Časově kritické části kódu jsou přesunuty na GPU a vykonány paralelně. Jedním z výsledků je demonstrační aplikace pro porovnání výkonnosti obou architektur: CPU, a GPU v kombinaci s CPU. Pro referenční implementaci jsou použity vysoce optimalizované algoritmy z knihovny OpenCV, od firmy Intel. This master's thesis deals with acceleration of geometrical image transfo...
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Regular Polygons and Geometric Series.
Jarrett, Joscelyn A.
1982-01-01
Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)
Geometric Invariants and Object Recognition.
1992-08-01
University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of
Transmuted Complementary Weibull Geometric Distribution
Directory of Open Access Journals (Sweden)
Ahmed Z. A fify
2014-12-01
Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the complementary Weibull geometric distribution.
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Geometric inequalities for black holes
International Nuclear Information System (INIS)
Dain, Sergio
2013-01-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Optical traps with geometric aberrations
International Nuclear Information System (INIS)
Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.
2006-01-01
We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Discrete geometric structures for architecture
Pottmann, Helmut
2010-01-01
. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-01-01
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First
Geometrical optics in general relativity
Loinger, A.
2006-01-01
General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Directory of Open Access Journals (Sweden)
Jorge Arrieta
Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
A new geometrical gravitational theory
International Nuclear Information System (INIS)
Obata, T.; Chiba, J.; Oshima, H.
1981-01-01
A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
An introduction to geometrical physics
Aldrovandi, R
1995-01-01
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o
Geometric scaling as traveling waves
International Nuclear Information System (INIS)
Munier, S.; Peschanski, R.
2003-01-01
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Geometric integration for particle accelerators
International Nuclear Information System (INIS)
Forest, Etienne
2006-01-01
This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction
Geometrical spin symmetry and spin
International Nuclear Information System (INIS)
Pestov, I. B.
2011-01-01
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Geometric integration for particle accelerators
Forest, Étienne
2006-05-01
This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
Lattice degeneracies of geometric fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
In Defence of Geometrical Algebra
Blasjo, V.N.E.
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Geometrical interpretation of extended supergravity
International Nuclear Information System (INIS)
Townsend, P.K.; Nieuwenhuizen, P.van
1977-01-01
SO 2 extended supergravity is shown to be a geometrical theory, whose underlying gauge group is OSp(4,2). The couplings which gauge the SO 2 symmetry as well as the accompanying cosmological and masslike terms are directly obtained, and the usual SO 2 model is obtained after a Wigner-Inoenue group contraction. (Auth.)
Geometric scaling in exclusive processes
International Nuclear Information System (INIS)
Munier, S.; Wallon, S.
2003-01-01
We show that according to the present understanding of the energy evolution of the observables measured in deep-inelastic scattering, the photon-proton scattering amplitude has to exhibit geometric scaling at each impact parameter. We suggest a way to test this experimentally at HERA. A qualitative analysis based on published data is presented and discussed. (orig.)
Geometric quantization and general relativity
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-01-01
The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)
Geometric origin of central charges
International Nuclear Information System (INIS)
Lukierski, J.; Rytel, L.
1981-05-01
The complete set of N(N-1) central charge generators for D=4 N-extended super Poincare algebra is obtained by suitable contraction of OSp (2N; 4) superalgebra. The superspace realizations of the spinorial generators with central charges are derived. The conjugate set of N(N-1) additional bosonic superspace coordinates is introduced in an unique and geometric way. (author)
Vergence, Vision, and Geometric Optics
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Geometric phases and quantum computation
International Nuclear Information System (INIS)
Vedral, V.
2005-01-01
Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)
Cartan's geometrical structure of supergravity
International Nuclear Information System (INIS)
Baaklini, N.S.
1977-06-01
The geometrical partnership of the vierbein and the spin-3/2 field in the structure of the supergravity Lagrangian is emphasized. Both fields are introduced as component of the same matrix differential form. The only local symmetry of the theory is SL(2,C)
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the correct interpolation method is described. For the chromatic issues of calibration we present the acquisition of colour and multi-spectral images, the chromatic aberrations and the various lens/camera based non-uniformities of the illumination of the image plane. It is described how the monochromatic...... to design calibration targets for both geometrical and chromatic calibration are described. We present some possible systematical errors on the detection of the objects in the calibration targets, if viewed in a non orthogonal angle, if the intensities are uneven or if the image blurring is uneven. Finally...
Geometrical approach to tumor growth.
Escudero, Carlos
2006-08-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Parametric FEM for geometric biomembranes
Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.
2010-05-01
We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.
Geometrical methods in learning theory
International Nuclear Information System (INIS)
Burdet, G.; Combe, Ph.; Nencka, H.
2001-01-01
The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine
Geometrical approach to tumor growth
Escudero, Carlos
2006-01-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys. Rev. E 73, 020902(R) (200...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Moving walls and geometric phases
Energy Technology Data Exchange (ETDEWEB)
Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Marmo, Giuseppe [Dipartimento di Scienze Fisiche and MECENAS, Università di Napoli “Federico II”, I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); Samuel, Joseph [Raman Research Institute, 560080 Bangalore (India)
2016-09-15
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Geometric approach to soliton equations
International Nuclear Information System (INIS)
Sasaki, R.
1979-09-01
A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Geometric phase from dielectric matrix
International Nuclear Information System (INIS)
Banerjee, D.
2005-10-01
The dielectric property of the anisotropic optical medium is found by considering the polarized photon as two component spinor of spherical harmonics. The Geometric Phase of a polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies. (author)
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Geometrical optics and optimal transport.
Rubinstein, Jacob; Wolansky, Gershon
2017-10-01
The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Geometrical approach to fluid models
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Schep, T.J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics
A geometrical approach to two-dimensional Conformal Field Theory
Dijkgraaf, Robertus Henricus
1989-09-01
This thesis is organized in the following way. In Chapter 2 we will give a brief introduction to conformal field theory along the lines of standard quantum field theory, without any claims to originality. We introduce the important concepts of the stress-energy tensor, the Virasoro algebra, and primary fields. The general principles are demonstrated by fermionic and bosonic free field theories. This also allows us to discuss some general aspects of moduli spaces of CFT's. In particular, we describe in some detail the space of iiiequivalent toroidal comi)actificalions, giving examples of the quantum equivalences that we already mentioned. In Chapter 3 we will reconsider general quantum field theory from a more geometrical point of view, along the lines of the so-called operator formalism. Crucial to this approach will be the consideration of topology changing amplitudes. After a simple application to 2d topological theories, we proceed to give our second introduction to CFT, stressing the geometry behind it. In Chapter 4 the so-called rational conformal field theories are our object of study. These special CFT's have extended symmetries with only a finite number of representations. If an interpretation as non-linear sigma model exists, this extra symmetry can be seen as a kind of resonance effect due to the commensurability of the size of the string and the target space-time. The structure of rational CFT's is extremely rigid, and one of our results will be that the operator content of these models is—up to some discrete choices—completely determined by the symmetry algebra. The study of rational models is in its rigidity very analogous to finite group theory. In Chapter 5 this analogy is further pursued and substantiated. We will show how one can construct from general grounds rational conformal field theories from finite groups. These models are abstract versions of non-linear o-models describing string propagation on 'orbifoids.' An orbifold is a singular
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Geometrical setting of solid mechanics
International Nuclear Information System (INIS)
Fiala, Zdenek
2011-01-01
Highlights: → Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). → Generalized logarithmic strain. → Consistent linearization. → Incremental principle of virtual power. → Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Geometric Methods in Physics XXXV
Odzijewicz, Anatol; Previato, Emma
2018-01-01
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...
Geometric considerations in magnetron sputtering
International Nuclear Information System (INIS)
Thornton, J.A.
1982-01-01
The recent development of high performance magnetron type discharge sources has greatly enhaced the range of coating applications where sputtering is a viable deposition process. Magnetron sources can provide high current densities and sputtering rates, even at low pressures. They have much reduced substrate heating rates and can be scaled to large sizes. Magnetron sputter coating apparatuses can have a variety of geometric and plasma configurations. The target geometry affects the emission directions of both the sputtered atoms and the energetic ions which are neutralized and reflected at the cathode. This fact, coupled with the long mean free particle paths which are prevalent at low pressures, can make the coating properties very dependent on the apparatus geometry. This paper reviews the physics of magnetron operation and discusses the influences of apparatus geometry on the use of magnetrons for rf sputtering and reactive sputtering, as well as on the microstructure and internal stresses in sputtered metallic coatings. (author) [pt
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Operational geometric phase for mixed quantum states
International Nuclear Information System (INIS)
Andersson, O; Heydari, H
2013-01-01
The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. (paper)
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometr......Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness...... in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant....... Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping....
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Geometric asymmetry driven Janus micromotors
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
Information geometric methods for complexity
Felice, Domenico; Cafaro, Carlo; Mancini, Stefano
2018-03-01
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.
Geometrical aspects of quantum spaces
International Nuclear Information System (INIS)
Ho, P.M.
1996-01-01
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S 1 2 and the quantum complex projective space CP q (N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S q 2 and CP q (N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP q (N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given
Yang Mills instantons, geometrical aspects
International Nuclear Information System (INIS)
Stora, R.
1977-09-01
The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie
Geometric Reasoning for Automated Planning
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric structure of percolation clusters.
Xu, Xiao; Wang, Junfeng; Zhou, Zongzheng; Garoni, Timothy M; Deng, Youjin
2014-01-01
We investigate the geometric properties of percolation clusters by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo simulations, we study the probability that a given edge is not a bridge but has both its loop arcs in the same loop and find that it is governed by the two-arm exponent. We then classify bridges into two types: branches and junctions. A bridge is a branch iff at least one of the two clusters produced by its deletion is a tree. Starting from a percolation configuration and deleting the branches results in a leaf-free configuration, whereas, deleting all bridges produces a bridge-free configuration. Although branches account for ≈43% of all occupied bonds, we find that the fractal dimensions of the cluster size and hull length of leaf-free configurations are consistent with those for standard percolation configurations. By contrast, we find that the fractal dimensions of the cluster size and hull length of bridge-free configurations are given by the backbone and external perimeter dimensions, respectively. We estimate the backbone fractal dimension to be 1.643 36(10).
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Geometrical scaling, furry branching and minijets
International Nuclear Information System (INIS)
Hwa, R.C.
1988-01-01
Scaling properties and their violations in hadronic collisions are discussed in the framework of the geometrical branching model. Geometrical scaling supplemented by Furry branching characterizes the soft component, while the production of jets specifies the hard component. Many features of multiparticle production processes are well described by this model. 21 refs
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-01
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometrical optics and the diffraction phenomenon
International Nuclear Information System (INIS)
Timofeev, Aleksandr V
2005-01-01
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Solving Absolute Value Equations Algebraically and Geometrically
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Geometrical formulation of the conformal Ward identity
International Nuclear Information System (INIS)
Kachkachi, M.
2002-08-01
In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed, a geometrical interpretation of the conformal Ward identity in two dimensional conformal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classical structures. Then, we solve the conformal Ward identity by using this geometrical formalism. (author)
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
SOME PROPERTIES OF GEOMETRIC DEA MODELS
Directory of Open Access Journals (Sweden)
Ozren Despić
2013-02-01
Full Text Available Some specific geometric data envelopment analysis (DEA models are well known to the researchers in DEA through so-called multiplicative or log-linear efficiency models. Valuable properties of these models were noted by several authors but the models still remain somewhat obscure and rarely used in practice. The purpose of this paper is to show from a mathematical perspective where the geometric DEA fits in relation to the classical DEA, and to provide a brief overview of some benefits in using geometric DEA in practice of decision making and/or efficiency measurement.
Refined geometric transition and qq-characters
Kimura, Taro; Mori, Hironori; Sugimoto, Yuji
2018-01-01
We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe qq-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg-Witten curves called qq-characters in certain cases.
A Geometrical View of Higgs Effective Theory
CERN. Geneva
2016-01-01
A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.
Geometrical analysis of the interacting boson model
International Nuclear Information System (INIS)
Dieperink, A.E.L.
1983-01-01
The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)
Lectures on geometrical properties of nuclei
International Nuclear Information System (INIS)
Myers, W.D.
1975-11-01
Material concerning the geometrical properties of nuclei is drawn from a number of different sources. The leptodermous nature of nuclear density distributions and potential wells is used to draw together the various geometrical properties of these systems and to provide a unified means for their description. Extensive use is made of expansions of radial properties in terms of the surface diffuseness. A strong case is made for the use of convolution as a geometrical ansatz for generating diffuse surface distributions because of the number of simplifications that arise which are of practical importance. 7 figures
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Geometrical scaling of jet fragmentation photons
Energy Technology Data Exchange (ETDEWEB)
Hattori, Koichi, E-mail: koichi.hattori@riken.jp [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan); McLerran, Larry, E-mail: mclerran@bnl.gov [RIKEN BNL Research Center, Brookhaven National Laboratory, Upton NY 11973 (United States); Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States); Physics Dept., China Central Normal University, Wuhan (China); Schenke, Björn, E-mail: bschenke@bnl.gov [Physics Dept., Bdg. 510A, Brookhaven National Laboratory, Upton, NY-11973 (United States)
2016-12-15
We discuss jet fragmentation photons in ultrarelativistic heavy-ion collisions. We argue that, if the jet distribution satisfies geometrical scaling and an anisotropic spectrum, these properties are transferred to photons during the jet fragmentation.
Geometric U-folds in four dimensions
Lazaroiu, C. I.; Shahbazi, C. S.
2018-01-01
We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
The perception of geometrical structure from congruence
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
Spherical projections and liftings in geometric tomography
DEFF Research Database (Denmark)
Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang
2011-01-01
We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad......We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies...... and to radial functions of star bodies. We then investigate averages of lifted projections and show that they correspond to self-adjoint intertwining operators. We obtain formulas for the eigenvalues of these operators and use them to ascertain circumstances under which tomographic measurements determine...... the original bodies. This approach via mean lifted projections leads us to some unexpected relationships between seemingly disparate geometric constructions....
The effect of photometric and geometric context on photometric and geometric lightness effects.
Lee, Thomas Y; Brainard, David H
2014-01-24
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.
Sudan-decoding generalized geometric Goppa codes
DEFF Research Database (Denmark)
Heydtmann, Agnes Eileen
2003-01-01
Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...... for these codes based on Sudan's improved algorithm is presented and its error-correcting capacity is analyzed. For the implementation of the algorithm it is necessary that the so-called increasing zero bases of certain spaces of functions are available. A method to obtain such bases is developed....
The geometric phase in quantum physics
International Nuclear Information System (INIS)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase
Geometric modular action and transformation groups
International Nuclear Information System (INIS)
Summers, S.J.
