WorldWideScience

Sample records for geometrical constraint equation

  1. Geometrical-integrability constraints and equations of motion in four plus extended super spaces

    International Nuclear Information System (INIS)

    Chau, L.L.

    1987-01-01

    It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion

  2. Diffusion Under Geometrical Constraint

    OpenAIRE

    Ogawa, Naohisa

    2014-01-01

    Here we discus the diffusion of particles in a curved tube. This kind of transport phenomenon is observed in biological cells and porous media. To solve such a problem, we discuss the three dimensional diffusion equation with a confining wall forming a thinner tube. We find that the curvature appears in a effective diffusion coefficient for such a quasi-one-dimensional system. As an application to higher dimensional case, we discuss the diffusion in a curved surface with ...

  3. 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.)

  4. Geometric Implications of Maxwell's Equations

    Science.gov (United States)

    Smith, Felix T.

    2015-03-01

    Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.

  5. Solving Absolute Value Equations Algebraically and Geometrically

    Science.gov (United States)

    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.

  6. Geometrical and Graphical Solutions of Quadratic Equations.

    Science.gov (United States)

    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)

  7. Linear determining equations for differential constraints

    International Nuclear Information System (INIS)

    Kaptsov, O V

    1998-01-01

    A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed

  8. ERC Workshop on Geometric Partial Differential Equations

    CERN Document Server

    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.

  9. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    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)

  10. Epidemics on adaptive networks with geometric constraints

    Science.gov (United States)

    Shaw, Leah; Schwartz, Ira

    2008-03-01

    When a population is faced with an epidemic outbreak, individuals may modify their social behavior to avoid exposure to the disease. Recent work has considered models in which the contact network is rewired dynamically so that susceptibles avoid contact with infectives. We consider extensions in which the rewiring is subject to constraints that preserve key properties of the social network structure. Constraining to a fixed degree distribution destroys previously observed bistable behavior. The most effective rewiring strategy is found to depend on the spreading rate.

  11. Modulation of collective cell behaviour by geometrical constraints

    Czech Academy of Sciences Publication Activity Database

    Lunova, M.; Zablotskyy, Vitaliy A.; Dempsey, N.M.; Devillers, T.; Jirsa, M.; Syková, E.; Kubinová, Šárka; Lunov, Oleg; Dejneka, Alexandr

    2016-01-01

    Roč. 8, č. 11 (2016), s. 1099-1110 ISSN 1757-9694 Grant - others:AV ČR(CZ) Fellowship J. E. Purkyně Institutional support: RVO:68378271 Keywords : modulation * collective cell * geometrical constraints Subject RIV: BO - Biophysics Impact factor: 3.252, year: 2016

  12. Shaping tissues by balancing active forces and geometric constraints

    Science.gov (United States)

    Foolen, Jasper; Yamashita, Tadahiro; Kollmannsberger, Philip

    2016-02-01

    The self-organization of cells into complex tissues during growth and regeneration is a combination of physical-mechanical events and biochemical signal processing. Cells actively generate forces at all stages in this process, and according to the laws of mechanics, these forces result in stress fields defined by the geometric boundary conditions of the cell and tissue. The unique ability of cells to translate such force patterns into biochemical information and vice versa sets biological tissues apart from any other material. In this topical review, we summarize the current knowledge and open questions of how forces and geometry act together on scales from the single cell to tissues and organisms, and how their interaction determines biological shape and structure. Starting with a planar surface as the simplest type of geometric constraint, we review literature on how forces during cell spreading and adhesion together with geometric constraints impact cell shape, stress patterns, and the resulting biological response. We then move on to include cell-cell interactions and the role of forces in monolayers and in collective cell migration, and introduce curvature at the transition from flat cell sheets to three-dimensional (3D) tissues. Fibrous 3D environments, as cells experience them in the body, introduce new mechanical boundary conditions and change cell behaviour compared to flat surfaces. Starting from early work on force transmission and collagen remodelling, we discuss recent discoveries on the interaction with geometric constraints and the resulting structure formation and network organization in 3D. Recent literature on two physiological scenarios—embryonic development and bone—is reviewed to demonstrate the role of the force-geometry balance in living organisms. Furthermore, the role of mechanics in pathological scenarios such as cancer is discussed. We conclude by highlighting common physical principles guiding cell mechanics, tissue patterning and

  13. Shaping tissues by balancing active forces and geometric constraints

    International Nuclear Information System (INIS)

    Foolen, Jasper; Yamashita, Tadahiro; Kollmannsberger, Philip

    2016-01-01

    The self-organization of cells into complex tissues during growth and regeneration is a combination of physical–mechanical events and biochemical signal processing. Cells actively generate forces at all stages in this process, and according to the laws of mechanics, these forces result in stress fields defined by the geometric boundary conditions of the cell and tissue. The unique ability of cells to translate such force patterns into biochemical information and vice versa sets biological tissues apart from any other material. In this topical review, we summarize the current knowledge and open questions of how forces and geometry act together on scales from the single cell to tissues and organisms, and how their interaction determines biological shape and structure. Starting with a planar surface as the simplest type of geometric constraint, we review literature on how forces during cell spreading and adhesion together with geometric constraints impact cell shape, stress patterns, and the resulting biological response. We then move on to include cell–cell interactions and the role of forces in monolayers and in collective cell migration, and introduce curvature at the transition from flat cell sheets to three-dimensional (3D) tissues. Fibrous 3D environments, as cells experience them in the body, introduce new mechanical boundary conditions and change cell behaviour compared to flat surfaces. Starting from early work on force transmission and collagen remodelling, we discuss recent discoveries on the interaction with geometric constraints and the resulting structure formation and network organization in 3D. Recent literature on two physiological scenarios—embryonic development and bone—is reviewed to demonstrate the role of the force-geometry balance in living organisms. Furthermore, the role of mechanics in pathological scenarios such as cancer is discussed. We conclude by highlighting common physical principles guiding cell mechanics, tissue patterning

  14. Differential constraints and exact solutions of nonlinear diffusion equations

    International Nuclear Information System (INIS)

    Kaptsov, Oleg V; Verevkin, Igor V

    2003-01-01

    The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries

  15. Size and mobility of lipid domains tuned by geometrical constraints.

    Science.gov (United States)

    Schütte, Ole M; Mey, Ingo; Enderlein, Jörg; Savić, Filip; Geil, Burkhard; Janshoff, Andreas; Steinem, Claudia

    2017-07-25

    In the plasma membrane of eukaryotic cells, proteins and lipids are organized in clusters, the latter ones often called lipid domains or "lipid rafts." Recent findings highlight the dynamic nature of such domains and the key role of membrane geometry and spatial boundaries. In this study, we used porous substrates with different pore radii to address precisely the extent of the geometric constraint, permitting us to modulate and investigate the size and mobility of lipid domains in phase-separated continuous pore-spanning membranes (PSMs). Fluorescence video microscopy revealed two types of liquid-ordered ( l o ) domains in the freestanding parts of the PSMs: ( i ) immobile domains that were attached to the pore rims and ( ii ) mobile, round-shaped l o domains within the center of the PSMs. Analysis of the diffusion of the mobile l o domains by video microscopy and particle tracking showed that the domains' mobility is slowed down by orders of magnitude compared with the unrestricted case. We attribute the reduced mobility to the geometric confinement of the PSM, because the drag force is increased substantially due to hydrodynamic effects generated by the presence of these boundaries. Our system can serve as an experimental test bed for diffusion of 2D objects in confined geometry. The impact of hydrodynamics on the mobility of enclosed lipid domains can have great implications for the formation and lateral transport of signaling platforms.

  16. Geometric Insight into Scalar Combination of Linear Equations

    Indian Academy of Sciences (India)

    ... Journals; Resonance – Journal of Science Education; Volume 14; Issue 11. Geometric Insight into Scalar Combination of Linear Equations. Ranjit Konkar. Classroom Volume 14 Issue 11 November 2009 pp 1092-1097 ... Keywords. Linear algebra; linear dependence; linear combination; family of lines; family of planes.

  17. The Impact of Geometrical Constraints on Collisionless Magnetic Reconnection

    Science.gov (United States)

    Hesse, Michael; Aunai, Nico; Kuznetsova, Masha; Frolov, Rebekah; Black, Carrrie

    2012-01-01

    One of the most often cited features associated with collisionless magnetic reconnection is a Hall-type magnetic field, which leads, in antiparallel geometries, to a quadrupolar magnetic field signature. The combination of this out of plane magnetic field with the reconnection in-plane magnetic field leads to angling of magnetic flux tubes out of the plane defined by the incoming magnetic flux. Because it is propagated by Whistler waves, the quadrupolar field can extend over large distances in relatively short amounts of time - in fact, it will extend to the boundary of any modeling domain. In reality, however, the surrounding plasma and magnetic field geometry, defined, for example, by the overall solar wind flow, will in practice limit the extend over which a flux tube can be angled out of the main plain. This poses the question to what extent geometric constraints limit or control the reconnection process and this is the question investigated in this presentation. The investigation will involve a comparison of calculations, where open boundary conditions are set up to mimic either free or constrained geometries. We will compare momentum transport, the geometry of the reconnection regions, and the acceleration if ions and electrons to provide the current sheet in the outflow jet.