1996-01-01
We study a weak form of geometric modular action, which is naturally associated with transformation groups of partially ordered sets and which provides these groups with projective representations. Under suitable conditions it is shown that these groups are implemented by point transformations of topological spaces serving as models for space-times, leading to groups which may be interpreted as symmetry groups of the space-times. As concrete examples, it is shown that the Poincare group and the de Sitter group can be derived from this condition of geometric modular action. Further consequences and examples are discussed. (orig.)
Geometrical methods for power network analysis
Energy Technology Data Exchange (ETDEWEB)
Bellucci, Stefano; Tiwari, Bhupendra Nath [Istituto Nazioneale di Fisica Nucleare, Frascati, Rome (Italy). Lab. Nazionali di Frascati; Gupta, Neeraj [Indian Institute of Technology, Kanpur (India). Dept. of Electrical Engineering
2013-02-01
Uses advanced geometrical methods to analyse power networks. Provides a self-contained and tutorial introduction. Includes a fully worked-out example for the IEEE 5 bus system. This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.
Aspects of the geometrical approach to supermanifolds
International Nuclear Information System (INIS)
Rogers, A.
1984-01-01
Various topics in the theory and application of the geometrical approach to supermanifolds are discussed. The construction of the superspace used in supergravity over an arbitrary spacetime manifold is described. Super Lie groups and their relation to graded Lie algebras (and more general structures referred to as 'graded Lie modules') are discussed, with examples. Certain supermanifolds, allowed in the geometric approach (using the fine topology), but having no analogue in the algebraic approach, are discussed. Finally lattice supersymmetry, and its relation to the differential geometry of supermanifolds, is discussed. (orig.)
Geometrical superresolved imaging using nonperiodic spatial masking.
Borkowski, Amikam; Zalevsky, Zeev; Javidi, Bahram
2009-03-01
The resolution of every imaging system is limited either by the F-number of its optics or by the geometry of its detection array. The geometrical limitation is caused by lack of spatial sampling points as well as by the shape of every sampling pixel that generates spectral low-pass filtering. We present a novel approach to overcome the low-pass filtering that is due to the shape of the sampling pixels. The approach combines special algorithms together with spatial masking placed in the intermediate image plane and eventually allows geometrical superresolved imaging without relation to the actual shape of the pixels.
Workshop on Topology and Geometric Group Theory
Fowler, James; Lafont, Jean-Francois; Leary, Ian
2016-01-01
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
Theoretical frameworks for the learning of geometrical reasoning
Jones, Keith
1998-01-01
With the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical...
Two particle entanglement and its geometric duals
Energy Technology Data Exchange (ETDEWEB)
Wasay, Muhammad Abdul [University of Agriculture, Department of Physics, Faisalabad (Pakistan); Quaid-i-Azam University Campus, National Centre for Physics, Islamabad (Pakistan); Bashir, Asma [University of Agriculture, Department of Physics, Faisalabad (Pakistan)
2017-12-15
We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)
Impossible Geometric Constructions: A Calculus Writing Project
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
Rejuvenating Allen's Arc with the Geometric Mean.
Phillips, William A.
1994-01-01
Contends that, despite ongoing criticism, Allen's arc elasticity formula remains entrenched in the microeconomics principles curriculum. Reviews the evolution and continuing scrutiny of the formula. Argues that the use of the geometric mean offers pedagogical advantages over the traditional arithmetic mean approach. (CFR)
Geometric Models for Collaborative Search and Filtering
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
Two particle entanglement and its geometric duals
International Nuclear Information System (INIS)
Wasay, Muhammad Abdul; Bashir, Asma
2017-01-01
We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations. (orig.)
Geometric Abstract Art and Public Health Data
Centers for Disease Control (CDC) Podcasts
2016-10-18
Dr. Salaam Semaan, a CDC behavioral scientist, discusses the similarities between geometric abstract art and public health data analysis. Created: 10/18/2016 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 10/18/2016.
Geometric phase topology in weak measurement
Samlan, C. T.; Viswanathan, Nirmal K.
2017-12-01
The geometric phase visualization proposed by Bhandari (R Bhandari 1997 Phys. Rep. 281 1-64) in the ellipticity-ellipse orientation basis of the polarization ellipse of light is implemented to understand the geometric aspects of weak measurement. The weak interaction of a pre-selected state, acheived via spin-Hall effect of light (SHEL), results in a spread in the polarization ellipticity (η) or ellipse orientation (χ) depending on the resulting spatial or angular shift, respectively. The post-selection leads to the projection of the η spread in the complementary χ basis results in the appearance of a geometric phase with helical phase topology in the η - χ parameter space. By representing the weak measurement on the Poincaré sphere and using Jones calculus, the complex weak value and the geometric phase topology are obtained. This deeper understanding of the weak measurement process enabled us to explore the techniques’ capabilities maximally, as demonstrated via SHEL in two examples—external reflection at glass-air interface and transmission through a tilted half-wave plate.
Geometrical tile design for complex neighborhoods.
Czeizler, Eugen; Kari, Lila
2009-01-01
Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e., square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a "tall" von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 "filled" rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k + 1) rectangle.
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Geometric Series and Computers--An Application.
McNerney, Charles R.
1983-01-01
This article considers the sum of a finite geometric series as applied to numeric data storage in the memory of an electronic digital computer. The presentation is viewed as relevant to programing in several languages and removes some of the mystique associated with syntax constraints that any language imposes. (MP)
Geometric Transformations in Middle School Mathematics Textbooks
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
Geometric calibration of ERS satellite SAR images
DEFF Research Database (Denmark)
Mohr, Johan Jacob; Madsen, Søren Nørvang
2001-01-01
Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed...
Non-crossing geometric steiner arborescences
Kostitsyna, I.; Speckmann, B.; Verbeek, K.A.B.; Okamoto, Yoshio; Tokuyama, Takeshi
2017-01-01
Motivated by the question of simultaneous embedding of several flow maps, we consider the problem of drawing multiple geometric Steiner arborescences with no crossings in the rectilinear and in the angle-restricted setting. When terminal-to-root paths are allowed to turn freely, we show that two
On Kaehler's geometric description of dirac fields
International Nuclear Information System (INIS)
Goeckeler, M.; Joos, H.
1983-12-01
A differential geometric generalization of the Dirac equation due to E. Kaehler seems to be an appropriate starting point for the lattice approximation of matter fields. It is the purpose of this lecture to illustrate several aspects of this approach. (orig./HSI)
Robust Geometric Control of a Distillation Column
DEFF Research Database (Denmark)
Kymmel, Mogens; Andersen, Henrik Weisberg
1987-01-01
A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....
Geometric Algorithms for Part Orienting and Probing
Panahi, F.
2015-01-01
In this thesis, detailed solutions are presented to several problems dealing with geometric shape and orientation of an object in the field of robotics and automation. We first have considered a general model for shape variations that allows variation along the entire boundary of an object, both in
Non-equilibrium current via geometric scatterers
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Neidhardt, H.; Tater, Miloš; Zagrebnov, V. A.
2014-01-01
Roč. 47, č. 39 (2014), s. 395301 ISSN 1751-8113 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-equilibrioum steady states * geometric scatterer * Landauer-Buttiker formula Subject RIV: BE - Theoretical Physics Impact factor: 1.583, year: 2014
Geometrical scaling in high energy hadron collisions
International Nuclear Information System (INIS)
Kundrat, V.; Lokajicek, M.V.
1984-06-01
The concept of geometrical scaling for high energy elastic hadron scattering is analyzed and its basic equations are solved in a consistent way. It is shown that they are applicable to a rather small interval of momentum transfers, e.g. maximally for |t| 2 for pp scattering at the ISR energies. (author)
Geometrical efficiency in computerized tomography: generalized model
International Nuclear Information System (INIS)
Costa, P.R.; Robilotta, C.C.
1992-01-01
A simplified model for producing sensitivity and exposure profiles in computerized tomographic system was recently developed allowing the forecast of profiles behaviour in the rotation center of the system. The generalization of this model for some point of the image plane was described, and the geometrical efficiency could be evaluated. (C.G.C.)
Can EPR non-locality be geometrical?
International Nuclear Information System (INIS)
Ne'eman, Y.
1995-01-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
International Nuclear Information System (INIS)
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V.
2010-01-01
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
Geometric description of images as topographic maps
Caselles, Vicent
2010-01-01
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8...
Towards a theory of geometric graphs
Pach, Janos
2004-01-01
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...
Plasmon Geometric Phase and Plasmon Hall Shift
Shi, Li-kun; Song, Justin C. W.
2018-04-01
The collective plasmonic modes of a metal comprise a simple pattern of oscillating charge density that yields enhanced light-matter interaction. Here we unveil that beneath this familiar facade plasmons possess a hidden internal structure that fundamentally alters its dynamics. In particular, we find that metals with nonzero Hall conductivity host plasmons with an intricate current density configuration that sharply departs from that of ordinary zero Hall conductivity metals. This nontrivial internal structure dramatically enriches the dynamics of plasmon propagation, enabling plasmon wave packets to acquire geometric phases as they scatter. At boundaries, these phases accumulate allowing plasmon waves that reflect off to experience a nonreciprocal parallel shift. This plasmon Hall shift, tunable by Hall conductivity as well as plasmon wavelength, displaces the incident and reflected plasmon trajectories and can be readily probed by near-field photonics techniques. Anomalous plasmon geometric phases dramatically enrich the nanophotonics toolbox, and yield radical new means for directing plasmonic beams.
Geometric mechanics of periodic pleated origami.
Wei, Z Y; Guo, Z V; Dudte, L; Liang, H Y; Mahadevan, L
2013-05-24
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco
2015-01-01
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .
A Practical Guide to Experimental Geometrical Optics
Garbovskiy, Yuriy A.; Glushchenko, Anatoliy V.
2017-12-01
Preface; 1. Markets of optical materials, components, accessories, light sources and detectors; 2. Introduction to optical experiments: light producing, light managing, light detection and measuring; 3. Light detectors based on semiconductors: photoresistors, photodiodes in a photo-galvanic regime. Principles of operation and measurements; 4. Linear light detectors based on photodiodes; 5. Basic laws of geometrical optics: experimental verification; 6. Converging and diverging thin lenses; 7. Thick lenses; 8. Lens systems; 9. Simple optical instruments I: the eye and the magnifier, eyepieces and telescopes; 10. Simple optical instruments II: light illuminators and microscope; 11. Spherical mirrors; 12. Introduction to optical aberrations; 13. Elements of optical radiometry; 14. Cylindrical lenses and vials; 15. Methods of geometrical optics to measure refractive index; 16. Dispersion of light and prism spectroscope; 17. Elements of computer aided optical design; Index.
Coated sphere scattering by geometric optics approximation.
Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang
2014-10-01
A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.
Geometrical Description of fractional quantum Hall quasiparticles
Park, Yeje; Yang, Bo; Haldane, F. D. M.
2012-02-01
We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Geometrical dynamics of Born-Infeld objects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2007-03-21
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.
Geometrical dynamics of Born-Infeld objects
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2007-01-01
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS 3 x S 3 background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation
A practical guide to experimental geometrical optics
Garbovskiy, Yuriy A
2017-01-01
A concise, yet deep introduction to experimental, geometrical optics, this book begins with fundamental concepts and then develops the practical skills and research techniques routinely used in modern laboratories. Suitable for students, researchers and optical engineers, this accessible text teaches readers how to build their own optical laboratory and to design and perform optical experiments. It uses a hands-on approach which fills a gap between theory-based textbooks and laboratory manuals, allowing the reader to develop their practical skills in this interdisciplinary field, and also explores the ways in which this knowledge can be applied to the design and production of commercial optical devices. Including supplementary online resources to help readers track and evaluate their experimental results, this text is the ideal companion for anyone with a practical interest in experimental geometrical optics.
Fast decoding algorithms for geometric coded apertures
International Nuclear Information System (INIS)
Byard, Kevin
2015-01-01
Fast decoding algorithms are described for the class of coded aperture designs known as geometric coded apertures which were introduced by Gourlay and Stephen. When compared to the direct decoding method, the algorithms significantly reduce the number of calculations required when performing the decoding for these apertures and hence speed up the decoding process. Experimental tests confirm the efficacy of these fast algorithms, demonstrating a speed up of approximately two to three orders of magnitude over direct decoding.
Geometrical framework for robust portfolio optimization
Bazovkin, Pavel
2014-01-01
We consider a vector-valued multivariate risk measure that depends on the user's profile given by the user's utility. It is constructed on the basis of weighted-mean trimmed regions and represents the solution of an optimization problem. The key feature of this measure is convexity. We apply the measure to the portfolio selection problem, employing different measures of performance as objective functions in a common geometrical framework.
Geometric measure theory a beginner's guide
Morgan, Frank
1995-01-01
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Geometrical Aspects of non-gravitational interactions
Roldan, Omar; Barros Jr, C. C.
2016-01-01
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the concept of proper space-time, that allow us to describe this interaction in a way analogous to the one that the general relativity theory does for gravitation. The field equations that define this geometry are similar to the Einstein's equations, where in general...
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term. © 2013 Wiley Periodicals, Inc.
Geometric (Berry) phases in neutron molecular spectroscopy
International Nuclear Information System (INIS)
Lovesey, S.W.
1992-02-01
A theory of neutron scattering by nuclei in a molecule, accompanied by an electronic transition, is formulated with attention to gauge potentials and geometric phases in the Born-Oppenheimer scheme. Non-degenerate and nearly degenerate electronic levels are considered. For nearly degenerate levels it is shown that, the cross-section is free of the singular structure which characterizes the corresponding gauge potential for the phase, and much larger than for well separated electronic states. (author)
Geometric continuum regularization of quantum field theory
International Nuclear Information System (INIS)
Halpern, M.B.
1989-01-01
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs
Graph Treewidth and Geometric Thickness Parameters
Dujmović, Vida; Wood, David R.
2005-01-01
Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for grap...
Geometric morphometric footprint analysis of young women
Domjanic, Jacqueline; Fieder, Martin; Seidler, Horst; Mitteroecker, Philipp
2013-01-01
Background Most published attempts to quantify footprint shape are based on a small number of measurements. We applied geometric morphometric methods to study shape variation of the complete footprint outline in a sample of 83 adult women. Methods The outline of the footprint, including the toes, was represented by a comprehensive set of 85 landmarks and semilandmarks. Shape coordinates were computed by Generalized Procrustes Analysis. Results The first four principal components represented t...
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Geometrical optics in correlated imaging systems
International Nuclear Information System (INIS)
Cao Dezhong; Xiong Jun; Wang Kaige
2005-01-01
We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging
Nociones de geometría vectorial
Ospina Arteaga, Omar Evelio
1990-01-01
Las presentes notas de geometría vectorial pretenden ser una ayuda para los estudiantes que se inician en el tema de vectores y deberá ser complementado con ejercicios sobre el tema. Este texto contiene temas de interés tales como: Espacios euclidianos, Distancian entre dos puntos, Concepto de vector, Igualdad de vectores, entre otros relacionados con el estudio de vectores.