  18. Interferometric constraints on quantum geometrical shear noise correlations

    Energy Technology Data Exchange (ETDEWEB)

    Chou, Aaron; Glass, Henry; Richard Gustafson, H.; Hogan, Craig J.; Kamai, Brittany L.; Kwon, Ohkyung; Lanza, Robert; McCuller, Lee; Meyer, Stephan S.; Richardson, Jonathan W.; Stoughton, Chris; Tomlin, Ray; Weiss, Rainer

    2017-07-20

    Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.

  19. Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

    OpenAIRE

    Wu, Lei

    2014-01-01

    We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

  20. First passage time for a diffusive process under a geometric constraint

    International Nuclear Information System (INIS)

    Tateishi, A A; Michels, F S; Dos Santos, M A F; Lenzi, E K; Ribeiro, H V

    2013-01-01

    We investigate the solutions, survival probability, and first passage time for a two-dimensional diffusive process subjected to the geometric constraints of a backbone structure. We consider this process governed by a fractional Fokker–Planck equation by taking into account the boundary conditions ρ(0,y;t) = ρ(∞,y;t) = 0, ρ(x, ± ∞;t) = 0, and an arbitrary initial condition. Our results show an anomalous spreading and, consequently, a nonusual behavior for the survival probability and for the first passage time distribution that may be characterized by different regimes. In addition, depending on the choice of the parameters present in the fractional Fokker–Planck equation, the survival probability indicates that part of the system may be trapped in the branches of the backbone structure. (paper)

  1. Cosmographic constraints from The Raychaudhuri Equation

    Energy Technology Data Exchange (ETDEWEB)

    Santos, Crislane S.; Santos, Janilo [Universidade Federal do Rio Grande do Norte (UFRN), RN (Brazil)

    2011-07-01

    Full text: There is nowadays a great debate about the mechanism behind the observed cosmic acceleration. In the absence of a fundamental new physical theory, capable of joining the macro and the microphysics, a number of cosmological scenarios have been risen presupposing the existence of new fields in nature, such as quintessence scalar field and Chaplygin gas, for example. The aim of these cosmological models is indeed to derive a smooth function H(z), the so called Hubble function, which describes the expansion history of the universe, and as a further step to confront predictions with the observations. However, there is a direct method to map the expansion history of the universe in a model independent way. Recently it has been shown that luminous red galaxies can provide us with direct measurements of the expansion rate H(z) using differential age techniques. Indeed, at the moment we have only 11 estimates of H(z) lying in the redshift interval 0.1 ≤ z ≥ 1.75; however, in the near future, it is expected ∼ 1, 000 values of the Hubble function. In this way, cosmography is becoming a promising branch in cosmology. Here we investigate and discuss the use of the Raychaudhury equation as a cosmographic description and relate the expansion rate Θ of a congruence of world lines with the evolution of the Hubble function H(z). As is well known, the Raychaudhury equation is central to the understanding of gravitational attraction in astrophysics and cosmology. Our assumptions are that the underlying geometry of the universe is a flat Friedmann-Lemaitre-Robertson-Walker one and that gravity has an attractive effect. For a comoving observer we find that the expansion rate of a congruence is given by Θ = -3/2(1 + z)dH{sup 2}/dz, which we use to compare with the computed derivatives of H(z) measurements. We use this equation in order to put constraints in the parameters of the cosmological models of quintessence scalar field and Chaplygin gas. (author)

  2. The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

    Science.gov (United States)

    Estabrook, F. B.; Wahlquist, H. D.

    1975-01-01

    The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

  3. The Young-Laplace equation links capillarity with geometrical optics

    International Nuclear Information System (INIS)

    Rodriguez-Valverde, M A; Cabrerizo-Vilchez, M A; Hidalgo-Alvarez, R

    2003-01-01

    Analogies in physics are unusual coincidences that can be very useful to solve problems and to clarify some theoretical concepts. Apart from their own curiosity, analogies are attractive tools because they reduce the abstraction of some complex phenomena in such a way that these can be understood by means of other phenomena closer to daily experience. Usually, two analogous systems share a common aspect, like the movement of particles or transport of matter. On account of this, the analogy presented is exceptional since the involved phenomena are a priori disjoined. The most important equation of capillarity, the Young-Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates the optic power of a thick lens to its geometry and the properties of the media

  4. Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms

    Directory of Open Access Journals (Sweden)

    Oscar E Ruiz

    2006-06-01

    Full Text Available Geometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments. An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations. Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities. If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints. Otherwise, a diagnostic of inconsistency is expected. The three main approaches used for this problem are numerical, procedural or operational and mathematical. Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one. The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations. The common roots to this set of polynomials characterizes the solution space for such a problem. That work presents the use of Groebner basis techniques for verifying the consistency of the constraints. It also integrates subgroups of the Special Euclidean Group of Displacements SE(3 in the problem formulation to exploit the structure implied by geometric relations. Although theoretically sound, these techniques require large amounts of computing resources. This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities. The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem. Cluster identification can be related to identifying short cycles in the Spatial Constraint graph for the GCS/SF problem. Their preprocessing

  5. The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

    Science.gov (United States)

    Gallouët, Thomas; Vialard, François-Xavier

    2018-04-01

    The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

  6. On geometric approach to Lie symmetries of differential-difference equations

    International Nuclear Information System (INIS)

    Li Hongjing; Wang Dengshan; Wang Shikun; Wu Ke; Zhao Weizhong

    2008-01-01

    Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach

  7. Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

    Science.gov (United States)

    Pathak, H. K.; Grewal, A. S.

    2002-01-01

    This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

  8. Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion

    Science.gov (United States)

    Ohkitani, Koji

    2018-02-01

    After surveying analyses of the 3D Euler equations using the Clebsch potentials scattered over the literature, we report some preliminary new results. 1. Assuming that flow fields are free from nulls of the impulse and the vorticity fields, we study how constraints imposed by the Clebsch potentials lead to a degenerate geometrical structure, typically in the form of depletion of nonlinearity. We consider a vorticity surface spanned by \\boldsymbol ω and another material vector \\boldsymbol {W} such that \\boldsymbol γ=\\boldsymbol ω× \\boldsymbol {W}, where \\boldsymbol γ is the impulse variable in geometric gauge. We identify dual mechanism for geometric depletion and show that at least of one them is acting if \\boldsymbol {W} does not develop a null. This suggests that formation of singularity in flows endowed with Clebsch potentials is less likely to happen than in more general flows. Some arguments are given towards exclusion of ‘type I’ blowup. A mathematical challenge remains to rule out singularity formation for flows which have Clebsch potentials everywhere. 2. We exploit classical differential geometry kinematically to write down the Gauss-Weingarten equations for the vorticity surface of the Clebsch potential in terms of fluid dynamical variables, as are the first, second and third fundamental forms. In particular, we derive a constraint on the size of the Gaussian curvature near the point of a possible singularity. On the other hand, an application of the Gauss-Bonnet theorem reveals that the tangential curvature of the surface becomes large in the neighborhood of near-singularity. 3. Using spatially-periodic flows with highly-symmetry, i.e. initial conditions of the Taylor-Green vortex and the Kida-Pelz flow, we present explicit formulas of the Clebsch potentials with exceptional singular surfaces where the Clebsch potentials are undefined. This is done by connecting the known expressions with the solenoidal impulse variable (i.e. the

  9. A mathematical formulation for interface-based modular product design with geometric and weight constraints

    Science.gov (United States)

    Jung-Woon Yoo, John

    2016-06-01

    Since customer preferences change rapidly, there is a need for design processes with shorter product development cycles. Modularization plays a key role in achieving mass customization, which is crucial in today's competitive global market environments. Standardized interfaces among modularized parts have facilitated computational product design. To incorporate product size and weight constraints during computational design procedures, a mixed integer programming formulation is presented in this article. Product size and weight are two of the most important design parameters, as evidenced by recent smart-phone products. This article focuses on the integration of geometric, weight and interface constraints into the proposed mathematical formulation. The formulation generates the optimal selection of components for a target product, which satisfies geometric, weight and interface constraints. The formulation is verified through a case study and experiments are performed to demonstrate the performance of the formulation.