Geometrical Determinants of Neuronal Actin Waves
Tomba, Caterina; Bra?ni, C?line; Bugnicourt, Ghislain; Cohen, Floriane; Friedrich, Benjamin M.; Gov, Nir S.; Villard, Catherine
2017-01-01
Hippocampal neurons produce in their early stages of growth propagative, actin-rich dynamical structures called actin waves. The directional motion of actin waves from the soma to the tip of neuronal extensions has been associated with net forward growth, and ultimately with the specification of neurites into axon and dendrites. Here, geometrical cues are used to control actin wave dynamics by constraining neurons on adhesive stripes of various widths. A key observable, the average time betwe...
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which...... mainly are in the direction of the beam axis. The generalized Brazier effect is calculated as a linear load case based on these stresses....
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Ricci flow and geometrization of 3-manifolds
Morgan, John W
2010-01-01
This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincar� Conjecture and the more general Geometrization Conjecture for 3-dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3-dimensional Ricci flows and for 3-dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the time-slices as the time goes to infinity in order to deduce the topological consequences. The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of ...
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. Copyright © 2010 Wiley-Liss, Inc.
Geometric phase effects in ultracold chemistry
Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.
2016-05-01
In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).
Edit propagation using geometric relationship functions
Guerrero, Paul; Jeschke, Stefan; Wimmer, Michael; Wonka, Peter
2014-01-01
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Geometric transitions on non-Kaehler manifolds
International Nuclear Information System (INIS)
Knauf, A.
2007-01-01
We study geometric transitions on the supergravity level using the basic idea of an earlier paper (M. Becker et al., 2004), where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Edit propagation using geometric relationship functions
Guerrero, Paul
2014-04-15
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Geometric phase modulation for stellar interferometry
International Nuclear Information System (INIS)
Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.
2002-01-01
Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer
Plasma geometric optics analysis and computation
International Nuclear Information System (INIS)
Smith, T.M.
1983-01-01
Important practical applications in the generation, manipulation, and diagnosis of laboratory thermonuclear plasmas have created a need for elaborate computational capabilities in the study of high frequency wave propagation in plasmas. A reduced description of such waves suitable for digital computation is provided by the theory of plasma geometric optics. The existing theory is beset by a variety of special cases in which the straightforward analytical approach fails, and has been formulated with little attention to problems of numerical implementation of that analysis. The standard field equations are derived for the first time from kinetic theory. A discussion of certain terms previously, and erroneously, omitted from the expansion of the plasma constitutive relation is given. A powerful but little known computational prescription for determining the geometric optics field in the neighborhood of caustic singularities is rigorously developed, and a boundary layer analysis for the asymptotic matching of the plasma geometric optics field across caustic singularities is performed for the first time with considerable generality. A proper treatment of birefringence is detailed, wherein a breakdown of the fundamental perturbation theory is identified and circumvented. A general ray tracing computer code suitable for applications to radiation heating and diagnostic problems is presented and described
The Geometric Phase in Quantum Systems
International Nuclear Information System (INIS)
Pascazio, S
2003-01-01
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke 'after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Some Hermite–Hadamard Type Inequalities for Geometrically Quasi ...
Indian Academy of Sciences (India)
Abstract. In the paper, we introduce a new concept 'geometrically quasi-convex function' and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.
Nonadiabatic geometrical quantum gates in semiconductor quantum dots
International Nuclear Information System (INIS)
Solinas, Paolo; Zanghi, Nino; Zanardi, Paolo; Rossi, Fausto
2003-01-01
In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented
The representations of Lie groups and geometric quantizations
International Nuclear Information System (INIS)
Zhao Qiang
1998-01-01
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)
Identifying and Fostering Higher Levels of Geometric Thinking
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Optimization of biotechnological systems through geometric programming
Directory of Open Access Journals (Sweden)
Torres Nestor V
2007-09-01
Full Text Available Abstract Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into
Geometric derivation of the quantum speed limit
International Nuclear Information System (INIS)
Jones, Philip J.; Kok, Pieter
2010-01-01
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
A geometric form of the canonical commutation
International Nuclear Information System (INIS)
Guz, W.
1987-01-01
Some aspects of a geometric approach to quantum theory, in which the quantum-mechanical position and momentum operators are represented by covariant derivatives, are here developed. Here, the previously estabilished formalism of Caianiello and his co-workers is extended to the case of an integrable almost complex Hermitian manifold. The general theory is then applied to the two-dimensional case, where the structure of the 'quantum geometry' induced in the manifold by the quantum-mechanical CCR can be explicitly determined
Geometrical scaling vs factorizable eikonal models
Kiang, D
1975-01-01
Among various theoretical explanations or interpretations for the experimental data on the differential cross-sections of elastic proton-proton scattering at CERN ISR, the following two seem to be most remarkable: A) the excellent agreement of the Chou-Yang model prediction of d sigma /dt with data at square root s=53 GeV, B) the general manifestation of geometrical scaling (GS). The paper confronts GS with eikonal models with factorizable opaqueness, with special emphasis on the Chou-Yang model. (12 refs).
On geometrical splitting in nonanalog Monte Carlo
International Nuclear Information System (INIS)
Lux, I.
1985-01-01
A very general geometrical procedure is considered, and it is shown how the free flights, the statistical weights and the contribution of particles participating in splitting are to be chosen in order to reach unbiased estimates in games where the transition kernels are nonanalog. Equations governing the second moment of the score and the number of flights to be stimulated are derived. It is shown that the post-splitting weights of the fragments are to be chosen equal to reach maximum gain in variance. Conditions are derived under which the expected number of flights remains finite. Simplified example illustrate the optimization of the procedure (author)
Projective geometry for polarization in geometric quantization
International Nuclear Information System (INIS)
Campbell, P.; Dodson, C.T.J.
1976-12-01
It is important to know the extent to which the procedure of geometric quantization depends on a choice of polarization of the symplectic manifold that is the classical phase space. Published results have so far been restricted to real and transversal polarizations. Here we also consider these cases by presenting a formulation in terms of projective geometry. It turns out that there is a natural characterization of real transversal polarizations and maps among them using projective concepts. We give explicit constructions for Rsup(2n)
Irreducible geometric subgroups of classical algebraic groups
Burness, Timothy C; Testerman, Donna M
2016-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p \\ge 0 with natural module W. Let H be a closed subgroup of G and let V be a non-trivial irreducible tensor-indecomposable p-restricted rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where H is a disconnected maximal positive-dimensional closed subgroup of G preserving a natural geometric structure on W.
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
Geometric Algebra Techniques in Flux Compactifications
International Nuclear Information System (INIS)
Coman, Ioana Alexandra; Lazaroiu, Calin Iuliu; Babalic, Elena Mirela
2016-01-01
We study “constrained generalized Killing (s)pinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat N=1 compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature.
Geometric Total Variation for Texture Deformation
DEFF Research Database (Denmark)
Bespalov, Dmitriy; Dahl, Anders Lindbjerg; Shokoufandeh, Ali
2010-01-01
In this work we propose a novel variational method that we intend to use for estimating non-rigid texture deformation. The method is able to capture variation in grayscale images with respect to the geometry of its features. Our experimental evaluations demonstrate that accounting for geometry...... of features in texture images leads to significant improvements in localization of these features, when textures undergo geometrical transformations. Accurate localization of features in the presense of unkown deformations is a crucial property for texture characterization methods, and we intend to expoit...
Universal geometrical module for MARS program
International Nuclear Information System (INIS)
Talanov, V.V.
1992-01-01
Geometrical program module for modeling hadron and electromagnetic cascades, which accomplishes comparison of physical coordinates with the particle current state of one of the auxilliary cells, is described. The whole medium wherein the particles are tracked, is divided into a certain number of auxilliary cells. The identification algorithm of the cell, through which the particle trajectory passes, is considered in detail. The described algorithm for cell identification was developed for the MARS program and realized in form of a set of subprograms written in the FORTRAN language. 4 refs., 1 tab
Geometrical optics model of Mie resonances
Roll; Schweiger
2000-07-01
The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.
On the geometrization of electromagnetism by torsion
International Nuclear Information System (INIS)
Fonseca Neto, J.B. da.
1984-01-01
The possibility of electromagnetism geometrization using an four dimension Cartan geometry is investigated. The Lagrangian density which presents dual invariance for dyons electrodynamics formulated in term of two potentials is constructed. This theory by association of two potentials with track and with torsion pseudo-track and of the field with torsion covariant divergent is described. The minimum coupling of particle gravitational field of scalar and spinorial fields with dyon geometry theory by the minimum coupling of these fields with Cartan geometry was obtained. (author)
Electronic and geometric structures of calcium metaborates
International Nuclear Information System (INIS)
Baranovskij, V.I.; Lopatin, S.I.; Sizov, V.V.
2000-01-01
Calculations of geometric structure, vibration frequencies, ionization potentials and atomization energies of CaBO 2 and CaB 2 O 4 molecules were made. It is shown that linear conformations of the molecules are the most stable ones. In the metaborates studied calcium atom coordination with oxygen is a monodentate one, meanwhile CaB 2 O 4 can be considered as a Ca 2+ compound, whereas CaBO 2 - as a Ca + compound, which explains similarity of the molecule (from the viewpoint of its geometry, spectral and energy characteristics) to alkaline metal metaborates [ru
Geometric and Texture Inpainting by Gibbs Sampling
DEFF Research Database (Denmark)
Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Nielsen, Mads
2007-01-01
. In this paper we use the well-known FRAME (Filters, Random Fields and Maximum Entropy) for inpainting. We introduce a temperature term in the learned FRAME Gibbs distribution. By sampling using different temperature in the FRAME Gibbs distribution, different contents of the image are reconstructed. We propose...... a two step method for inpainting using FRAME. First the geometric structure of the image is reconstructed by sampling from a cooled Gibbs distribution, then the stochastic component is reconstructed by sample froma heated Gibbs distribution. Both steps in the reconstruction process are necessary...
Geometric interpretation of optimal iteration strategies
International Nuclear Information System (INIS)
Jones, R.B.
1977-01-01
The relationship between inner and outer iteration errors is extremely complex, and even formal description of total error behavior is difficult. Inner and outer iteration error propagation is analyzed in a variational formalism for a reactor model describing multidimensional, one-group theory. In a generalization the work of Akimov and Sabek, the number of inner iterations performed during each outer serial that minimizes the total computation time is determined. The generalized analysis admits a geometric interpretation of total error behavior. The results can be applied to both transport and diffusion theory computer methods. 1 figure
Fundamentos de geometría euclidiana
Salazar Salazar, Luis Álvaro
1984-01-01
Este texto no pretende hacer un desfile monótono de definiciones, teoremas, demostraciones o corolarios sino que procurará hacer entender las definiciones, interpretar los enunciados de los principales teoremas y aplicarlos en la solución de algunos problemas. Tampoco se busca negar la importancia de las demostraciones de los teoremas y sus repercusiones en el desarrollo intelectual del lector, teniendo en cuenta que la geometría es la matemática por excelencia, entendiéndose por esto que la...
Femtosecond pulse shaping using the geometric phase.
Gökce, Bilal; Li, Yanming; Escuti, Michael J; Gundogdu, Kenan
2014-03-15
We demonstrate a femtosecond pulse shaper that utilizes polarization gratings to manipulate the geometric phase of an optical pulse. This unique approach enables circular polarization-dependent shaping of femtosecond pulses. As a result, it is possible to create coherent pulse pairs with orthogonal polarizations in a 4f pulse shaper setup, something until now that, to our knowledge, was only achieved via much more complex configurations. This approach could be used to greatly simplify and enhance the functionality of multidimensional spectroscopy and coherent control experiments, in which multiple coherent pulses are used to manipulate quantum states in materials of interest.
Toroidal Precession as a Geometric Phase
Energy Technology Data Exchange (ETDEWEB)
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Moduli stabilization in non-geometric backgrounds
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Vafa, Cumrun; Walcher, Johannes
2007-01-01
Type II orientifolds based on Landau-Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kaehler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as anti-de Sitter vacua. This construction provides the first string vacuum with all moduli frozen and leading to a 4D Minkowski background
In the realm of the geometric transitions
International Nuclear Information System (INIS)
Alexander, Stephon; Becker, Katrin; Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu
2005-01-01
We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kaehler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kaehler (both before and after the transition). On the other hand, the type I and heterotic backgrounds are non-Kaehler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
Geometric phases for mixed states during cyclic evolutions
International Nuclear Information System (INIS)
Fu Libin; Chen Jingling
2004-01-01
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical 1-form is defined whose line integral gives the geometric phase, which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment (Sjoeqvist et al 2000 Phys. Rev. Lett. 85 2845) for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states
Geometric reconstruction methods for electron tomography
Energy Technology Data Exchange (ETDEWEB)
Alpers, Andreas, E-mail: alpers@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching bei München (Germany); Gardner, Richard J., E-mail: Richard.Gardner@wwu.edu [Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063 (United States); König, Stefan, E-mail: koenig@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching bei München (Germany); Pennington, Robert S., E-mail: robert.pennington@uni-ulm.de [Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kongens Lyngby (Denmark); Boothroyd, Chris B., E-mail: ChrisBoothroyd@cantab.net [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Houben, Lothar, E-mail: l.houben@fz-juelich.de [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Dunin-Borkowski, Rafal E., E-mail: rdb@fz-juelich.de [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, D-52425 Jülich (Germany); Joost Batenburg, Kees, E-mail: Joost.Batenburg@cwi.nl [Centrum Wiskunde and Informatica, NL-1098XG, Amsterdam, The Netherlands and Vision Lab, Department of Physics, University of Antwerp, B-2610 Wilrijk (Belgium)
2013-05-15
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire. - Highlights: ► Four algorithms for electron tomography are introduced that utilize prior knowledge. ► Objects are assumed to be homogeneous; convexity and regularity is also discussed. ► We are able to reconstruct slices of a nanowire from as few as four projections. ► Algorithms should be selected based on the specific reconstruction task at hand.
Implicit face prototype learning from geometric information.
Or, Charles C-F; Wilson, Hugh R
2013-04-19
There is evidence that humans implicitly learn an average or prototype of previously studied faces, as the unseen face prototype is falsely recognized as having been learned (Solso & McCarthy, 1981). Here we investigated the extent and nature of face prototype formation where observers' memory was tested after they studied synthetic faces defined purely in geometric terms in a multidimensional face space. We found a strong prototype effect: The basic results showed that the unseen prototype averaged from the studied faces was falsely identified as learned at a rate of 86.3%, whereas individual studied faces were identified correctly 66.3% of the time and the distractors were incorrectly identified as having been learned only 32.4% of the time. This prototype learning lasted at least 1 week. Face prototype learning occurred even when the studied faces were further from the unseen prototype than the median variation in the population. Prototype memory formation was evident in addition to memory formation of studied face exemplars as demonstrated in our models. Additional studies showed that the prototype effect can be generalized across viewpoints, and head shape and internal features separately contribute to prototype formation. Thus, implicit face prototype extraction in a multidimensional space is a very general aspect of geometric face learning. Copyright © 2013 Elsevier Ltd. All rights reserved.
A geometric viewpoint on generalized hydrodynamics
Directory of Open Access Journals (Sweden)
Benjamin Doyon
2018-01-01
Full Text Available Generalized hydrodynamics (GHD is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective (“dressed” velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.
Geometrical effects in X-mode scattering
International Nuclear Information System (INIS)
Bretz, N.
1986-10-01
One technique to extend microwave scattering as a probe of long wavelength density fluctuations in magnetically confined plasmas is to consider the launching and scattering of extraordinary (X-mode) waves nearly perpendicular to the field. When the incident frequency is less than the electron cyclotron frequency, this mode can penetrate beyond the ordinary mode cutoff at the plasma frequency and avoid significant distortions from density gradients typical of tokamak plasmas. In the more familiar case, where the incident and scattered waves are ordinary, the scattering is isotropic perpendicular to the field. However, because the X-mode polarization depends on the frequency ratios and the ray angle to the magnetic field, the coupling between the incident and scattered waves is complicated. This geometrical form factor must be unfolded from the observed scattering in order to interpret the scattering due to density fluctuations alone. The geometrical factor is calculated here for the special case of scattering perpendicular to the magnetic field. For frequencies above the ordinary mode cutoff the scattering is relatively isotropic, while below cutoff there are minima in the forward and backward directions which go to zero at approximately half the ordinary mode cutoff density
Geometrical analysis of cytochrome c unfolding
Urie, Kristopher G.; Pletneva, Ekaterina; Gray, Harry B.; Winkler, Jay R.; Kozak, John J.
2011-01-01
A geometrical model has been developed to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n = 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. The calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, lattice Monte Carlo simulations were performed to study systematically the possible importance of asynchronicity. Calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.
GEOMETRIC AND RADIOMETRIC EVALUATION OF RASAT IMAGES
Directory of Open Access Journals (Sweden)
A. Cam
2016-06-01
Full Text Available RASAT, the second remote sensing satellite of Turkey, was designed and assembled, and also is being operated by TÜBİTAK Uzay (Space Technologies Research Institute (Ankara. RASAT images in various levels are available free-of-charge via Gezgin portal for Turkish citizens. In this paper, the images in panchromatic (7.5 m GSD and RGB (15 m GSD bands in various levels were investigated with respect to its geometric and radiometric characteristics. The first geometric analysis is the estimation of the effective GSD as less than 1 pixel for radiometrically processed level (L1R of both panchromatic and RGB images. Secondly, 2D georeferencing accuracy is estimated by various non-physical transformation models (similarity, 2D affine, polynomial, affine projection, projective, DLT and GCP based RFM reaching sub-pixel accuracy using minimum 39 and maximum 52 GCPs. The radiometric characteristics are also investigated for 8 bits, estimating SNR between 21.8-42.2, and noise 0.0-3.5 for panchromatic and MS images for L1R when the sea is masked to obtain the results for land areas. The analysis show that RASAT images satisfies requirements for various applications. The research is carried out in Zonguldak test site which is mountainous and partly covered by dense forest and urban areas.
Geometric Modelling of Octagonal Lamp Poles
Chan, T. O.; Lichti, D. D.
2014-06-01
Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.
Geometric correction of APEX hyperspectral data
Directory of Open Access Journals (Sweden)
Vreys Kristin
2016-03-01
Full Text Available Hyperspectral imagery originating from airborne sensors is nowadays widely used for the detailed characterization of land surface. The correct mapping of the pixel positions to ground locations largely contributes to the success of the applications. Accurate geometric correction, also referred to as “orthorectification”, is thus an important prerequisite which must be performed prior to using airborne imagery for evaluations like change detection, or mapping or overlaying the imagery with existing data sets or maps. A so-called “ortho-image” provides an accurate representation of the earth’s surface, having been adjusted for lens distortions, camera tilt and topographic relief. In this paper, we describe the different steps in the geometric correction process of APEX hyperspectral data, as applied in the Central Data Processing Center (CDPC at the Flemish Institute for Technological Research (VITO, Mol, Belgium. APEX ortho-images are generated through direct georeferencing of the raw images, thereby making use of sensor interior and exterior orientation data, boresight calibration data and elevation data. They can be referenced to any userspecified output projection system and can be resampled to any output pixel size.
Geometric-optical illusions at isoluminance.
Hamburger, Kai; Hansen, Thorsten; Gegenfurtner, Karl R
2007-12-01
The idea of a largely segregated processing of color and form was initially supported by observations that geometric-optical illusions vanish under isoluminance. However, this finding is inconsistent with some psychophysical studies and also with physiological evidence showing that color and luminance are processed together by largely overlapping sets of neurons in the LGN, in V1, and in extrastriate areas. Here we examined the strength of nine geometric-optical illusions under isoluminance (Delboeuf, Ebbinghaus, Hering, Judd, Müller-Lyer, Poggendorff, Ponzo, Vertical, Zöllner). Subjects interactively manipulated computer-generated line drawings to counteract the illusory effect. In all cases, illusions presented under isoluminance (both for colors drawn from the cardinal L-M or S-(L+M) directions of DKL color space) were as effective as the luminance versions (both for high and low contrast). The magnitudes of the illusion effects were highly correlated across subjects for the different conditions. In two additional experiments we determined that the strong illusions observed under isoluminance were not due to individual deviations from the photometric point of isoluminance or due to chromatic aberrations. Our findings show that our conscious percept is affected similarly for both isoluminance and luminance conditions, suggesting that the joint processing for chromatic and luminance defined contours may extend well beyond early visual areas.
Geometrical basis for the Standard Model
Potter, Franklin
1994-02-01
The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary plane C 2, the quaternion space Q, and the real space R 4—as well as the real space R 3 uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge group SU(2) L × U(1) Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The ( u, d) and ( c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/ c 2, the b' quark at 80 GeV/ c 2, and the t' quark at 2600 GeV/ c 2.
New developments in geometric dynamic recrystallization
International Nuclear Information System (INIS)
Kassner, M.E.; Barrabes, S.R.
2005-01-01
The concept of geometric dynamic recrystallization (GDX) originated in 1980s with work on elevated-temperature deformation aluminum to large strains. In this case, substantial grain refinement occurs through a process of grain elongation and thinning leading to a dramatic increase in grain boundary area. The grain boundaries become serrated as a result of subgrain (low angle) boundary formation. Pinching off and annihilation of high-angle grain boundaries occurs as the original grains thin to about twice the subgrain diameter to and a 'steady-state' structure. This concept has since been carefully verified in pure Al, as well as Al-Mg alloys deforming in the three-power regime. Large strain deformation of Al single crystals is also consistent with the concept. Also, data in the literature on large strain deformation of a bcc iron alloy are consistent with GDX. Recent experiments on α-zirconium show that GDX applies to this hcp metal. Thus, it appears that GDX is a general phenomenon that can lead to grain refinement in the absence of any discontinuous dynamic recrystallization (DRX) or continuous dynamic recrystallization (CDX). A discussion of continuous dynamic recrystallization and geometric necessary boundaries in relation to GDX will also be discussed. This may be particularly relevant to severe plastic deformation such as rolling and equal-channel angular pressing where dramatic increases in the number of high-angle boundaries are observed
Geometric reconstruction methods for electron tomography
International Nuclear Information System (INIS)
Alpers, Andreas; Gardner, Richard J.; König, Stefan; Pennington, Robert S.; Boothroyd, Chris B.; Houben, Lothar; Dunin-Borkowski, Rafal E.; Joost Batenburg, Kees
2013-01-01
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire. - Highlights: ► Four algorithms for electron tomography are introduced that utilize prior knowledge. ► Objects are assumed to be homogeneous; convexity and regularity is also discussed. ► We are able to reconstruct slices of a nanowire from as few as four projections. ► Algorithms should be selected based on the specific reconstruction task at hand
Geometric entanglement in topologically ordered states
International Nuclear Information System (INIS)
Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; Nest, Maarten Van den
2014-01-01
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically ordered systems such as the toric code, double semion, colour code and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks and a contribution quantifying the underlying pattern of long-range entanglement of the topologically ordered state. This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterization of topological order for these quantum states based on a multipartite entanglement measure. In particular, we see that the topological term for the two-dimensional colour code is twice as much as the one for the toric code, in accordance with recent renormalization group arguments (Bombin et al 2012 New J. Phys. 14 073048). Motivated by these results, we also derive a general formalism to obtain upper- and lower-bounds to the geometric entanglement of states with a non-Abelian group symmetry, and which we explicitly use to analyse quantum double models. Furthermore, we also provide an analysis of the robustness of the topological contribution in terms of renormalization and perturbation theory arguments, as well as a numerical estimation for small systems. Some of the results in this paper rely on the ability to disentangle single sites from the quantum state, which is always possible for the systems that we consider. Additionally we relate our results to the behaviour of the relative entropy of entanglement in topologically ordered systems, and discuss a number of numerical approaches based on tensor networks that could be
Modern Geometric Methods of Distance Determination
Thévenin, Frédéric; Falanga, Maurizio; Kuo, Cheng Yu; Pietrzyński, Grzegorz; Yamaguchi, Masaki
2017-11-01
Building a 3D picture of the Universe at any distance is one of the major challenges in astronomy, from the nearby Solar System to distant Quasars and galaxies. This goal has forced astronomers to develop techniques to estimate or to measure the distance of point sources on the sky. While most distance estimates used since the beginning of the 20th century are based on our understanding of the physics of objects of the Universe: stars, galaxies, QSOs, the direct measures of distances are based on the geometric methods as developed in ancient Greece: the parallax, which has been applied to stars for the first time in the mid-19th century. In this review, different techniques of geometrical astrometry applied to various stellar and cosmological (Megamaser) objects are presented. They consist in parallax measurements from ground based equipment or from space missions, but also in the study of binary stars or, as we shall see, of binary systems in distant extragalactic sources using radio telescopes. The Gaia mission will be presented in the context of stellar physics and galactic structure, because this key space mission in astronomy will bring a breakthrough in our understanding of stars, galaxies and the Universe in their nature and evolution with time. Measuring the distance to a star is the starting point for an unbiased description of its physics and the estimate of its fundamental parameters like its age. Applying these studies to candles such as the Cepheids will impact our large distance studies and calibration of other candles. The text is constructed as follows: introducing the parallax concept and measurement, we shall present briefly the Gaia satellite which will be the future base catalogue of stellar astronomy in the near future. Cepheids will be discussed just after to demonstrate the state of the art in distance measurements in the Universe with these variable stars, with the objective of 1% of error in distances that could be applied to our closest
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Gauge field vacuum structure in geometrical aspect
International Nuclear Information System (INIS)
Konopleva, N.P.
2003-01-01
Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations
Geometrical scaling in charm structure function ratios
International Nuclear Information System (INIS)
Boroun, G.R.; Rezaei, B.
2014-01-01
By using a Laplace-transform technique, we solve the next-to-leading-order master equation for charm production and derive a compact formula for the ratio R c =F L cc ¯ /F 2 cc ¯ , which is useful for extracting the charm structure function from the reduced charm cross section, in particular, at DESY HERA, at small x. Our results show that this ratio is independent of x at small x. In this method of determining the ratios, we apply geometrical scaling in charm production in deep inelastic scattering (DIS). Our analysis shows that the renormalization scales have a sizable impact on the ratio R c at high Q 2 . Our results for the ratio of the charm structure functions are in a good agreement with some phenomenological models
On the Distribution of Random Geometric Graphs
DEFF Research Database (Denmark)
Badiu, Mihai Alin; Coon, Justin P.
2018-01-01
as a measure of the graph’s topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution......Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy...... of the n(n − 1)/2 distances between n nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in R 2. This enables the calculation of the probability distribution...
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Geometric covers, graph orientations, counter games
DEFF Research Database (Denmark)
Berglin, Edvin
-directed graph is dynamic (can be altered by some outside actor), some orientations may need to be reversed in order to maintain the low out-degree. We present a new algorithm that is simpler than earlier work, yet matches or outperforms the efficiency of these results with very few exceptions. Counter games...... example is Line Cover, also known as Point-Line Cover, where a set of points in a geometric space are to be covered by placing a restricted number of lines. We present new FPT algorithms for the sub-family Curve Cover (which includes Line Cover), as well as for Hyperplane Cover restricted to R 3 (i...... are a type of abstract game played over a set of counters holding values, and these values may be moved between counters according to some set of rules. Typically they are played between two players: the adversary who tries to concentrate the greatest value possible in a single counter, and the benevolent...
Geometric flows in Horava-Lifshitz gravity
Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios
2010-01-01
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...
Geometric Properties of Grassmannian Frames for and
Directory of Open Access Journals (Sweden)
Benedetto John J
2006-01-01
Full Text Available Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( and into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of specific examples of Grassmannian frames. Many of the results are known by other techniques, and even more generally, so that this paper can be viewed as tutorial. However, our analytic method is presented with the goal of developing it to address unresovled problems in -dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.
Geometric extension through Schwarzschild r = 0
International Nuclear Information System (INIS)
Lynden-Bell, D.; Katz, J.; Hebrew Univ., Jerusalem
1990-01-01
Singularities in space-time are not necessarily cancers in the manifold but can herald interesting topological change in the space-time at places where there are several different tangent Minkowski spaces. Most discussions of gravitational collapse cease when space-time becomes singular. In the 'hour-glass' universe we have an example where the singularity develops in empty space; here we give a geometrical extension through the singularity in which geodesics that enter it emerge into a new space. The result extends Schwarzschild space and is periodic in 'extended' Penrose coordinates. There is a topological singularity but no mass at r = 0. The extension is mildly nonanalytic but unique. It is based on the concept that time does not stop and that empty space-times which develop singularities must still have zero Ricci tensors even where the Riemann tensor becomes infinite. (author)
Time Series Analysis Using Geometric Template Matching.
Frank, Jordan; Mannor, Shie; Pineau, Joelle; Precup, Doina
2013-03-01
We present a novel framework for analyzing univariate time series data. At the heart of the approach is a versatile algorithm for measuring the similarity of two segments of time series called geometric template matching (GeTeM). First, we use GeTeM to compute a similarity measure for clustering and nearest-neighbor classification. Next, we present a semi-supervised learning algorithm that uses the similarity measure with hierarchical clustering in order to improve classification performance when unlabeled training data are available. Finally, we present a boosting framework called TDEBOOST, which uses an ensemble of GeTeM classifiers. TDEBOOST augments the traditional boosting approach with an additional step in which the features used as inputs to the classifier are adapted at each step to improve the training error. We empirically evaluate the proposed approaches on several datasets, such as accelerometer data collected from wearable sensors and ECG data.