  10. Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

    International Nuclear Information System (INIS)

    Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

    2009-01-01

    Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)

  11. Fast and Easy 3D Reconstruction with the Help of Geometric Constraints and Genetic Algorithms

    Science.gov (United States)

    Annich, Afafe; El Abderrahmani, Abdellatif; Satori, Khalid

    2017-09-01

    The purpose of the work presented in this paper is to describe new method of 3D reconstruction from one or more uncalibrated images. This method is based on two important concepts: geometric constraints and genetic algorithms (GAs). At first, we are going to discuss the combination between bundle adjustment and GAs that we have proposed in order to improve 3D reconstruction efficiency and success. We used GAs in order to improve fitness quality of initial values that are used in the optimization problem. It will increase surely convergence rate. Extracted geometric constraints are used first to obtain an estimated value of focal length that helps us in the initialization step. Matching homologous points and constraints is used to estimate the 3D model. In fact, our new method gives us a lot of advantages: reducing the estimated parameter number in optimization step, decreasing used image number, winning time and stabilizing good quality of 3D results. At the end, without any prior information about our 3D scene, we obtain an accurate calibration of the cameras, and a realistic 3D model that strictly respects the geometric constraints defined before in an easy way. Various data and examples will be used to highlight the efficiency and competitiveness of our present approach.

  12. Symmetries of stochastic differential equations: A geometric approach

    Energy Technology Data Exchange (ETDEWEB)

    De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

    2016-06-15

    A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

  13. An introduction to geometric theory of fully nonlinear parabolic equations

    International Nuclear Information System (INIS)

    Lunardi, A.

    1991-01-01

    We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

  14. Analytic, Algebraic and Geometric Aspects of Differential Equations

    CERN Document Server

    Haraoka, Yoshishige; Michalik, Sławomir

    2017-01-01

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

  15. Optimal geometric structure for nanofluid-cooled microchannel heat sink under various constraint conditions

    International Nuclear Information System (INIS)

    Wang Xiaodong; Bin An; Xu Jinliang

    2013-01-01

    Highlights: ► An inverse geometry optimization method is used to optimize heat sink structure. ► Nanofluid is used as coolant of heat sink. ► Three parameters are simultaneously optimized at various constraint conditions. ► The optimal designs of nanofluid-cooled heat sink are obtained. - Abstract: A numerical model is developed to analyze the flow and heat transfer in nanofluid-cooled microchannel heat sink (MCHS). In the MCHS model, temperature-dependent thermophysical properties are taken into account due to large temperature differences in the MCHS and strong temperature-dependent characteristics of nanofluids, the model is validated by experimental data with good agreement. The simplified conjugate-gradient method is coupled with MCHS model as optimization tool. Three geometric parameters, including channel number, channel aspect ratio, and width ratio of channel to pitch, are simultaneously optimized at fixed inlet volume flow rate, fixed pumping power, and fixed pressure drop as constraint condition, respectively. The optimal designs of MCHS are obtained for various constraint conditions and the effects of inlet volume flow rate, pumping power, and pressure drop on the optimal geometric parameters are discussed.

  16. A geometric theory for semilinear almost-periodic parabolic partial differential equations on RN

    International Nuclear Information System (INIS)

    Vuillermot, P.A.

    1991-01-01

    In this short expository article we review various applications of some geometric methods which have been recently devised to investigate the long time behaviour of classical solutions to certain semilinear almost-periodic reaction-diffusion equations on R N . As a consequence, we also show how to construct almost-periodic attractors for such equations and how to investigate their stability properties. The class of problems which we analyse here contains in particular well known equations of population genetics. (author). 17 refs

  17. The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations

    International Nuclear Information System (INIS)

    Chen Jinbing; Qiao Zhijun

    2011-01-01

    A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.

  18. Sampling-based exploration of folded state of a protein under kinematic and geometric constraints

    KAUST Repository

    Yao, Peggy

    2011-10-04

    Flexibility is critical for a folded protein to bind to other molecules (ligands) and achieve its functions. The conformational selection theory suggests that a folded protein deforms continuously and its ligand selects the most favorable conformations to bind to. Therefore, one of the best options to study protein-ligand binding is to sample conformations broadly distributed over the protein-folded state. This article presents a new sampler, called kino-geometric sampler (KGS). This sampler encodes dominant energy terms implicitly by simple kinematic and geometric constraints. Two key technical contributions of KGS are (1) a robotics-inspired Jacobian-based method to simultaneously deform a large number of interdependent kinematic cycles without any significant break-up of the closure constraints, and (2) a diffusive strategy to generate conformation distributions that diffuse quickly throughout the protein folded state. Experiments on four very different test proteins demonstrate that KGS can efficiently compute distributions containing conformations close to target (e.g., functional) conformations. These targets are not given to KGS, hence are not used to bias the sampling process. In particular, for a lysine-binding protein, KGS was able to sample conformations in both the intermediate and functional states without the ligand, while previous work using molecular dynamics simulation had required the ligand to be taken into account in the potential function. Overall, KGS demonstrates that kino-geometric constraints characterize the folded subset of a protein conformation space and that this subset is small enough to be approximated by a relatively small distribution of conformations. © 2011 Wiley Periodicals, Inc.

  19. Simulation of deep penetration welding of stainless steel using geometric constraints based on experimental information

    International Nuclear Information System (INIS)

    Milewski, J.O.; Lambrakos, S.G.

    1995-01-01

    This report presents a general overview of a method of numerically modelling deep penetration welding processes using geometric constraints based on boundary information obtained from experiment. General issues are considered concerning accurate numerical calculation of temperature and velocity fields in regions of the meltpool where the flow of fluid is characterized by quasi-stationary Stokes flow. It is this region of the meltpool which is closest to the heat-affected-zone (HAZ) and which represents a significant fraction of the fusion zone (FZ)

  20. Affine-Invariant Geometric Constraints-Based High Accuracy Simultaneous Localization and Mapping

    Directory of Open Access Journals (Sweden)

    Gangchen Hua

    2017-01-01

    Full Text Available In this study we describe a new appearance-based loop-closure detection method for online incremental simultaneous localization and mapping (SLAM using affine-invariant-based geometric constraints. Unlike other pure bag-of-words-based approaches, our proposed method uses geometric constraints as a supplement to improve accuracy. By establishing an affine-invariant hypothesis, the proposed method excludes incorrect visual words and calculates the dispersion of correctly matched visual words to improve the accuracy of the likelihood calculation. In addition, camera’s intrinsic parameters and distortion coefficients are adequate for this method. 3D measuring is not necessary. We use the mechanism of Long-Term Memory and Working Memory (WM to manage the memory. Only a limited size of the WM is used for loop-closure detection; therefore the proposed method is suitable for large-scale real-time SLAM. We tested our method using the CityCenter and Lip6Indoor datasets. Our proposed method results can effectively correct the typical false-positive localization of previous methods, thus gaining better recall ratios and better precision.

  1. A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

    Science.gov (United States)

    Haddout, Soufiane

    2018-01-01

    The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

  2. Preconditioning for partial differential equation constrained optimization with control constraints

    KAUST Repository

    Stoll, Martin; Wathen, Andy

    2011-01-01

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  3. Preconditioning for partial differential equation constrained optimization with control constraints

    KAUST Repository

    Stoll, Martin

    2011-10-18

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  4. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.

    2015-01-01

    We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or

  5. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.

    A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity

  6. Equations of motion as constraints: superselection rules, Ward identities

    Energy Technology Data Exchange (ETDEWEB)

    Asorey, M. [Departamento de Física Teórica, Universidad de Zaragoza,C/Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Balachandran, A.P. [Physics Department, Syracuse University,Physics Building Syracuse, NY 13244 (United States); Institute of Mathematical Sciences, C.I.T Campus,Taramani Chennai 600113 (India); Lizzi, F. [Dipartimento di Fisica “E. Pancini” Università di Napoli Federico II,Via Cintia, 80126 Napoli (Italy); INFN - Sezione di Napoli,Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Matèria, Institut de Ciéncies del Cosmos,Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia (Spain); Marmo, G. [Dipartimento di Fisica “E. Pancini” Università di Napoli Federico II,Via Cintia, 80126 Napoli (Italy); INFN - Sezione di Napoli,Via Cintia, 80126 Napoli (Italy)

    2017-03-27

    The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) transformations in local quantum physics. Our observables are smeared by test functions, at first vanishing at infinity. In this context we show that the equations of motion can be seen as constraints, which generate a group, the group of space and time dependent gauge transformations. This is one of the main points of the paper. Infrared nontrivial effects are captured allowing test functions which do not vanish at infinity. These extended operators generate a larger group. The quotient of the two groups generate superselection sectors, which differentiate different infrared sectors. The BMS group changes the superselection sector, a result long known for its Lorentz subgroup. It is hence spontaneously broken. Ward identities implied by the gauge invariance of the S-matrix generalize the standard results and lead to charge conservation and low energy theorems. Their validity does not require Lorentz invariance.