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Fluid mechanics a geometrical point of view
Rajeev, S G
2018-01-01
Fluid Mechanics: A Geometrical Point of View emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to fluid mechanics. This follows on from the author's book Advanced Mechanics (Oxford University Press, 2013). After introducing the fundamental equations (Euler and Navier-Stokes), the book provides particular cases: ideal and viscous flows, shocks, boundary layers, instabilities, and transients. A restrained look at integrable systems (KdV) leads into a formulation of an ideal fluid as a hamiltonian system. Arnold's deep idea, that the instability of a fluid can be understood using the curvature of the diffeomorphism group, will be explained. Leray's work on regularity of Navier-Stokes solutions, and the modern developments arising from it, will be explained in language for physicists...
Noncyclic geometric changes of quantum states
International Nuclear Information System (INIS)
Kult, David; Sjoeqvist, Erik; Aaberg, Johan
2006-01-01
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems
Geometrically weighted semiconductor Frisch grid radiation spectrometers
Energy Technology Data Exchange (ETDEWEB)
McGregor, D.S. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Rojeski, R.A. [Etec Systems, Inc., 26460 Corporate Ave., Hayward, CA 94545 (United States); He, Z. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Wehe, D.K. [Dept. of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 (United States); Driver, M. [eV Products, 375 Saxonburg Blvd., Saxonburg, PA 16056 (United States); Blakely, M. [eV Products, 375 Saxonburg Blvd., Saxonburg, PA 16056 (United States)
1999-02-11
A new detector geometry is described with relatively high gamma ray energy resolution at room temperature. The device uses the geometric weighting effect, the small pixel effect and the Frisch grid effect to produce high gamma ray energy resolution. The design is simple and easy to construct. The device performs as a gamma ray spectrometer without the need for pulse shape rejection or correction, and it requires only one signal output to any commercially available charge sensitive preamplifier. The device operates very well with conventional NIM electronic systems. Presently, room temperature (23 deg. C) energy resolutions of 2.68% FWHM at 662 keV and 2.45% FWHM at 1.332 MeV have been measured with a 1 cm{sup 3} prism shaped CdZnTe device.
Hydrodynamical winds from a geometrically thin disk
International Nuclear Information System (INIS)
Fukue, Jun
1989-01-01
Hydrodynamical winds emanating from the surface of a geometrically thin disk under the gravitational field of the central object are examined. The attention is focused on the transonic nature of the flow. For a given configuration of streamlines, the flow fields are divided into three regions: the inner region where the gas near the disk plane is gravitationally bound to form a corona; the intermediate wind region where multiple critical points appear and the gas flows out from the disk passing through critical points; and the outer region where the gas is unbound to escape to infinity without passing through critical points. This behavior of disk winds is due to the shape of the gravitational potential of the central object along the streamline and due to the energy source distribution at the flow base on the disk plane where the potential in finite. (author)
Point- and curve-based geometric conflation
Ló pez-Vá zquez, C.; Manso Callejo, M.A.
2013-01-01
Geometric conflation is the process undertaken to modify the coordinates of features in dataset A in order to match corresponding ones in dataset B. The overwhelming majority of the literature considers the use of points as features to define the transformation. In this article we present a procedure to consider one-dimensional curves also, which are commonly available as Global Navigation Satellite System (GNSS) tracks, routes, coastlines, and so on, in order to define the estimate of the displacements to be applied to each object in A. The procedure involves three steps, including the partial matching of corresponding curves, the computation of some analytical expression, and the addition of a correction term in order to satisfy basic cartographic rules. A numerical example is presented. © 2013 Copyright Taylor and Francis Group, LLC.
Two solvable problems of planar geometrical optics.
Borghero, Francesco; Bozis, George
2006-12-01
In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.
Rayleigh's hypothesis and the geometrical optics limit.
Elfouhaily, Tanos; Hahn, Thomas
2006-09-22
The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... is modeled by means of a scalar non-Gaussian random field, which is represented as a translation process. The underlying Gaussian field is simulated by means of the EOLE method. The second type of imperfections is modeled as a Gaussian vector-valued random field, which is simulated directly by means...... of the EOLE method. In each iteration of the optimization process, the relevant statistics of the structural response are evaluated by means of a Monte Carlo simulation. The proposed methodology is successfully applied to a test problem involving the design of a compliant mechanism (for the first type...
Random geometric graphs with general connection functions
Dettmann, Carl P.; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Geometric regularizations and dual conifold transitions
International Nuclear Information System (INIS)
Landsteiner, Karl; Lazaroiu, Calin I.
2003-01-01
We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach. (author)
Geometrical resonance effects in thin superconducting films
International Nuclear Information System (INIS)
Nedellec, P.
1977-01-01
Electron tunneling density of states measurements on thick and clear superconducting films (S 1 ) backed by films in the normal or superconducting state (S 2 ) show geometrical resonance effects associated with the spatial variation of Δ(x), the pair potential, near the interface S 1 -S 2 . The present understanding of this so-called 'Tomasch effect' is described. The dispersion relation and the nature of excitations in the superconducting state are introduced. It is shown that the introduction of Green functions give a general description of the superconducting state. The notion of Andreev scattering at the S 1 -S 2 interface is presented and connect the geometrical resonance effects to interference process between excitations. The different physical parameters involved are defined and used in the discussion of some experimental results: the variation of the period in energy with the superconducting thickness is connected to the renormalized group velocity of excitations traveling perpendicular to the film. The role of the barrier potential at the interface on the Tomasch effect is described. The main results discussed are: the decrease of the amplitude of the Tomasch structures with energy is due to the loss of the mixed electron-hole character of the superconducting excitations far away from the Fermi level; the variation of the pair potential at the interface is directly related to the amplitude of the oscillations; the tunneling selectivity is an important parameter as the amplitude as well as the phase of the oscillations are modified depending on the value of the selectivity; the phase of the Tomasch oscillations is different for an abrupt change of Δ at the interface and for a smooth variation. An ambiguity arises due to the interplay between these parameters. Finally, some experiments, which illustrate clearly the predicted effects are described [fr
COMPARISON OF METHODS FOR GEOMETRIC CAMERA CALIBRATION
Directory of Open Access Journals (Sweden)
J. Hieronymus
2012-09-01
Full Text Available Methods for geometric calibration of cameras in close-range photogrammetry are established and well investigated. The most common one is based on test-fields with well-known pattern, which are observed from different directions. The parameters of a distortion model are calculated using bundle-block-adjustment-algorithms. This methods works well for short focal lengths, but is essentially more problematic to use with large focal lengths. Those would require very large test-fields and surrounding space. To overcome this problem, there is another common method for calibration used in remote sensing. It employs measurements using collimator and a goniometer. A third calibration method uses diffractive optical elements (DOE to project holograms of well known pattern. In this paper these three calibration methods are compared empirically, especially in terms of accuracy. A camera has been calibrated with those methods mentioned above. All methods provide a set of distortion correction parameters as used by the photogrammetric software Australis. The resulting parameter values are very similar for all investigated methods. The three sets of distortion parameters are crosscompared against all three calibration methods. This is achieved by inserting the gained distortion parameters as fixed input into the calibration algorithms and only adjusting the exterior orientation. The RMS (root mean square of the remaining image coordinate residuals are taken as a measure of distortion correction quality. There are differences resulting from the different calibration methods. Nevertheless the measure is small for every comparison, which means that all three calibration methods can be used for accurate geometric calibration.
A Geometric Representation of Collective Attention Flows.
Directory of Open Access Journals (Sweden)
Peiteng Shi
Full Text Available With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery. 20% popular sites (Google.com, Myspace.com, Facebook.com, etc. attracting 75% attention flows with only 55% dissipations (log off users locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
A Geometric Representation of Collective Attention Flows.
Shi, Peiteng; Huang, Xiaohan; Wang, Jun; Zhang, Jiang; Deng, Su; Wu, Yahui
2015-01-01
With the fast development of Internet and WWW, "information overload" has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery). 20% popular sites (Google.com, Myspace.com, Facebook.com, etc.) attracting 75% attention flows with only 55% dissipations (log off users) locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by "S"-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation.
Advances on geometric flux optical design method
García-Botella, Ángel; Fernández-Balbuena, Antonio Álvarez; Vázquez, Daniel
2017-09-01
Nonimaging optics is focused on the study of methods to design concentrators or illuminators systems. It can be included in the area of photometry and radiometry and it is governed by the laws of geometrical optics. The field vector method, which starts with the definition of the irradiance vector E, is one of the techniques used in nonimaging optics. Called "Geometrical flux vector" it has provide ideal designs. The main property of this model is, its ability to estimate how radiant energy is transferred by the optical system, from the concepts of field line, flux tube and pseudopotential surface, overcoming traditional raytrace methods. Nevertheless this model has been developed only at an academic level, where characteristic optical parameters are ideal not real and the studied geometries are simple. The main objective of the present paper is the application of the vector field method to the analysis and design of real concentration and illumination systems. We propose the development of a calculation tool for optical simulations by vector field, using algorithms based on Fermat`s principle, as an alternative to traditional tools for optical simulations by raytrace, based on reflection and refraction law. This new tool provides, first, traditional simulations results: efficiency, illuminance/irradiance calculations, angular distribution of light- with lower computation time, photometrical information needs about a few tens of field lines, in comparison with million rays needed nowadays. On the other hand the tool will provides new information as vector field maps produced by the system, composed by field lines and quasipotential surfaces. We show our first results with the vector field simulation tool.
Geometric Phases for Mixed States in Trapped Ions
International Nuclear Information System (INIS)
Lu Hongxia
2006-01-01
The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover, special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.
Forward error correction based on algebraic-geometric theory
A Alzubi, Jafar; M Chen, Thomas
2014-01-01
This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.
The Spacetime Memory of Geometric Phases and Quantum Computing
Binder, B
2002-01-01
Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.
Geometric convergence of some two-point Pade approximations
International Nuclear Information System (INIS)
Nemeth, G.
1983-01-01
The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)
Geometrical intuition and the learning and teaching of geometry
Fujita, Taro; Jones, Keith; Yamamoto, Shinya
2004-01-01
Intuition is often regarded as essential in the learning of geometry, but how such skills might be effectively developed in students remains an open question. This paper reviews the role and importance of geometrical intuition and suggests it involves the skills to create and manipulate geometrical figures in the mind, to see geometrical properties, to relate images to concepts and theorems in geometry, and decide where and how to start when solving problems in geometry. Based on these theore...
From the geometric quantization to conformal field theory
International Nuclear Information System (INIS)
Alekseev, A.; Shatashvili, S.
1990-01-01
Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant) r-matrices and this geometrical approach. (orig.)
A Color Image Watermarking Scheme Resistant against Geometrical Attacks
Directory of Open Access Journals (Sweden)
Y. Xing
2010-04-01
Full Text Available The geometrical attacks are still a problem for many digital watermarking algorithms at present. In this paper, we propose a watermarking algorithm for color images resistant to geometrical distortions (rotation and scaling. The singular value decomposition is used for watermark embedding and extraction. The log-polar map- ping (LPM and phase correlation method are used to register the position of geometrical distortion suffered by the watermarked image. Experiments with different kinds of color images and watermarks demonstrate that the watermarking algorithm is robust to common image processing attacks, especially geometrical attacks.
Geometric phases for nonlinear coherent and squeezed states
International Nuclear Information System (INIS)
Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin
2011-01-01
The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.
International Nuclear Information System (INIS)
Horn, Martin Erik
2014-01-01
It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics
Efficient Geometric Sound Propagation Using Visibility Culling
Chandak, Anish
2011-07-01
Simulating propagation of sound can improve the sense of realism in interactive applications such as video games and can lead to better designs in engineering applications such as architectural acoustics. In this thesis, we present geometric sound propagation techniques which are faster than prior methods and map well to upcoming parallel multi-core CPUs. We model specular reflections by using the image-source method and model finite-edge diffraction by using the well-known Biot-Tolstoy-Medwin (BTM) model. We accelerate the computation of specular reflections by applying novel visibility algorithms, FastV and AD-Frustum, which compute visibility from a point. We accelerate finite-edge diffraction modeling by applying a novel visibility algorithm which computes visibility from a region. Our visibility algorithms are based on frustum tracing and exploit recent advances in fast ray-hierarchy intersections, data-parallel computations, and scalable, multi-core algorithms. The AD-Frustum algorithm adapts its computation to the scene complexity and allows small errors in computing specular reflection paths for higher computational efficiency. FastV and our visibility algorithm from a region are general, object-space, conservative visibility algorithms that together significantly reduce the number of image sources compared to other techniques while preserving the same accuracy. Our geometric propagation algorithms are an order of magnitude faster than prior approaches for modeling specular reflections and two to ten times faster for modeling finite-edge diffraction. Our algorithms are interactive, scale almost linearly on multi-core CPUs, and can handle large, complex, and dynamic scenes. We also compare the accuracy of our sound propagation algorithms with other methods. Once sound propagation is performed, it is desirable to listen to the propagated sound in interactive and engineering applications. We can generate smooth, artifact-free output audio signals by applying
Klapa, Przemyslaw; Mitka, Bartosz; Zygmunt, Mariusz
2017-12-01
Capability of obtaining a multimillion point cloud in a very short time has made the Terrestrial Laser Scanning (TLS) a widely used tool in many fields of science and technology. The TLS accuracy matches traditional devices used in land surveying (tacheometry, GNSS - RTK), but like any measurement it is burdened with error which affects the precise identification of objects based on their image in the form of a point cloud. The point’s coordinates are determined indirectly by means of measuring the angles and calculating the time of travel of the electromagnetic wave. Each such component has a measurement error which is translated into the final result. The XYZ coordinates of a measuring point are determined with some uncertainty and the very accuracy of determining these coordinates is reduced as the distance to the instrument increases. The paper presents the results of examination of geometrical stability of a point cloud obtained by means terrestrial laser scanner and accuracy evaluation of solids determined using the cloud. Leica P40 scanner and two different settings of measuring points were used in the tests. The first concept involved placing a few balls in the field and then scanning them from various sides at similar distances. The second part of measurement involved placing balls and scanning them a few times from one side but at varying distances from the instrument to the object. Each measurement encompassed a scan of the object with automatic determination of its position and geometry. The desk studies involved a semiautomatic fitting of solids and measurement of their geometrical elements, and comparison of parameters that determine their geometry and location in space. The differences of measures of geometrical elements of balls and translations vectors of the solids centres indicate the geometrical changes of the point cloud depending on the scanning distance and parameters. The results indicate the changes in the geometry of scanned objects
OSCILLATING FILAMENTS. I. OSCILLATION AND GEOMETRICAL FRAGMENTATION
Energy Technology Data Exchange (ETDEWEB)
Gritschneder, Matthias; Heigl, Stefan; Burkert, Andreas, E-mail: gritschm@usm.uni-muenchen.de [University Observatory Munich, LMU Munich, Scheinerstrasse 1, D-81679 Munich (Germany)
2017-01-10
We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid-based AMR code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if the cylinder is bent, such as with a slight sinusoidal perturbation, an otherwise stable configuration starts to oscillate, is triggered into fragmentation, and collapses. This previously unstudied behavior allows a filament to fragment at any given scale, as long as it has slight bends. We call this process “geometrical fragmentation.” In our realization, the spacing between the cores matches the wavelength of the sinusoidal perturbation, whereas up to now, filaments were thought to be only fragmenting on the characteristic scale set by the mass-to-line ratio. Using first principles, we derive the oscillation period as well as the collapse timescale analytically. To enable a direct comparison with observations, we study the line-of-sight velocity for different inclinations. We show that the overall oscillation pattern can hide the infall signature of cores.
Exploring Eucladoceros ecomorphology using geometric morphometrics.
Curran, Sabrina C
2015-01-01
An increasingly common method for reconstructing paleoenvironmental parameters of hominin sites is ecological functional morphology (ecomorphology). This study provides a geometric morphometric study of cervid rearlimb morphology as it relates to phylogeny, size, and ecomorphology. These methods are then applied to an extinct Pleistocene cervid, Eucladoceros, which is found in some of the earliest hominin-occupied sites in Eurasia. Variation in cervid postcranial functional morphology associated with different habitats can be summarized as trade-offs between joint stability versus mobility and rapid movement versus power-generation. Cervids in open habitats emphasize limb stability to avoid joint dislocation during rapid flight from predators. Closed-adapted cervids require more joint mobility to rapidly switch directions in complex habitats. Two skeletal features (of the tibia and calcaneus) have significant phylogenetic signals, while two (the femur and third phalanx) do not. Additionally, morphology of two of these features (tibia and third phalanx) were correlated with body size. For the tibial analysis (but not the third phalanx) this correlation was ameliorated when phylogeny was taken into account. Eucladoceros specimens from France and Romania fall on the more open side of the habitat continuum, a result that is at odds with reconstructions of their diet as browsers, suggesting that they may have had a behavioral regime unlike any extant cervid. © 2014 Wiley Periodicals, Inc.
Optimization of Gad Pattern with Geometrical Weight
International Nuclear Information System (INIS)
Chang, Do Ik; Woo, Hae Seuk; Choi, Seong Min
2009-01-01
The prevailing burnable absorber for domestic nuclear power plants is a gad fuel rod which is used for the partial control of excess reactivity and power peaking. The radial peaking factor, which is one of the critical constraints for the plant safety depends largely on the number of gad bearing rods and the location of gad rods within fuel assembly. Also the concentration of gad, UO 2 enrichment in the gad fuel rod, and fuel lattice type play important roles for the resultant radial power peaking. Since fuel is upgraded periodically and longer fuel cycle management requires more burnable absorbers or higher gad weight percent, it is required frequently to search for the optimized gad patterns, i.e., the distribution of gad fuel rods within assembly, for the various fuel environment and fuel management changes. In this study, the gad pattern optimization algorithm with respect to radial power peaking factor using geometrical weight is proposed for a single gad weight percent, in which the candidates of the optimized gad pattern are determined based on the weighting of the gad rod location and the guide tube. Also the pattern evaluation is performed systematically to determine the optimal gad pattern for the various situation
Geometrical optimization of the dense plasma focus
International Nuclear Information System (INIS)
Lee, S.; Chen, Y.H.
1982-01-01
A 12 kJ DPF device with a periodic time of 12μsec, UMDPF1 has been optimized geometrically to produce a higher neutron yield of 1.5x10 9 at 10 torr filling pressure than from the same device before optimization. With the same optimization procedure a faster DPF device with a periodic time of 3.7μsec, UMDPF2, of the same energy has also been optimized to give a peak neutron yield of 6.3x10 9 at 16 torr filling pressure. Experimental evidence shows that over and above the increase in neutron production due to an increase in current according to the Isup(3.3) scaling law, a faster current rise time may have an additional effect of enhancement in neutron production. The outcome of this project is that a new high pressure regime of 16 torr with an enhanced neutron yield of 6.3x10 9 and improved yield reproducibility for an input energy of 12 kJ has thus been established. There is every reason to believe that this optimization procedure can be extended to other DPF devices. (author)
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations
Geometric Model of a Coronal Cavity
Kucera, Therese A.; Gibson, S. E.; Ratawicki, D.; Dove, J.; deToma, G.; Hao, J.; Hudson, H. S.; Marque, C.; McIntosh, P. S.; Reeves, K. K.;
2010-01-01
We observed a coronal cavity from August 8-18 2007 during a multi-instrument observing campaign organized under the auspices of the International Heliophysical Year (IHY). Here we present initial efforts to model the cavity with a geometrical streamer-cavity model. The model is based the white-light streamer mode] of Gibson et a]. (2003 ), which has been enhanced by the addition of a cavity and the capability to model EUV and X-ray emission. The cavity is modeled with an elliptical cross-section and Gaussian fall-off in length and width inside the streamer. Density and temperature can be varied in the streamer and cavity and constrained via comparison with data. Although this model is purely morphological, it allows for three-dimensional, multi-temperature analysis and characterization of the data, which can then provide constraints for future physical modeling. Initial comparisons to STEREO/EUVI images of the cavity and streamer show that the model can provide a good fit to the data. This work is part of the effort of the International Space Science Institute International Team on Prominence Cavities
Geometrically based optimization for extracranial radiosurgery
International Nuclear Information System (INIS)
Liu Ruiguo; Wagner, Thomas H; Buatti, John M; Modrick, Joseph; Dill, John; Meeks, Sanford L
2004-01-01
For static beam conformal intracranial radiosurgery, geometry of the beam arrangement dominates overall dose distribution. Maximizing beam separation in three dimensions decreases beam overlap, thus maximizing dose conformality and gradient outside of the target volume. Webb proposed arrangements of isotropically convergent beams that could be used as the starting point for a radiotherapy optimization process. We have developed an extracranial radiosurgery optimization method by extending Webb's isotropic beam arrangements to deliverable beam arrangements. This method uses an arrangement of N maximally separated converging vectors within the space available for beam delivery. Each bouquet of isotropic beam vectors is generated by a random sampling process that iteratively maximizes beam separation. Next, beam arrangement is optimized for critical structure avoidance while maintaining minimal overlap between beam entrance and exit pathways. This geometrically optimized beam set can then be used as a template for either conformal beam or intensity modulated extracranial radiosurgery. Preliminary results suggest that using this technique with conformal beam planning provides high plan conformality, a steep dose gradient outside of the tumour volume and acceptable critical structure avoidance in the majority of clinical cases
Geometrical properties of a 'snowflake' divertor
International Nuclear Information System (INIS)
Ryutov, D. D.
2007-01-01
Using a simple set of poloidal field coils, one can reach the situation in which the null of the poloidal magnetic field in the divertor region is of second order, not of first order as in the usual X-point divertor. Then, the separatrix in the vicinity of the null point splits the poloidal plane not into four sectors, but into six sectors, making the whole structure look like a snowflake (hence the name). This arrangement allows one to spread the heat load over a much broader area than in the case of a standard divertor. A disadvantage of this configuration is that it is topologically unstable, and, with the current in the plasma varying with time, it would switch either to the standard X-point mode, or to the mode with two X-points close to each other. To avoid this problem, it is suggested to have a current in the divertor coils that is roughly 5% higher than in an ''optimum'' regime (the one in which a snowflake separatrix is formed). In this mode, the configuration becomes stable and can be controlled by varying the current in the divertor coils in concert with the plasma current; on the other hand, a strong flaring of the scrape-off layer still remains in force. Geometrical properties of this configuration are analyzed. Potential advantages and disadvantages of this scheme are discussed
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V.
2016-01-01
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometric effects of ICMEs on geomagnetic storms
Cho, KyungSuk; Lee, Jae-Ok
2017-04-01
It has been known that the geomagnetic storm is occurred by the interaction between the Interplanetary Coronal Mass Ejection (ICME) and the Earth's magnetosphere; especially, the southward Bz component of ICME is thought as the main trigger. In this study, we investigate the relationship between Dst index and solar wind conditions; which are the southward Bz, electric field (VBz), and time integral of electric field as well as ICME parameters derived from toroidal fitting model in order to find what is main factor to the geomagnetic storm. We also inspect locations of Earth in ICMEs to understand the geometric effects of the Interplanetary Flux Ropes (IFRs) on the geomagnetic storms. Among 59 CDAW ICME lists, we select 30 IFR events that are available by the toroidal fitting model and classify them into two sub-groups: geomagnetic storms associated with the Magnetic Clouds (MCs) and the compression regions ahead of the MCs (sheath). The main results are as follows: (1) The time integral of electric field has a higher correlation coefficient (cc) with Dst index than the other parameters: cc=0.85 for 25 MC events and cc=0.99 for 5 sheath events. (2) The sheath associated intense storms (Dst ≤-100nT) having usually occur at flank regions of ICMEs while the MC associated intense storms occur regardless of the locations of the Earth in ICMEs. The strength of a geomagnetic storm strongly depends on electric field of IFR and durations of the IFR passages through the Earth.
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Geometric investigation of a gaming active device
Menna, Fabio; Remondino, Fabio; Battisti, Roberto; Nocerino, Erica
2011-07-01
3D imaging systems are widely available and used for surveying, modeling and entertainment applications, but clear statements regarding their characteristics, performances and limitations are still missing. The VDI/VDE and the ASTME57 committees are trying to set some standards but the commercial market is not reacting properly. Since many new users are approaching these 3D recording methodologies, clear statements and information clarifying if a package or system satisfies certain requirements before investing are fundamental for those users who are not really familiar with these technologies. Recently small and portable consumer-grade active sensors came on the market, like TOF rangeimaging cameras or low-cost triangulation-based range sensor. A quite interesting active system was produced by PrimeSense and launched on the market thanks to the Microsoft Xbox project with the name of Kinect. The article reports the geometric investigation of the Kinect active sensors, considering its measurement performances, the accuracy of the retrieved range data and the possibility to use it for 3D modeling application.
GEOMETRICAL CHARACTERIZATION OF MICRO END MILLING TOOLS
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo
The milling process is one of the most common metal removal operation used in industry. This machining process is well known since the beginning of last century and has experienced, along the years, many improvements of the basic technology, as concerns tools, machine tools, coolants/lubricants, ......The milling process is one of the most common metal removal operation used in industry. This machining process is well known since the beginning of last century and has experienced, along the years, many improvements of the basic technology, as concerns tools, machine tools, coolants....../lubricants, milling strategies and controls. Moreover the accuracy of tool geometry directly affects the performance of the milling process influencing the dimensional tolerances of the machined part, the surface topography, the chip formation, the cutting forces and the tool-life. The dimensions of certain...... geometrical details, as for instance the cutting edge radius, are determined by characteristics of the manufacturing process, tool material, coating etc. While for conventional size end mills the basic tool manufacturing process is well established, the reduction of the size of the tools required...
Mathematical methods in geometrization of coal field
Shurygin, D. N.; Kalinchenko, V. M.; Tkachev, V. A.; Tretyak, A. Ya
2017-10-01
In the work, the approach to increase overall performance of collieries on the basis of an increase in accuracy of geometrization of coal thicknesses is considered. The sequence of stages of mathematical modelling of spatial placing of indicators of a deposit taking into account allocation of homogeneous sites of thickness and an establishment of quantitative interrelations between mountain-geological indicators of coal layers is offered. As a uniform mathematical method for modelling of various interrelations, it is offered to use a method of the group accounting of arguments (MGUA), one of versions of the regressive analysis. This approach can find application during delimitation between geological homogeneous sites of coal thicknesses in the form of a linear discriminant function. By an example of division into districts of a mine field in the conditions of mine “Sadkinsky” (East Donbass), the use of the complex approach for forecasting of zones of the small amplitude of disturbance of a coal layer on the basis of the discriminant analysis and MGUA is shown.
A geometrical interpretation of renormalisation group flow
International Nuclear Information System (INIS)
Dolan, B.P.
1993-05-01
The renormalisation group (RG) equation in D-dimensional Euclidean space, R D , is analysed from a geometrical point of view. A general form of the RG equation is derived which is applicable to composite operators as well tensor operators (on R D ) which may depend on the Euclidean metric. It is argued that physical N-point amplitudes should be interpreted as rank N co-variant tensors on the space of couplings, G, and that the RG equation can be viewed as an equation for Lie transport on G with respect to the vector field generated by the β-functions of the theory. In one sense it is nothing more than the definition of a Lie derivative. The source of the anomalous dimensions can be interpreted as being due to the change of the basis vectors on G under Lie transport. The RG equation acts as a bridge between Euclidean space and coupling constant space in that the effect on amplitudes of a diffeomorphism of R D (that of dilations) is completely equivalent to a diffeomorphism of G generated by the β-functions of the theory. A form of the RG equation for operators is also given. These ideas are developed in detail for the example of massive λΦ 4 theory in 4 dimensions. (orig.)
Cepheids Geometrical Distances Using Space Interferometry
Marengo, M.; Karovska, M.; Sasselov, D. D.; Sanchez, M.
2004-05-01
A space based interferometer with a sub-milliarcsecond resolution in the UV-optical will provide a new avenue for the calibration of primary distance indicators with unprecedented accuracy, by allowing very accurate and stable measurements of Cepheids pulsation amplitudes at wavelengths not accessible from the ground. Sasselov & Karovska (1994) have shown that interferometers allow very accurate measurements of Cepheids distances by using a ``geometric'' variant of the Baade-Wesselink method. This method has been succesfully applied to derive distances and radii of nearby Cepheids using ground-based near-IR and optical interferometers, within a 15% accuracy level. Our study shows that the main source of error in these measurements is due to the perturbing effects of the Earth atmosphere, which is the limiting factor in the interferometer stability. A space interferometer will not suffer from this intrinsic limitations, and can potentially lead to improve astronomical distance measurements by an order of magnitude in precision. We discuss here the technical requirements that a space based facility will need to carry out this project, allowing distance measurements within a few percent accuracy level. We will finally discuss how a sub-milliarcsecond resolution will allow the direct distance determination for hundreds of galactic sources, and provide a substantial improvement in the zero-point of the Cepheid distance scale.
Geometric modeling for computer aided design
Schwing, James L.; Olariu, Stephen
1995-01-01
The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes.
Digital polarization holography advancing geometrical phase optics.
De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R
2016-08-08
Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed.
Austerity and geometric structure of field theories
International Nuclear Information System (INIS)
Kheyfets, A.