  7. Edge effects and geometric constraints: a landscape-level empirical test.

    Science.gov (United States)

    Ribeiro, Suzy E; Prevedello, Jayme A; Delciellos, Ana Cláudia; Vieira, Marcus Vinícius

    2016-01-01

    Edge effects are pervasive in landscapes yet their causal mechanisms are still poorly understood. Traditionally, edge effects have been attributed to differences in habitat quality along the edge-interior gradient of habitat patches, under the assumption that no edge effects would occur if habitat quality was uniform. This assumption was questioned recently after the recognition that geometric constraints tend to reduce population abundances near the edges of habitat patches, the so-called geometric edge effect (GEE). Here, we present the first empirical, landscape-level evaluation of the importance of the GEE in shaping abundance patterns in fragmented landscapes. Using a data set on the distribution of small mammals across 18 forest fragments, we assessed whether the incorporation of the GEE into the analysis changes the interpretation of edge effects and the degree to which predictions based on the GEE match observed responses. Quantitative predictions were generated for each fragment using simulations that took into account home range, density and matrix use for each species. The incorporation of the GEE into the analysis changed substantially the interpretation of overall observed edge responses at the landscape scale. Observed abundances alone would lead to the conclusion that the small mammals as a group have no consistent preference for forest edges or interiors and that the black-eared opossum Didelphis aurita (a numerically dominant species in the community) has on average a preference for forest interiors. In contrast, incorporation of the GEE suggested that the small mammal community as a whole has a preference for forest edges, whereas D. aurita has no preference for forest edges or interiors. Unexplained variance in edge responses was reduced by the incorporation of GEE, but remained large, varying greatly on a fragment-by-fragment basis. This study demonstrates how to model and incorporate the GEE in analyses of edge effects and that this

  8. The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

    Science.gov (United States)

    Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

    2018-04-01

    The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

  9. Simple renormalization group method for calculating geometrical and other equations of states

    International Nuclear Information System (INIS)

    Tsallis, C.; Schwaccheim, G.; Coniglio, A.

    1984-01-01

    A real space renormalization group procedure to calculate geometrical and thermal equations of states for the entire range of values of the external parameters is described. Its use is as simple as a Mean Field Approximation; however, it yields non trivial results and can be systematically improved. Such a procedure is illustrated by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory. (Author) [pt

  10. Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations

    Science.gov (United States)

    Watson, Michael D.; Jayroe, Robert, Jr.

    1999-01-01

    Fresnel lenses have been used for years as solar concentrators in a variety of applications. Several variables effect the final design of these lenses including: lens diameter, image spot distance from the lens, and bandwidth focused in the image spot. Defining the image spot as the geometrical optics circle of least confusion and applying blackbody radiation equations the spot energy distribution can be determined. These equations are used to design a fresnel lens to produce maximum flux for a given spot size, lens diameter, and image distance. This approach results in significant increases in solar efficiency over traditional single wavelength designs.

  11. Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

    International Nuclear Information System (INIS)

    Anco, Stephen C

    2006-01-01

    Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps

  12. Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

    Energy Technology Data Exchange (ETDEWEB)

    Anco, Stephen C [Department of Mathematics, Brock University, St Catharines, ON (Canada)

    2006-03-03

    Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps.

  13. Protein-induced geometric constraints and charge transfer in bacteriochlorophyll-histidine complexes in LH2.

    Science.gov (United States)

    Wawrzyniak, Piotr K; Alia, A; Schaap, Roland G; Heemskerk, Mattijs M; de Groot, Huub J M; Buda, Francesco

    2008-12-14

    Bacteriochlorophyll-histidine complexes are ubiquitous in nature and are essential structural motifs supporting the conversion of solar energy into chemically useful compounds in a wide range of photosynthesis processes. A systematic density functional theory study of the NMR chemical shifts for histidine and for bacteriochlorophyll-a-histidine complexes in the light-harvesting complex II (LH2) is performed using the BLYP functional in combination with the 6-311++G(d,p) basis set. The computed chemical shift patterns are consistent with available experimental data for positive and neutral(tau) (N(tau) protonated) crystalline histidines. The results for the bacteriochlorophyll-a-histidine complexes in LH2 provide evidence that the protein environment is stabilizing the histidine close to the Mg ion, thereby inducing a large charge transfer of approximately 0.5 electronic equivalent. Due to this protein-induced geometric constraint, the Mg-coordinated histidine in LH2 appears to be in a frustrated state very different from the formal neutral(pi) (N(pi) protonated) form. This finding could be important for the understanding of basic functional mechanisms involved in tuning the electronic properties and exciton coupling in LH2.

  14. Integration of sparse multi-modality representation and geometrical constraint for isointense infant brain segmentation.

    Science.gov (United States)

    Wang, Li; Shi, Feng; Li, Gang; Lin, Weili; Gilmore, John H; Shen, Dinggang

    2013-01-01

    Segmentation of infant brain MR images is challenging due to insufficient image quality, severe partial volume effect, and ongoing maturation and myelination process. During the first year of life, the signal contrast between white matter (WM) and gray matter (GM) in MR images undergoes inverse changes. In particular, the inversion of WM/GM signal contrast appears around 6-8 months of age, where brain tissues appear isointense and hence exhibit extremely low tissue contrast, posing significant challenges for automated segmentation. In this paper, we propose a novel segmentation method to address the above-mentioned challenge based on the sparse representation of the complementary tissue distribution information from T1, T2 and diffusion-weighted images. Specifically, we first derive an initial segmentation from a library of aligned multi-modality images with ground-truth segmentations by using sparse representation in a patch-based fashion. The segmentation is further refined by the integration of the geometrical constraint information. The proposed method was evaluated on 22 6-month-old training subjects using leave-one-out cross-validation, as well as 10 additional infant testing subjects, showing superior results in comparison to other state-of-the-art methods.

  15. Quasivariational Solutions for First Order Quasilinear Equations with Gradient Constraint

    Science.gov (United States)

    Rodrigues, José Francisco; Santos, Lisa

    2012-08-01

    We prove the existence of solutions for a quasi-variational inequality of evolution with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable a priori estimates. We also obtain the existence of stationary solutions by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.

  16. Fluence map optimization (FMO) with dose–volume constraints in IMRT using the geometric distance sorting method

    International Nuclear Information System (INIS)

    Lan Yihua; Li Cunhua; Ren Haozheng; Zhang Yong; Min Zhifang

    2012-01-01

    A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose–volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose–volume constraints, and then the dose constraints for the voxels violating the dose–volume constraints are gradually added into the quadratic optimization model step by step until all the dose–volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head–neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than

  17. Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

    Science.gov (United States)

    Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

    2012-10-21

    A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose

  18. From the Snell-Descartes refraction law, to the Hamilton equations in the phase space of geometrical optics

    International Nuclear Information System (INIS)

    Lopez Moreno, E.; Wolf, K.B.

    1989-01-01

    Starting from the Snell-Descartes' refraction law, we obtain in a brief and direct way the Hamilton equations of Geometrical Optics. We show the global structure of phase space and compare it with that used in paraxial optics. (Author)

  19. A novel scheme for automatic nonrigid image registration using deformation invariant feature and geometric constraint

    Science.gov (United States)

    Deng, Zhipeng; Lei, Lin; Zhou, Shilin

    2015-10-01

    Automatic image registration is a vital yet challenging task, particularly for non-rigid deformation images which are more complicated and common in remote sensing images, such as distorted UAV (unmanned aerial vehicle) images or scanning imaging images caused by flutter. Traditional non-rigid image registration methods are based on the correctly matched corresponding landmarks, which usually needs artificial markers. It is a rather challenging task to locate the accurate position of the points and get accurate homonymy point sets. In this paper, we proposed an automatic non-rigid image registration algorithm which mainly consists of three steps: To begin with, we introduce an automatic feature point extraction method based on non-linear scale space and uniform distribution strategy to extract the points which are uniform distributed along the edge of the image. Next, we propose a hybrid point matching algorithm using DaLI (Deformation and Light Invariant) descriptor and local affine invariant geometric constraint based on triangulation which is constructed by K-nearest neighbor algorithm. Based on the accurate homonymy point sets, the two images are registrated by the model of TPS (Thin Plate Spline). Our method is demonstrated by three deliberately designed experiments. The first two experiments are designed to evaluate the distribution of point set and the correctly matching rate on synthetic data and real data respectively. The last experiment is designed on the non-rigid deformation remote sensing images and the three experimental results demonstrate the accuracy, robustness, and efficiency of the proposed algorithm compared with other traditional methods.

  20. Backscattering Properties of Nonspherical Ice Particles Calculated by Geometrical-Optics-Integral-Equation Method

    Directory of Open Access Journals (Sweden)

    Masuda Kazuhiko

    2016-01-01

    Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.

  1. Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

    Energy Technology Data Exchange (ETDEWEB)

    Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)

    2008-09-07

    We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.

  2. Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

    International Nuclear Information System (INIS)

    Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano

    2008-01-01

    We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions

  3. Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

    KAUST Repository

    Carles, Ré mi; Dumas, Eric; Sparber, Christof

    2010-01-01

    We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

  4. A geometric classification of traveling front propagation in the Nagumo equation with cut-off

    International Nuclear Information System (INIS)

    Popovic, N

    2011-01-01

    An important category of solutions to reaction-diffusion systems of partial differential equations is given by traveling fronts, which provide a monotonic connection between rest states and maintain a fixed profile when considered in a co-moving frame. Reaction-diffusion equations are frequently employed in the mean-field (continuum) approximation of discrete (many-particle) models; however, the quality of this approximation deteriorates when the number of particles is not sufficiently large. The (stochastic) effects of this discreteness have been modeled via the introduction of (deterministic) 'cut-offs' that effectively deactivate the reaction terms at points where the particle concentration is below a certain threshold. In this article, we present an overview of the effects of such a cut-off on the front propagation dynamics in a prototypical reaction-diffusion system, the classical Nagumo equation. Our analysis is based on the method of geometric desingularization ('blow-up'), in combination with dynamical systems techniques such as invariant manifolds and normal forms. Using these techniques, we categorize front propagation in the cut-off Nagumo equation in dependence of a control parameter, and we classify the corresponding propagation regimes ('pulled,' 'pushed,' and 'bistable') in terms of the bifurcation structure of a projectivized system of equations that is obtained from the original traveling front problem, after blow-up. In particular, our approach allows us to determine rigorously the asymptotics (in the cut-off parameter) of the correction to the front propagation speed in the Nagumo equation that is due to a cut-off. Moreover, it explains the structure of that asymptotics (logarithmic, superlinear, or sublinear) in dependence of the front propagation regime. Finally, it enables us to calculate the corresponding leading-order coefficients in the resulting expansions in closed form.

  5. The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

    International Nuclear Information System (INIS)

    Gurau, Razvan

    2012-01-01

    Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.

  6. Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

    International Nuclear Information System (INIS)

    Xu Xixiang

    2012-01-01

    A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)

  7. Geometric description of a discrete power function associated with the sixth Painlevé equation.

    Science.gov (United States)

    Joshi, Nalini; Kajiwara, Kenji; Masuda, Tetsu; Nakazono, Nobutaka; Shi, Yang

    2017-11-01

    In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with [Formula: see text] symmetry. By constructing the action of [Formula: see text] as a subgroup of [Formula: see text], i.e. the symmetry group of P VI , we show how to relate [Formula: see text] to the symmetry group of the lattice. Moreover, by using translations in [Formula: see text], we explain the odd-even structure appearing in previously known explicit formulae in terms of the τ function.

  8. Introducing geometric constraint expressions into robot constrained motion specification and control

    NARCIS (Netherlands)

    Borghesan, G.; Scioni, E.; Kheddar, A.; Bruyninckx, H.P.J.

    2016-01-01

    The problem of robotic task definition and execution was pioneered by Mason, who defined setpoint constraints where the position, velocity, and/or forces are expressed in one particular task frame for a 6-DOF robot. Later extensions generalized this approach to constraints in 1) multiple frames; 2)

  9. Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data

    Science.gov (United States)

    Schikorra, Armin

    2018-02-01

    We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.

  10. Constraints on the nuclear matter equation of state from pulsar glitches

    International Nuclear Information System (INIS)

    Link, B.; Epstein, R.I.; Van Riper, K.A.

    1992-01-01

    We study the post-glitch response of four pulsars to obtain lower limits on the total moment of inertia of the inner crust superfluid. In contrast to previous work, our constraints are independent of the form of the crust-superfluid coupling. We conclude that the superfluid must comprise approx-gt 0.8% of the total moment of inertia of the star. This constraint rules out the softest equations of state

  11. Constraints on hyperon couplings from neutron star equations of state

    CERN Document Server

    Miyazaki, K

    2005-01-01

    Based on the constituent quark picture of baryons and taking into account the contributions of isovector and strange mesons, we have developed the extended Zimanyi-Moszkowski model of dense baryon matter for studying neutron star (NS) equations of state (EOSs). Four sets of meson-hyperons coupling constants are investigated. The first is characterized by strong attractive N\\Sigma interaction while the others have repulsive N\\Sigma interactions. The second is characterized by strong attractive \\Lambda\\Lambda interaction. The third has weak \\Lambda\\Lambda but strong attractive \\Sigma\\Sigma interactions. The last one has much weaker \\Sigma\\Sigma interaction than the third one. By systematic analyses of the EOSs and mass sequences of NSs, it has been found that the strong attractive N\\Sigma, \\Lambda\\Lambda and \\Sigma\\Sigma interactions are ruled out. The result is consistent to the most recent information on hyperon interactions from the experimental and theoretical i! nvestigations of hypernuclei.

  12. Topics in black-hole physics: geometric constraints on noncollapsing, gravitating systems, and tidal distortions of a Schwarzschild black hole

    International Nuclear Information System (INIS)

    Redmount, I.H.

    1984-01-01

    This dissertation consists of two studies on the general-relativistic theory of black holes. The first work concerns the fundamental issue of black-hole formation: in it geometric constraints are sought on gravitating matter systems, in the special case of axial symmetry, which determine whether or not those systems undergo gravitational collapse to form black holes. The second project deals with mechanical behavior of a black hole: specifically, the tidal deformation of a static black hole is studied by the gravitational fields of external bodies

  13. Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

    Energy Technology Data Exchange (ETDEWEB)

    Bhalla, Amneet Pal Singh [Univ. of North Carolina, Chapel Hill, NC (United States); Knepley, Matthew G. [Rice Univ., Houston, TX (United States); Adams, Mark F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Guy, Robert D. [Univ. of California, Davis, CA (United States); Griffith, Boyce E. [Univ. of North Carolina, Chapel Hill, NC (United States)

    2016-12-20

    The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically, we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.

  14. An online interactive geometric database including exact solutions of Einstein's field equations

    International Nuclear Information System (INIS)

    Ishak, Mustapha; Lake, Kayll

    2002-01-01

    We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed for the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII, used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows systematic internal self-checking and minimization of the required internal records. This new database is now available online at http://grdb.org

  15. Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

    Science.gov (United States)

    Ray, S. Saha

    2018-04-01

    In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

  16. Sensitivity theory for general non-linear algebraic equations with constraints

    International Nuclear Information System (INIS)

    Oblow, E.M.

    1977-04-01

    Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

  17. Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy.

    Science.gov (United States)

    Issack, Bilkiss B; Roy, Pierre-Nicholas

    2005-08-22

    An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

  18. The Obstacle Version of the Geometric Dynamic Programming Principle: Application to the Pricing of American Options Under Constraints

    International Nuclear Information System (INIS)

    Bouchard, Bruno; Vu, Thanh Nam

    2010-01-01

    We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201-236, 2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.

  19. Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

    International Nuclear Information System (INIS)

    Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

    1993-01-01

    We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O(N) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalism. (orig.)

  20. Solution of underdetermined systems of equations with gridded a priori constraints.

    Science.gov (United States)

    Stiros, Stathis C; Saltogianni, Vasso

    2014-01-01

    The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

  1. Operational equations for the five-point rectangle, the geometric mean, and data in prismatic arrray

    Energy Technology Data Exchange (ETDEWEB)

    Silver, Gary L [Los Alamos National Laboratory

    2009-01-01

    This paper describes the results of three applications of operational calculus: new representations of five data in a rectangular array, new relationships among data in a prismatic array, and the operational analog of the geometric mean.

  2. Constraint propagation equations of the 3+1 decomposition of f(R) gravity

    International Nuclear Information System (INIS)

    Paschalidis, Vasileios; Shapiro, Stuart L; Halataei, Seyyed M H; Sawicki, Ignacy

    2011-01-01

    Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term (ω = 0). Using this equivalence and a 3+1 decomposition of the theory, it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (Hamiltonian and momentum) constraints. In this paper, we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.

  3. Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations VIASM 2016

    CERN Document Server

    Tran, Hung

    2017-01-01

    Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the n...

  4. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Korobkin, Oleg; Pazos, Enrique [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Aksoylu, Burak [Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 (United States); Holst, Michael [Department of Mathematics, University of California at San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 (United States); Tiglio, Manuel [Department of Physics, University of Maryland, College Park, MD 20742 (United States)

    2009-07-21

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor psi. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  5. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    International Nuclear Information System (INIS)

    Korobkin, Oleg; Pazos, Enrique; Aksoylu, Burak; Holst, Michael; Tiglio, Manuel

    2009-01-01

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor ψ. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  6. The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

    International Nuclear Information System (INIS)

    Mourad, J.; Sazdjian, H.

    1994-01-01

    The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

  7. Threatened species richness along a Himalayan elevational gradient: quantifying the influences of human population density, range size, and geometric constraints.