1986-01-01
The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories
Geometric Methods in Physics : XXXIII Workshop
Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore
2015-01-01
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and m...
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometric Methods in Physics : XXXII Workshop
Bieliavsky, Pierre; Odesskii, Alexander; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore; Geometric Methods in Physics
2014-01-01
The Białowieża Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Białowieża natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100 participants from both the mathematics and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work was supplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, and on this occasion the discussion mainly focused on his contributions to mathematical physics such as ...
Geometrical Determinants of Neuronal Actin Waves.
Tomba, Caterina; Braïni, Céline; Bugnicourt, Ghislain; Cohen, Floriane; Friedrich, Benjamin M; Gov, Nir S; Villard, Catherine
2017-01-01
Hippocampal neurons produce in their early stages of growth propagative, actin-rich dynamical structures called actin waves. The directional motion of actin waves from the soma to the tip of neuronal extensions has been associated with net forward growth, and ultimately with the specification of neurites into axon and dendrites. Here, geometrical cues are used to control actin wave dynamics by constraining neurons on adhesive stripes of various widths. A key observable, the average time between the production of consecutive actin waves, or mean inter-wave interval (IWI), was identified. It scales with the neurite width, and more precisely with the width of the proximal segment close to the soma. In addition, the IWI is independent of the total number of neurites. These two results suggest a mechanistic model of actin wave production, by which the material conveyed by actin waves is assembled in the soma until it reaches the threshold leading to the initiation and propagation of a new actin wave. Based on these observations, we formulate a predictive theoretical description of actin wave-driven neuronal growth and polarization, which consistently accounts for different sets of experiments.
Induced subgraph searching for geometric model fitting
Xiao, Fan; Xiao, Guobao; Yan, Yan; Wang, Xing; Wang, Hanzi
2017-11-01
In this paper, we propose a novel model fitting method based on graphs to fit and segment multiple-structure data. In the graph constructed on data, each model instance is represented as an induced subgraph. Following the idea of pursuing the maximum consensus, the multiple geometric model fitting problem is formulated as searching for a set of induced subgraphs including the maximum union set of vertices. After the generation and refinement of the induced subgraphs that represent the model hypotheses, the searching process is conducted on the "qualified" subgraphs. Multiple model instances can be simultaneously estimated by solving a converted problem. Then, we introduce the energy evaluation function to determine the number of model instances in data. The proposed method is able to effectively estimate the number and the parameters of model instances in data severely corrupted by outliers and noises. Experimental results on synthetic data and real images validate the favorable performance of the proposed method compared with several state-of-the-art fitting methods.
A new Weyl-like tensor of geometric origin
Vishwakarma, Ram Gopal
2018-04-01
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.
Multiscale Path Metrics for the Analysis of Discrete Geometric Structures
2017-11-30
Report: Multiscale Path Metrics for the Analysis of Discrete Geometric Structures The views, opinions and/or findings contained in this report are those...Analysis of Discrete Geometric Structures Report Term: 0-Other Email: tomasi@cs.duke.edu Distribution Statement: 1-Approved for public release
Aspects of random geometric graphs : Pursuit-evasion and treewidth
Li, A.
2015-01-01
In this thesis, we studied two aspects of random geometric graphs: pursuit-evasion and treewidth. We first studied one pursuit-evasion game: Cops and Robbers. This game, which dates back to 1970s, are studied extensively in recent years. We investigate this game on random geometric graphs, and get
Geometric calculus: a new computational tool for Riemannian geometry
International Nuclear Information System (INIS)
Moussiaux, A.; Tombal, P.
1988-01-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus
Geometric Aspects of Quantum Mechanics and Quantum Entanglement
International Nuclear Information System (INIS)
Chruscinski, Dariusz
2006-01-01
It is shown that the standard non-relativistic Quantum Mechanics gives rise to elegant and rich geometrical structures. The space of quantum states is endowed with nontrivial Fubini-Study metric which is responsible for the 'peculiarities' of the quantum world. We show that there is also intricate connection between geometrical structures and quantum entanglement
Off-Diagonal Geometric Phase in a Neutron Interferometer Experiment
International Nuclear Information System (INIS)
Hasegawa, Y.; Loidl, R.; Baron, M.; Badurek, G.; Rauch, H.
2001-01-01
Off-diagonal geometric phases acquired by an evolution of a 1/2 -spin system have been observed by means of a polarized neutron interferometer. We have successfully measured the off-diagonal phase for noncyclic evolutions even when the diagonal geometric phase is undefined. Our data confirm theoretical predictions and the results illustrate the significance of the off-diagonal phase
A fast method for linear waves based on geometrical optics
Stolk, C.C.
2009-01-01
We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the
Calculation of the geometrical intensity on an image surface
International Nuclear Information System (INIS)
Seppala, L.G.
1975-01-01
Laser fusion experiments involve the focusing of high power laser beams onto fuel pellets. The geometrical intensity is of interest in the cases where the laser is focused to the center of the pellet. Analytic expressions and ray trace methods for evaluating the geometrical intensity are presented
A Framework for Assessing Reading Comprehension of Geometric Construction Texts
Yang, Kai-Lin; Li, Jian-Lin
2018-01-01
This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three…
Active Learning Environment with Lenses in Geometric Optics
Tural, Güner
2015-01-01
Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…
Geometric control theory and sub-Riemannian geometry
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.
GEOMETRICAL PARAMETERS OF EGGS IN BIRD SYSTEMATICS
Directory of Open Access Journals (Sweden)
I. S. Mityay
2014-12-01
Full Text Available Our ideas are based on the following assumptions. Egg as a standalone system is formed within another system, which is the body of the female. Both systems are implemented on the basis of a common genetic code. In this regard, for example, the dendrogram constructed by morphological criteria eggs should be approximately equal to those constructed by other molecular or morphological criteria adult birds. It should be noted that the dendrogram show only the degree of genetic similarity of taxa, therefore, the identity of materials depends on the number of analyzed criteria and their quality, ie, they should be the backbone. The greater the number of system-features will be included in the analysis and in one other case, the like are dendrogram. In other cases, we will have a fragmentary similarity, which is also very important when dealing with controversial issues. The main message of our research was to figure out the eligibility of usage the morphological characteristics of eggs as additional information in taxonomy and phylogeny of birds. Our studies show that the shape parameters of bird eggs show a stable attachment to certain types of birds and complex traits are species-specific. Dendrogram and diagrams built by the quantitative value of these signs, exhibit significant similarity with the dendrogram constructed by morphological, comparative anatomy, paleontology and molecular criteria for adult birds. This suggests the possibility of using morphological parameters eggs as additional information in dealing with taxonomy and phylogeny of birds. Keywords: oology, geometrical parameters of eggs, bird systematics
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism
Geometrization and Generalization of the Kowalevski Top
Dragović, Vladimir
2010-08-01
A new view on the Kowalevski top and the Kowalevski integration procedure is presented. For more than a century, the Kowalevski 1889 case, has attracted full attention of a wide community as the highlight of the classical theory of integrable systems. Despite hundreds of papers on the subject, the Kowalevski integration is still understood as a magic recipe, an unbelievable sequence of skillful tricks, unexpected identities and smart changes of variables. The novelty of our present approach is based on our four observations. The first one is that the so-called fundamental Kowalevski equation is an instance of a pencil equation of the theory of conics which leads us to a new geometric interpretation of the Kowalevski variables w, x 1, x 2 as the pencil parameter and the Darboux coordinates, respectively. The second is observation of the key algebraic property of the pencil equation which is followed by introduction and study of a new class of discriminantly separable polynomials. All steps of the Kowalevski integration procedure are now derived as easy and transparent logical consequences of our theory of discriminantly separable polynomials. The third observation connects the Kowalevski integration and the pencil equation with the theory of multi-valued groups. The Kowalevski change of variables is now recognized as an example of a two-valued group operation and its action. The final observation is surprising equivalence of the associativity of the two-valued group operation and its action to the n = 3 case of the Great Poncelet Theorem for pencils of conics.
Geometrical charged-particle optics. 2. ed.
International Nuclear Information System (INIS)
Rose, Harald
2013-01-01
Provides a unique theoretical treatment of charged-particle optics. Displays novel unpublished results on several topics. Provides insight into the properties of charged-particle devices. Treats wave optical properties of the electron. Presents the resolution limit of electron microscopes and novel theoretical treatment of the Stern-Gerlach effect. This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern
On orbifold criteria for symplectic toric quotients
DEFF Research Database (Denmark)
Farsi, Carla; Herbig, Hans-Christian; Seaton, Christopher
2013-01-01
We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic...
Geometric constructions for repulsive gravity and quantization
International Nuclear Information System (INIS)
Hohmann, Manuel
2010-11-01
In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite
Geometric constructions for repulsive gravity and quantization
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel
2010-11-15
In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis we propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite
Colors and geometric forms in the work process information coding
Directory of Open Access Journals (Sweden)
Čizmić Svetlana
2006-01-01
Full Text Available The aim of the research was to establish the meaning of the colors and geometric shapes in transmitting information in the work process. The sample of 100 students connected 50 situations which could be associated with regular tasks in the work process with 12 colors and 4 geometric forms in previously chosen color. Based on chosen color-geometric shape-situation regulation, the idea of the research was to find out regularities in coding of information and to examine if those regularities can provide meaningful data assigned to each individual code and to explain which codes are better and applicable represents of examined situations.
Quantum renormalization group approach to geometric phases in spin chains
International Nuclear Information System (INIS)
Jafari, R.
2013-01-01
A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size
Observation of the geometric phase using photon echoes
International Nuclear Information System (INIS)
Tian, Mingzhen; Reibel, Randy R.; Barber, Zeb W.; Fischer, Joe A.; Babbitt, Wm. Randall
2003-01-01
The geometric phase of an atomic system has been observed in V-type three-level barium atoms using photon echoes. The geometric phase results from a cyclic evolution of a two-level subsystem driven by a laser pulse. The phase change is observed on the echo field produced on a different subsystem that is coupled via the ground state to the driven subsystem. The measured geometric phase was half of the solid angle subtended by the Bloch vector along the driven evolution circuit. This evolution has the potential to form universal operations of quantum bits
Implementation and efficiency of two geometric stiffening approaches
International Nuclear Information System (INIS)
Lugris, Urbano; Naya, Miguel A.; Perez, Jose A.; Cuadrado, Javier
2008-01-01
When the modeling of flexible bodies is required in multibody systems, the floating frame of reference formulations are probably the most efficient methods available. In the case of beams undergoing high speed rotations, the geometric stiffening effect can appear due to geometric nonlinearities, and it is often not captured by the aforementioned methods, since it is common to linearize the elastic forces assuming small deformations. The present work discusses the implementation of different existing methods developed to consider such geometric nonlinearities within a floating frame of reference formulation in natural coordinates, making emphasis on the relation between efficiency and accuracy of the resulting algorithms, seeking to provide practical criteria of use
Geometric phase of neutrinos: Differences between Dirac and Majorana neutrinos
Capolupo, A.; Giampaolo, S. M.; Hiesmayr, B. C.; Vitiello, G.
2018-05-01
We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental parameters in our formulas in order to make contact with experiments. Although it remains an open question how the geometric phase of neutrinos could be detected, our theoretical results may open new scenarios in the investigation of the neutrino nature.
Geometric transitions, flops and non-Kahler manifolds: I
International Nuclear Information System (INIS)
Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu
2004-01-01
We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over non-Kahler manifolds is presented
Proof in geometry with "mistakes in geometric proofs"
Fetisov, A I
2006-01-01
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Multipartite geometric entanglement in finite size XY model
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Giampaolo, Salvatore Marco; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
We investigate the behavior of the multipartite entanglement in the finite size XY model by means of the hierarchical geometric measure of entanglement. By selecting specific components of the hierarchy, we study both global entanglement and genuinely multipartite entanglement.
The geometrical theory of diffraction for axially symmetric reflectors
DEFF Research Database (Denmark)
Rusch, W.; Sørensen, O.
1975-01-01
The geometrical theory of diffraction (GTD) (cf. [1], for example) may be applied advantageously to many axially symmetric reflector antenna geometries. The material in this communication presents analytical, computational, and experimental results for commonly encountered reflector geometries...
Remarks on the geometric quantization of the Kepler problem
International Nuclear Information System (INIS)
Gaeta, G.; Spera, M.
1988-01-01
The geometric quantization of the (three-dimensional) Kepler problem is readily obtained from the one of the harmonic oscillator using a Segre map. The physical meaning of the latter is discussed. (orig.)
geometric models for lateritic soil stabilized with cement
African Journals Online (AJOL)
user
stabilized lateritic soil and also to develop geometric models. The compaction, California .... on how effective limited field data are put to use in decision-making. ..... silicates was described as the most important phase of cement and the ...
Some geometric properties of magneto-fluid flows
Gangwar, S. S.; Babu, Ram
1982-01-01
By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non-dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.
The Duality Principle in Teaching Arithmetic and Geometric Series
Yeshurun, Shraga
1978-01-01
The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)
A geometric renormalization group in discrete quantum space-time
International Nuclear Information System (INIS)
Requardt, Manfred
2003-01-01
We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality
Geometric Theory of Reduction of Nonlinear Control Systems
Elkin, V. I.
2018-02-01
The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).
A visualization method for teaching the geometric design of highways
2000-04-11
In this project the authors employed state-of-the-art technology for developing visualization tools for teaching highway design. Specifically, the authors used photolog images as the basis for developing dynamic 3-D models of selected geometric eleme...
On the geometrical factor in the off-centre diffusion
International Nuclear Information System (INIS)
Despa, F.; Apostol, M.
1995-07-01
The geometrical factor of the off-centre diffusion coefficient is computed for certain two- and three-dimensional cubic lattice, and a method is indicated for estimating this factor in more general cases. (author). 7 refs, 4 figs
Maintenance of Traffic for Innovative Geometric Design Work Zones
2015-12-01
Currently there are no guidelines within the Manual on Uniform Traffic Control Devices (MUTCD) on construction phasing and maintenance of traffic (MOT) for retrofit construction and maintenance projects involving innovative geometric designs. The res...
Geometrical scaling and the real part of the Pomeron
International Nuclear Information System (INIS)
Dias de Deus, J.