    Science.gov (United States)

    Paudel, Prakash Kumar; Sipos, Jan; Brodie, Jedediah F

    2018-02-07

    A crucial step in conserving biodiversity is to identify the distributions of threatened species and the factors associated with species threat status. In the biodiversity hotspot of the Himalaya, very little is known about which locations harbour the highest diversity of threatened species and whether diversity of such species is related to area, mid-domain effects (MDE), range size, or human density. In this study, we assessed the drivers of variation in richness of threatened birds, mammals, reptiles, actinopterygii, and amphibians along an elevational gradient in Nepal Himalaya. Although geometric constraints (MDE), species range size, and human population density were significantly related to threatened species richness, the interaction between range size and human population density was of greater importance. Threatened species richness was positively associated with human population density and negatively associated with range size. In areas with high richness of threatened species, species ranges tend to be small. The preponderance of species at risk of extinction at low elevations in the subtropical biodiversity hotspot could be due to the double impact of smaller range sizes and higher human density.

  8. Improvement of nonlinear diffusion equation using relaxed geometric mean filter for low PSNR images

    DEFF Research Database (Denmark)

    Nadernejad, Ehsan

    2013-01-01

    A new method to improve the performance of low PSNR image denoising is presented. The proposed scheme estimates edge gradient from an image that is regularised with a relaxed geometric mean filter. The proposed method consists of two stages; the first stage consists of a second order nonlinear an...

  9. A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

    Science.gov (United States)

    Li, Jinquan; Feng, Shuang; Mi, Honghai

    In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

  10. Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

    Directory of Open Access Journals (Sweden)

    Suresh Kumar

    2014-10-01

    Full Text Available In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann–Robertson–Walker space–time filled with ordinary matter (baryonic, radiation, dark matter and dark energy, where the latter two components are described by Chevallier–Polarski–Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

  11. Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

    International Nuclear Information System (INIS)

    Sharov, G.S.

    2016-01-01

    Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r s ( z d ). Among the considered models the best value of χ 2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.

  12. The ESS and replicator equation in matrix games under time constraints.

    Science.gov (United States)

    Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás

    2018-06-01

    Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

  13. Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

    International Nuclear Information System (INIS)

    Kumar, Suresh; Xu, Lixin

    2014-01-01

    In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann–Robertson–Walker space–time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier–Polarski–Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch

  14. Dynamics and causality constraints

    International Nuclear Information System (INIS)

    Sousa, Manoelito M. de

    2001-04-01

    The physical meaning and the geometrical interpretation of causality implementation in classical field theories are discussed. Causality in field theory are kinematical constraints dynamically implemented via solutions of the field equation, but in a limit of zero-distance from the field sources part of these constraints carries a dynamical content that explains old problems of classical electrodynamics away with deep implications to the nature of physicals interactions. (author)

  15. Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

    DEFF Research Database (Denmark)

    Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

    Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

  16. Limit equation for vacuum Einstein constraints with a translational Killing vector field in the compact hyperbolic case

    Science.gov (United States)

    Gicquaud, Romain; Huneau, Cécile

    2016-09-01

    We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced in Dahl et al. (2012). We focus on solutions over compact 3-manifolds admitting a S1-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.

  17. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

    Science.gov (United States)

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

  18. Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

    Science.gov (United States)

    Borghero, Francesco; Demontis, Francesco

    2016-09-01

    In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

  19. Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

    Science.gov (United States)

    Boronin, Ivan; Shevlyakov, Andrey

    2018-03-01

    Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

  20. Geometric methods of global attraction in systems of delay differential equations

    Science.gov (United States)

    El-Morshedy, Hassan A.; Ruiz-Herrera, Alfonso

    2017-11-01

    In this paper we deduce criteria of global attraction in systems of delay differential equations. Our methodology is new and consists in "dominating" the nonlinear terms of the system by a scalar function and then studying some dynamical properties of that function. One of the crucial benefits of our approach is that we obtain delay-dependent results of global attraction that cover the best delay-independent conditions. We apply our results in a gene regulatory model and the classical Nicholson's blowfly equation with patch structure.

  1. Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints.

    Science.gov (United States)

    Fiedler, Anna; Raeth, Sebastian; Theis, Fabian J; Hausser, Angelika; Hasenauer, Jan

    2016-08-22

    Ordinary differential equation (ODE) models are widely used to describe (bio-)chemical and biological processes. To enhance the predictive power of these models, their unknown parameters are estimated from experimental data. These experimental data are mostly collected in perturbation experiments, in which the processes are pushed out of steady state by applying a stimulus. The information that the initial condition is a steady state of the unperturbed process provides valuable information, as it restricts the dynamics of the process and thereby the parameters. However, implementing steady-state constraints in the optimization often results in convergence problems. In this manuscript, we propose two new methods for solving optimization problems with steady-state constraints. The first method exploits ideas from optimization algorithms on manifolds and introduces a retraction operator, essentially reducing the dimension of the optimization problem. The second method is based on the continuous analogue of the optimization problem. This continuous analogue is an ODE whose equilibrium points are the optima of the constrained optimization problem. This equivalence enables the use of adaptive numerical methods for solving optimization problems with steady-state constraints. Both methods are tailored to the problem structure and exploit the local geometry of the steady-state manifold and its stability properties. A parameterization of the steady-state manifold is not required. The efficiency and reliability of the proposed methods is evaluated using one toy example and two applications. The first application example uses published data while the second uses a novel dataset for Raf/MEK/ERK signaling. The proposed methods demonstrated better convergence properties than state-of-the-art methods employed in systems and computational biology. Furthermore, the average computation time per converged start is significantly lower. In addition to the theoretical results, the

  2. arXiv Gravitational-wave constraints on the neutron-star-matter Equation of State

    CERN Document Server

    Annala, Eemeli; Kurkela, Aleksi; Vuorinen, Aleksi

    The LIGO/Virgo detection of gravitational waves originating from a neutron-star merger, GW170817, has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter Equations of State (EoSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EoSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that smallest allowed tidal deformability of a similar-mass star is $\\Lambda(1.4 M_\\odot) = 120$.

  3. Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State

    Science.gov (United States)

    Annala, Eemeli; Gorda, Tyler; Kurkela, Aleksi; Vuorinen, Aleksi

    2018-04-01

    The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ (1.4 M⊙)=120 .

  4. Constraints on the symmetry energy from neutron star equation of state

    CERN Document Server

    Miyazaki, K

    2006-01-01

    We develop an equation of state (EOS) for neutron star (NS) matter, which forbids the direct URCA cooling and satisfies the recent information on the mass and the radius, simultaneously. At sub-saturation densities, the symmetry energy of the EOS is well described by a function E_{sym}(\\rho)=31.6(\\rho/\\rho_0)^{\\gamma} with 0.70\\leq\\gamma\\leq0.77. This constraint on the density dependence of the symmetry energy is much severer than that obtained from the analysis of the isospin diffusion date in heavy-ion collisions. Consequently, we can obtain the valuable information on nuclear matter from the astrophysical observations of NSs.

  5. arXiv Gravitational-wave constraints on the neutron-star-matter Equation of State

    CERN Document Server

    Annala, Eemeli; Kurkela, Aleksi; Vuorinen, Aleksi

    2018-04-26

    The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ(1.4  M⊙)=120.

  6. On the numerical evaluation of algebro-geometric solutions to integrable equations

    International Nuclear Information System (INIS)

    Kalla, C; Klein, C

    2012-01-01

    Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations

  7. Elliptic–hyperbolic partial differential equations a mini-course in geometric and quasilinear methods

    CERN Document Server

    Otway, Thomas H

    2015-01-01

    This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example:   • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space   They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvatur...

  8. Geometrical approach to tumor growth

    OpenAIRE

    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...

  9. Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations

    International Nuclear Information System (INIS)

    Frittelli, Simonetta; Gomez, Roberto

    2004-01-01

    We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the Arnowitt-Deser-Misner formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as nontrivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced 'constraint-preserving' boundary conditions becomes apparent

  10. A Minimum Variance Algorithm for Overdetermined TOA Equations with an Altitude Constraint.

    Energy Technology Data Exchange (ETDEWEB)

    Romero, Louis A; Mason, John J.

    2018-04-01

    We present a direct (non-iterative) method for solving for the location of a radio frequency (RF) emitter, or an RF navigation receiver, using four or more time of arrival (TOA) measurements and an assumed altitude above an ellipsoidal earth. Both the emitter tracking problem and the navigation application are governed by the same equations, but with slightly different interpreta- tions of several variables. We treat the assumed altitude as a soft constraint, with a specified noise level, just as the TOA measurements are handled, with their respective noise levels. With 4 or more TOA measurements and the assumed altitude, the problem is overdetermined and is solved in the weighted least squares sense for the 4 unknowns, the 3-dimensional position and time. We call the new technique the TAQMV (TOA Altitude Quartic Minimum Variance) algorithm, and it achieves the minimum possible error variance for given levels of TOA and altitude estimate noise. The method algebraically produces four solutions, the least-squares solution, and potentially three other low residual solutions, if they exist. In the lightly overdermined cases where multiple local minima in the residual error surface are more likely to occur, this algebraic approach can produce all of the minima even when an iterative approach fails to converge. Algorithm performance in terms of solution error variance and divergence rate for bas eline (iterative) and proposed approach are given in tables.

  11. How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

    Science.gov (United States)

    Nestler, Steffen

    2014-05-01

    Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

  12. Improving the Accuracy of Direct Geo-referencing of Smartphone-Based Mobile Mapping Systems Using Relative Orientation and Scene Geometric Constraints

    Directory of Open Access Journals (Sweden)

    Naif M. Alsubaie

    2017-09-01

    Full Text Available This paper introduces a new method which facilitate the use of smartphones as a handheld low-cost mobile mapping system (MMS. Smartphones are becoming more sophisticated and smarter and are quickly closing the gap between computers and portable tablet devices. The current generation of smartphones are equipped with low-cost GPS receivers, high-resolution digital cameras, and micro-electro mechanical systems (MEMS-based navigation sensors (e.g., accelerometers, gyroscopes, magnetic compasses, and barometers. These sensors are in fact the essential components for a MMS. However, smartphone navigation sensors suffer from the poor accuracy of global navigation satellite System (GNSS, accumulated drift, and high signal noise. These issues affect the accuracy of the initial Exterior Orientation Parameters (EOPs that are inputted into the bundle adjustment algorithm, which then produces inaccurate 3D mapping solutions. This paper proposes new methodologies for increasing the accuracy of direct geo-referencing of smartphones using relative orientation and smartphone motion sensor measurements as well as integrating geometric scene constraints into free network bundle adjustment. The new methodologies incorporate fusing the relative orientations of the captured images and their corresponding motion sensor measurements to improve the initial EOPs. Then, the geometric features (e.g., horizontal and vertical linear lines visible in each image are extracted and used as constraints in the bundle adjustment procedure which correct the relative position and orientation of the 3D mapping solution.

  13. Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

    Science.gov (United States)

    Holst, Michael; Meier, Caleb; Tsogtgerel, G.

    2018-01-01

    In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have

  14. Geometrical evidence for dark matter: X-ray constraints on the mass of the elliptical galaxy NGC 720

    Science.gov (United States)

    Buote, David A.; Canizares, Claude R.

    1994-01-01

    -dimensional isopotential surfaces -- we discuss the viability of this assumption for NGC 720. Milgrom's Modification of Newtonian Dynamics (MOND) cannot dispel this manifestation of dark matter. Hence, geometrical considerations require, without mention of pressure or temperature, the presence of an extended, massive dark matter halo in NGC 720. Employing essentially the technique of Buote & Canizares (1992; Buote 1992) we use the shape of the X-ray surface brightness to constrain the shape of the total gravitating matter. The total matter is modeled as either an oblate or prolate spheriod of constant shape and orientation having either a Ferrers (rho approximately r(exp -n)) or Hernquist density. Assuming the X-ray gas is in hydrostatic equilibrium, we construct a model X-ray gas distribution for various temperature profiles. We determine the ellipticity of the total gravitating matter to be epsilon approximately 0.50-0.70. Using the single-temperature model we estimate a total mass approximately (0.41-1.4) x 10(exp 12) h(sub 80) solar mass interior to the ellipsoid of semimajor axis 43.6 h(sub 80) kpc. Ferrers densities as steep as r(exp -3) do not fit the data, but the r(exp -2) and Hernquist models yield excellent fits. We estimate the mass distributions of the stars and the gas and fit the dark matter directly. For a given gas equation of state and functional forms for the visible stars, gas, and dark matter, these models yield a distance-independent and temperature-independent measurement of the ratio of dark mass to stellar mass M(sub DM)/M(sub stars). We estimate a minimum M(sub DM)/M(sub stars) greater than or equal to 4 which corresponds to a total mass slightly greater than that derived from the single-temperature models for distance D = 20h(sub 80) Mpc.

  15. Control-Informed Geometric Optimization of Wave Energy Converters: The Impact of Device Motion and Force Constraints

    Directory of Open Access Journals (Sweden)

    Paula B. Garcia-Rosa

    2015-12-01

    Full Text Available The energy cost for producing electricity via wave energy converters (WECs is still not competitive with other renewable energy sources, especially wind energy. It is well known that energy maximising control plays an important role to improve the performance of WECs, allowing the energy conversion to be performed as economically as possible. The control strategies are usually subsequently employed on a device that was designed and optimized in the absence of control for the prevailing sea conditions in a particular location. If an optimal unconstrained control strategy, such as pseudo-spectral optimal control (PSOC, is adopted, an overall optimized system can be obtained no matter whether the control design is incorporated at the geometry optimization stage or not. Nonetheless, strategies, such as latching control (LC, must be incorporated at the optimization design stage of the WEC geometry if an overall optimized system is to be realised. In this paper, the impact of device motion and force constraints in the design of control-informed optimized WEC geometries is addressed. The aim is to verify to what extent the constraints modify the connection between the control and the optimal device design. Intuitively, one might expect that if the constraints are very tight, the optimal device shape is the same regardless of incorporating or not the constrained control at the geometry optimization stage. However, this paper tests the hypothesis that the imposition of constraints will limit the control influence on the optimal device shape. PSOC, LC and passive control (PC are considered in this study. In addition, constrained versions of LC and PC are presented.

  16. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

    Energy Technology Data Exchange (ETDEWEB)

    Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)

    2016-07-15

    Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

  17. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

    International Nuclear Information System (INIS)

    Dubina, Sean Hyun; Wedgewood, Lewis Edward

    2016-01-01

    Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

  18. Geometric analysis

    CERN Document Server

    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.

  19. Schwinger-Dyson loop equations as the w1+∞-like constraints for hermitian multi-matrix chain model at finite N

    International Nuclear Information System (INIS)

    Cheng, Yi-Xin

    1992-01-01

    The Schwinger-Dyson loop equations for the hermitian multi-matrix chain models at finite N, are derived from the Ward identities of the partition functional under the infinitesimal field transformations. The constraint operators W n (m) satisfy the w 1+∞ -like algebra up to a linear combination of the lower spin operators. We find that the all the higher spin constraints are reducible to the Virasoro-type constraints for all the matrix chain models. (author)

  20. Modelling Hermetic Compressors Using Different Constraint Equations to Accommodate Multibody Dynamics and Hydrodynamic Lubrication

    DEFF Research Database (Denmark)

    Estupinan, Edgar Alberto; Santos, Ilmar

    2009-01-01

    elements are supported by fluid film bearings, where the hydrodynamic interaction forces are described by the Reynolds equation. The system of nonlinear equations is numerically solved for three different restrictive conditions of the motion of the crank, where the third case takes into account lateral...... and tilting oscillations of the extremity of the crankshaft. The numerical results of the behaviour of the journal bearings for each case are presented giving some insights into design parameters such as, maximum oil film pressure, minimum oil film thickness, maximum vibration levels and dynamic reaction...

  1. Impact of a Diagnostic Pressure Equation Constraint on Tornadic Supercell Thunderstorm Forecasts Initialized Using 3DVAR Radar Data Assimilation

    Directory of Open Access Journals (Sweden)

    Guoqing Ge

    2013-01-01

    Full Text Available A diagnostic pressure equation constraint has been incorporated into a storm-scale three-dimensional variational (3DVAR data assimilation system. This diagnostic pressure equation constraint (DPEC is aimed to improve dynamic consistency among different model variables so as to produce better data assimilation results and improve the subsequent forecasts. Ge et al. (2012 described the development of DPEC and testing of it with idealized experiments. DPEC was also applied to a real supercell case, but only radial velocity was assimilated. In this paper, DPEC is further applied to two real tornadic supercell thunderstorm cases, where both radial velocity and radar reflectivity data are assimilated. The impact of DPEC on radar data assimilation is examined mainly based on the storm forecasts. It is found that the experiments using DPEC generally predict higher low-level vertical vorticity than the experiments not using DPEC near the time of observed tornadoes. Therefore, it is concluded that the use of DPEC improves the forecast of mesocyclone rotation within supercell thunderstorms. The experiments using different weighting coefficients generate similar results. This suggests that DPEC is not very sensitive to the weighting coefficients.