1975-07-01
Consequences of the hypothesis of geometrical scaling of the inelastic overlap function applied to the Pomeron amplitude are discussed. From analiticity and crossing symmetry some predictions are given for the asymptotic real part of the Pomeron. (author)
Geometric Correction of PHI Hyperspectral Image without Ground Control Points
International Nuclear Information System (INIS)
Luan, Kuifeng; Tong, Xiaohua; Liu, Xiangfeng; Ma, Yanhua; Shu, Rong; Xu, Weiming
2014-01-01
Geometric correction without ground control points (GCPs) is a very important topic. Conventional airborne photogrammetry is difficult to implement in areas where the installation of GCPs is not available. The technical of integrated GPS/INS systems providing the positioning and attitude of airborne systems is a potential solution in such areas. This paper first states the principle of geometric correction based on a combination of GPS and INS then the error of the geometric correction of Pushbroom Hyperspectral Imager (PHI) without GCP was analysed, then a flight test was carried out in an area of Damxung, Tibet. The experiment result showed that the error at straight track was small, generally less than 1 pixel, while the maximum error at cross track direction, was close to 2 pixels. The results show that geometric correction of PHI without GCP enables a variety of mapping products to be generated from airborne navigation and imagery data
A geometric construction of traveling waves in a bioremediation model
Beck, M.A.; Doelman, A.; Kaper, T.J.
2006-01-01
Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory,
Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis
Hadasz, Leszek; Jaskólski, Zbigniew
The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.
Interplay between Peptide Bond Geometrical Parameters in Nonglobular Structural Contexts
Esposito, Luciana; Balasco, Nicole; De Simone, Alfonso; Berisio, Rita; Vitagliano, Luigi
2013-01-01
Several investigations performed in the last two decades have unveiled that geometrical parameters of protein backbone show a remarkable variability. Although these studies have provided interesting insights into one of the basic aspects of protein structure, they have been conducted on globular and water-soluble proteins. We report here a detailed analysis of backbone geometrical parameters in nonglobular proteins/peptides. We considered membrane proteins and two distinct fibrous systems (am...
Reconstruction of an InAs nanowire using geometric tomography
DEFF Research Database (Denmark)
Pennington, Robert S.; König, Stefan; Alpers, Andreas
Geometric tomography and conventional algebraic tomography algorithms are used to reconstruct cross-sections of an InAs nanowire from a tilt series of experimental annular dark-field images. Both algorithms are also applied to a test object to assess what factors affect the reconstruction quality....... When using the present algorithms, geometric tomography is faster, but artifacts in the reconstruction may be difficult to recognize....
GEOMETRIZATION OF NONHOLONOMIC MECHANICAL SYSTEMS AND THEIR SOLVABILITY
Institute of Scientific and Technical Information of China (English)
慕小武; 郭仲衡
1990-01-01
A new geometrization approach to nonholonomic mechanical systems is proposed and a series of solvability conditions under the proposed geometric frame are given. The proposed frame differs essentially from Hermann’s. The limitations of Hermann’s frame are also discussed. It is shown that a system under Hermann’s frame is solvable only if its constraints are given by natural conservation laws of the corresponding constraint-free system.
Geometric Calculus -- Engineering Mathematics for the 21st century
HITZER, Eckhard MS
2002-01-01
This paper treats important questions at the interface of mathmatics and the engineering science. It starts off with a quick quotation tour through 2300 years of mathmatical history. At the beginning of the 21 century,technology has developed beyond every expectation. But do we also learn and practice an adequately modern form of mathmatics? The papaer argues that this role is very likely to be played by universal geometric calculus. The fundamental geometric product of vectors is introduced....
Accelerated life testing design using geometric process for pareto distribution
Mustafa Kamal; Shazia Zarrin; Arif Ul Islam
2013-01-01
In this paper the geometric process is used for the analysis of accelerated life testing under constant stress for Pareto Distribution. Assuming that the lifetimes under increasing stress levels form a geometric process, estimates of the parameters are obtained by using the maximum likelihood method for complete data. In addition, asymptotic interval estimates of the parameters of the distribution using Fisher information matrix are also obtained. The statistical properties of the parameters ...
Quantum trajectory approach to the geometric phase: open bipartite systems
International Nuclear Information System (INIS)
Yi, X X; Liu, D P; Wang, W
2005-01-01
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other and then are entangled in the evolution. The geometric phase due to the quantum jump for both the bipartite system and its subsystems is calculated and analysed. As an example, we present two coupled spin-1/2 particles to detail the calculations
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
Geometric integrator for simulations in the canonical ensemble
Energy Technology Data Exchange (ETDEWEB)
Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico); Sanders, David P., E-mail: dpsanders@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico); Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States); Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510 (Mexico)
2016-08-28
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.
Geometric integrator for simulations in the canonical ensemble
International Nuclear Information System (INIS)
Tapias, Diego; Sanders, David P.; Bravetti, Alessandro
2016-01-01
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.
Multiscale geometric modeling of macromolecules II: Lagrangian representation
Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2013-01-01
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599
Symmetry analysis of talus bone: A Geometric morphometric approach.
Islam, K; Dobbe, A; Komeili, A; Duke, K; El-Rich, M; Dhillon, S; Adeeb, S; Jomha, N M
2014-01-01
The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139-45.
Geometric phases in astigmatic optical modes of arbitrary order
International Nuclear Information System (INIS)
Habraken, Steven J. M.; Nienhuis, Gerard
2010-01-01
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
A geometric framework for evaluating rare variant tests of association.
Liu, Keli; Fast, Shannon; Zawistowski, Matthew; Tintle, Nathan L
2013-05-01
The wave of next-generation sequencing data has arrived. However, many questions still remain about how to best analyze sequence data, particularly the contribution of rare genetic variants to human disease. Numerous statistical methods have been proposed to aggregate association signals across multiple rare variant sites in an effort to increase statistical power; however, the precise relation between the tests is often not well understood. We present a geometric representation for rare variant data in which rare allele counts in case and control samples are treated as vectors in Euclidean space. The geometric framework facilitates a rigorous classification of existing rare variant tests into two broad categories: tests for a difference in the lengths of the case and control vectors, and joint tests for a difference in either the lengths or angles of the two vectors. We demonstrate that genetic architecture of a trait, including the number and frequency of risk alleles, directly relates to the behavior of the length and joint tests. Hence, the geometric framework allows prediction of which tests will perform best under different disease models. Furthermore, the structure of the geometric framework immediately suggests additional classes and types of rare variant tests. We consider two general classes of tests which show robustness to noncausal and protective variants. The geometric framework introduces a novel and unique method to assess current rare variant methodology and provides guidelines for both applied and theoretical researchers. © 2013 Wiley Periodicals, Inc.
Geometric singular perturbation analysis of systems with friction
DEFF Research Database (Denmark)
Bossolini, Elena
This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter......, two mechanical problems with two diﬀerent formulations of the friction force are introduced and analysed. The ﬁrst mechanical problem is a one-dimensional spring-block model describing earthquake faulting. The dynamics of earthquakes is naturally a multiple timescale problem: the timescale...... scales. The action of friction is generally explained as the loss and restoration of linkages between the surface asperities at the molecular scale. However, the consequences of friction are noticeable at much larger scales, like hundreds of kilometers. By using geometric singular perturbation theory...
Geometrical primitives reconstruction from image sequence in an interactive context
International Nuclear Information System (INIS)
Monchal, L.; Aubry, P.
1995-01-01
We propose a method to recover 3D geometrical shape from image sequence, in a context of man machine co-operation. The human operator has to point out the edges of an object in the first image and choose a corresponding geometrical model. The algorithm tracks each relevant 2D segments describing surface discontinuities or limbs, in the images. Then, knowing motion of the camera between images, the positioning and the size of the virtual object are deduced by minimising a function. The function describes how well the virtual objects is linked to the extracted segments of the sequence, its geometrical model and pieces of information given by the operator. (author). 13 refs., 7 figs., 8 tabs
Geometrical determination of the constant of motion in General Relativity
International Nuclear Information System (INIS)
Catoni, F.; Cannata, R.; Zampetti, P.
2009-01-01
In recent time a theorem, due to E. Beltrami, through which the integration of the geodesic equations of a curved manifold is obtained by means of a merely geometric method, has been revisited. This way of dealing with the problem is well in accordance with the geometric spirit of the Theory of General Relativity. In this paper we show another relevant consequence of this method. Actually, the constants of the motion, introduced in this geometrical way that is completely independent of Newton theory, are related to the conservation laws for test particles in the Einstein theory. These conservation laws may be compared with the conservation laws of Newton. In particular, by the conservation of energy (E) and the L z component of angular momentum, the equivalence of the conservation laws for the Schwarzschild field is verified and the difference between Newton and Einstein theories for the rotating bodies (Kerr metric) is obtained in a straightforward way.
Traditional vectors as an introduction to geometric algebra
International Nuclear Information System (INIS)
Carroll, J E
2003-01-01
The 2002 Oersted Medal Lecture by David Hestenes concerns the many advantages for education in physics if geometric algebra were to replace standard vector algebra. However, such a change has difficulties for those who have been taught traditionally. A new way of introducing geometric algebra is presented here using a four-element array composed of traditional vector and scalar products. This leads to an explicit 4 x 4 matrix representation which contains key requirements for three-dimensional geometric algebra. The work can be extended to include Maxwell's equations where it is found that curl and divergence appear naturally together. However, to obtain an explicit representation of space-time algebra with the correct behaviour under Lorentz transformations, an 8 x 8 matrix representation has to be formed. This leads to a Dirac representation of Maxwell's equations showing that space-time algebra has hidden within its formalism the symmetry of 'parity, charge conjugation and time reversal'
An information geometric approach to least squares minimization
Transtrum, Mark; Machta, Benjamin; Sethna, James
2009-03-01
Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.
Geometric modeling in the problem of ball bearing accuracy
Glukhov, V. I.; Pushkarev, V. V.; Khomchenko, V. G.
2017-06-01
The manufacturing quality of ball bearings is an urgent problem for machine-building industry. The aim of the research is to improve the geometric specifications accuracy of bearings based on evidence-based systematic approach and the method of adequate size, location and form deviations modeling of the rings and assembled ball bearings. The present work addressed the problem of bearing geometric specifications identification and the study of these specifications. The deviation from symmetric planar of rings and bearings assembly and mounting width are among these specifications. A systematic approach to geometric specifications values and ball bearings tolerances normalization in coordinate systems will improve the quality of bearings by optimizing and minimizing the number of specifications. The introduction of systematic approach to the international standards on rolling bearings is a guarantee of a significant increase in accuracy of bearings and the quality of products where they are applied.
Uhlmann's geometric phase in presence of isotropic decoherence
International Nuclear Information System (INIS)
Tidstroem, Jonas; Sjoeqvist, Erik
2003-01-01
Uhlmann's mixed state geometric phase [Rep. Math. Phys. 24, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly with increasing decoherence rate and that it is most fragile to weak decoherence for pure or nearly pure initial states. In the unitary case, we compare Uhlmann's geometric phase for mixed states with that occurring in standard Mach-Zehnder interferometry [Phys. Rev. Lett. 85, 2845 (2000)] and show that the latter is more robust to reduction in the length of the Bloch vector. We also describe how Uhlmann's geometric phase in the present case could in principle be realized experimentally
The differential-geometric aspects of integrable dynamical systems
International Nuclear Information System (INIS)
Prykarpatsky, Y.A.; Samoilenko, A.M.; Prykarpatsky, A.K.; Bogolubov, N.N. Jr.; Blackmore, D.L.
2007-05-01
The canonical reduction method on canonically symplectic manifolds is analyzed in detail, and the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are described. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented. A symplectic theory approach is developed for partially solving the problem of algebraic-analytical construction of integral submanifold embeddings for integrable (via the abelian and nonabelian Liouville-Arnold theorems) Hamiltonian systems on canonically symplectic phase spaces. The fundamental role of the so-called Picard-Fuchs type equations is revealed, and their differential-geometric and algebraic properties are studied in detail. Some interesting examples of integrable Hamiltonian systems are are studied in detail in order to demonstrate the ease of implementation and effectiveness of the procedure for investigating the integral submanifold embedding mapping. (author)
Characteristic signatures of quantum criticality driven by geometrical frustration.
Tokiwa, Yoshifumi; Stingl, Christian; Kim, Moo-Sung; Takabatake, Toshiro; Gegenwart, Philipp
2015-04-01
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid-like state.
Numerical and experimental investigation of geometric parameters in projection welding
DEFF Research Database (Denmark)
Kristensen, Lars; Zhang, Wenqi; Bay, Niels
2000-01-01
parameters by numerical modeling and experimental studies. SORPAS, an FEM program for numerical modeling of resistance welding, is developed as a tool to help in the phase of product design and process optimization in both spot and projection welding. A systematic experimental investigation of projection...... on the numerical and experimental investigations of the geometric parameters in projection welding, guidelines for selection of the geometry and material combinations in product design are proposed. These will be useful and applicable to industry.......Resistance projection welding is widely used for joining of workpieces with almost any geometric combination. This makes standardization of projection welding impossible. In order to facilitate industrial applications of projection welding, systematic investigations are carried out on the geometric...
Geometric model from microscopic theory for nuclear absorption
International Nuclear Information System (INIS)
John, S.; Townsend, L.W.; Wilson, J.W.; Tripathi, R.K.
1993-07-01
A parameter-free geometric model for nuclear absorption is derived herein from microscopic theory. The expression for the absorption cross section in the eikonal approximation, taken in integral form, is separated into a geometric contribution that is described by an energy-dependent effective radius and two surface terms that cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived from harmonic oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half-density radius for the harmonic oscillator functions. Coulomb corrections are incorporated, and a simplified geometric form of the Bradt-Peters type is obtained. Results spanning the energy range from 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained
Geometric model for nuclear absorption from microscopic theory
International Nuclear Information System (INIS)
John, S.; Townsend, L.W.; Wilson, J.W.; Tripathi, R.K.
1993-01-01
A parameter-free geometric model for nuclear absorption is derived from microscopic theory. The expression for the absorption cross section in the eikonal approximation taken in integral form is separated into a geometric contribution, described by an energy-dependent effective radius, and two surface terms which are shown to cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived using harmonic-oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half density radius for the harmonic-oscillator functions. Coulomb corrections are incorporated and a simplified geometric form of the Bradt-Peters type obtained. Results spanning the energy range of 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained
Comparative Geometrical Investigations of Hand-Held Scanning Systems
Kersten, T. P.; Przybilla, H.-J.; Lindstaedt, M.; Tschirschwitz, F.; Misgaiski-Hass, M.
2016-06-01
An increasing number of hand-held scanning systems by different manufacturers are becoming available on the market. However, their geometrical performance is little-known to many users. Therefore the Laboratory for Photogrammetry & Laser Scanning of the HafenCity University Hamburg has carried out geometrical accuracy tests with the following systems in co-operation with the Bochum University of Applied Sciences (Laboratory for Photogrammetry) as well as the Humboldt University in Berlin (Institute for Computer Science): DOTProduct DPI-7, Artec Spider, Mantis Vision F5 SR, Kinect v1 + v2, Structure Sensor and Google's Project Tango. In the framework of these comparative investigations geometrically stable reference bodies were used. The appropriate reference data were acquired by measurement with two structured light projection systems (AICON smartSCAN and GOM ATOS I 2M). The comprehensive test results of the different test scenarios are presented and critically discussed in this contribution.