  2. Observational constraints on scalar field models of dark energy with barotropic equation of state

    International Nuclear Information System (INIS)

    Sergijenko, Olga; Novosyadlyj, Bohdan; Durrer, Ruth

    2011-01-01

    We constrain the parameters of dynamical dark energy in the form of a classical or tachyonic scalar field with barotropic equation of state jointly with other cosmological parameters using the following datasets: the CMB power spectra from WMAP7, the baryon acoustic oscillations in the space distribution of galaxies from SDSS DR7, the power spectrum of luminous red galaxies from SDSS DR7 and the light curves of SN Ia from 2 different compilations: Union2 (SALT2 light curve fitting) and SDSS (SALT2 and MLCS2k2 light curve fittings). It has been found that the initial value of dark energy equation of state parameter is constrained very weakly by most of the data while the other cosmological parameters are well constrained: their likelihoods and posteriors are similar, their forms are close to Gaussian (or half-Gaussian) and the confidence ranges are narrow. The most reliable determinations of the best-fit value and 1σ confidence range for the initial value of the dark energy equation of state parameter are obtained from the combined datasets including SN Ia data from the full SDSS compilation with MLCS2k2 light curve fitting. In all such cases the best-fit value of this parameter is lower than the value of corresponding parameter for current epoch. Such dark energy loses its repulsive properties and in future the expansion of the Universe changes into contraction. We also perform a forecast for the Planck mock data and show that they narrow significantly the confidence ranges of cosmological parameters values, moreover, their combination with SN SDSS compilation with MLCS2k2 light curve fitting may exclude the fields with initial equation of state parameter > −0.1 at 2σ confidence level

  3. The spinodal constraint on the equation of state of expanded fluids

    International Nuclear Information System (INIS)

    Brosh, Eli; Makov, Guy; Shneck, Roni Z

    2003-01-01

    The spinodal is a locus in the P-V diagram, which is the limit of metastability of a substance with respect to a phase transition. In particular, it is the limit to the negative (tensile) pressure exerted on a liquid, at which the liquid may still be metastable with respect to the gas phase. By requiring that the Helmholtz free energy should be analytic at the spinodal, it is possible to derive the limiting behaviour of thermodynamic properties near the spinodal. In the present paper we show how this analyticity requirement may be used to choose between available equations of state (EOSs). In particular it is shown that the universal equation of state (UEOS) proposed by Vinet et al, complies with the analyticity requirement and may be used to locate the spinodal by extrapolation from within the stable region. The Baonza or 'pseudospinodal' EOS, which is apparently based on the functional form of thermodynamic properties near the spinodal, actually contradicts the analyticity requirement and indeed yields manifestly wrong results in locating the spinodal. However it is shown that the Baonza equation may be viewed as an approximation to the UEOS in states of compression. Its technical importance, which stems from its algebraic simplicity, is also stressed in the present work

  4. Geometrical approach to tumor growth.

    Science.gov (United States)

    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.

  5. 三维装配几何约束闭环系统的递归分解方法%A Recursive Decomposition Algorithm for 3D Assembly Geometric Constraint System with Closed-loops

    Institute of Scientific and Technical Information of China (English)

    黄学良; 李娜; 陈立平

    2013-01-01

    Numerical methods are always employed to solve 3D assembly geometric constraint system with closed-loops which can not be decomposed by the existing decomposition methods,but their inherent inefficiency and instability can not be overcome.In this paper,with the analysis of the structural constraint of serial kinematic chain and the topological structure of geometric constraint closed-loop graph,a recursive decomposition algorithm for 3D geometric constraint system with closed-loops is proposed.The basic idea of the proposed algorithm is to introduce the equivalent geometric constraint combination to substitute the structural constraint of serial kinematic chain,and separate the geometric constraint subsystems which can be solved independently from the geometric constraint system with closed-loops.The proposed method can decompose most 3D geometric constraint closed-loop systems which are always solved by numerical method into a series of geometric constraint subsystems between two rigid bodies which can be solved by analytical or reasoning method,so that the computational efficiency and stability can be improved dramatically.Finally,a typical example has been given to validate the correctness and effectiveness of the proposed method.%由于现有几何约束分解方法无法分解三维装配几何约束闭环系统,故常采用数值迭代方法对其进行求解,但存在效率低、稳定性差等问题.为此,通过分析几何约束闭环图的拓扑结构和串联运动链的结构约束,提出基于串联运动链结构约束等价替换的三维几何约束闭环系统的递归分解方法.该方法通过不断地引入几何约束组合等价替换串联运动链的结构约束,从几何约束闭环系统中分离出可独立求解的子系统,实现几何约束闭环系统的递归分解.该方法可将此前许多必须整体迭代求解的三维几何约束闭环系统分解为一系列可解析求解的2个刚体之间的几何约束

  6. A far-from-CMC existence result for the constraint equations on manifolds with ends of cylindrical type

    International Nuclear Information System (INIS)

    Leach, Jeremy

    2014-01-01

    We extend the study of the vacuum Einstein constraint equations on manifolds with ends of cylindrical type initiated by Chruściel and Mazzeo (2012) and Chruściel et al (2012 Adv. Theor. Math. Phys. at press) by finding a class of solutions to the fully coupled system on such manifolds. We show that given a Yamabe positive metric g which is conformally asymptotically cylindrical on each end and a 2-tensor K such that (tr g K) 2 is bounded below away from zero and asymptotically constant, then we may find an initial data set ( g-bar , K-bar ) such that g-bar lies in the conformal class of g. (paper)

  7. Constraints on deflation from the equation of state of dark energy

    International Nuclear Information System (INIS)

    Baum, Lauris; Frampton, Paul H; Matsuzaki, Shinya

    2008-01-01

    In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE condition (comes back empty) imposes a lower bound on the number N cp of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state w = p/ρ = −1−φ with φ>0. More accurate measurement of φ will constrain N cp . The critical density ρ c in the model has a lower bound ρ c ≥(10 9 GeV) 4 or ρ c ≥(10 18 GeV) 4 when the smallest bound state has size 10 −15 m, or 10 −35 m, respectively

  8. Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints

    Directory of Open Access Journals (Sweden)

    Adom Giffin

    2014-09-01

    Full Text Available In this paper, we continue our efforts to show how maximum relative entropy (MrE can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF. However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA. Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.

  9. Impact of a Geometric Correction for Proximal Flow Constraint on the Assessment of Mitral Regurgitation Severity Using the Proximal Flow Convergence Method.

    Science.gov (United States)

    Jang, Jeong Yoon; Kang, Joon-Won; Yang, Dong Hyun; Lee, Sahmin; Sun, Byung Joo; Kim, Dae-Hee; Song, Jong-Min; Kang, Duk-Hyun; Song, Jae-Kwan

    2018-03-01

    Overestimation of the severity of mitral regurgitation (MR) by the proximal isovelocity surface area (PISA) method has been reported. We sought to test whether angle correction (AC) of the constrained flow field is helpful to eliminate overestimation in patients with eccentric MR. In a total of 33 patients with MR due to prolapse or flail mitral valve, both echocardiography and cardiac magnetic resonance image (CMR) were performed to calculate regurgitant volume (RV). In addition to RV by conventional PISA (RV PISA ), convergence angle (α) was measured from 2-dimensional Doppler color flow maps and RV was corrected by multiplying by α/180 (RV AC ). RV measured by CMR (RV CMR ) was used as a gold standard, which was calculated by the difference between total stroke volume measured by planimetry of the short axis slices and aortic stroke volume by phase-contrast image. The correlation between RV CMR and RV by echocardiography was modest [RV CMR vs. RV PISA (r = 0.712, p < 0.001) and RV CMR vs. RV AC (r = 0.766, p < 0.001)]. However, RV PISA showed significant overestimation (RV PISA - RV CMR = 50.6 ± 40.6 mL vs. RV AC - RV CMR = 7.7 ± 23.4 mL, p < 0.001). The overall accuracy of RV PISA for diagnosis of severe MR, defined as RV ≥ 60 mL, was 57.6% (19/33), whereas it increased to 84.8% (28/33) by using RV AC ( p = 0.028). Conventional PISA method tends to provide falsely large RV in patients with eccentric MR and a simple geometric AC of the proximal constraint flow largely eliminates overestimation.

  10. PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Kailiang [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn [HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)

    2017-01-01

    The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.

  11. Constraints on the Equation-of-State of neutron stars from nearby neutron star observations

    International Nuclear Information System (INIS)

    Neuhäuser, R; Hambaryan, V V; Hohle, M M; Eisenbeiss, T

    2012-01-01

    We try to constrain the Equation-of-State (EoS) of supra-nuclear-density matter in neutron stars (NSs) by observations of nearby NSs. There are seven thermally emitting NSs known from X-ray and optical observations, the so-called Magnificent Seven (M7), which are young (up to few Myrs), nearby (within a few hundred pc), and radio-quiet with blackbody-like X-ray spectra, so that we can observe their surfaces. As bright X-ray sources, we can determine their rotational (pulse) period and their period derivative from X-ray timing. From XMM and/or Chandra X-ray spectra, we can determine their temperature. With precise astrometric observations using the Hubble Space Telescope, we can determine their parallax (i.e. distance) and optical flux. From flux, distance, and temperature, one can derive the emitting area - with assumptions about the atmosphere and/or temperature distribution on the surface. This was recently done by us for the two brightest M7 NSs RXJ1856 and RXJ0720. Then, from identifying absorption lines in X-ray spectra, one can also try to determine gravitational redshift. Also, from rotational phase-resolved spectroscopy, we have for the first time determined the compactness (mass/radius) of the M7 NS RBS1223. If also applied to RXJ1856, radius (from luminosity and temperature) and compactness (from X-ray data) will yield the mass and radius - for the first time for an isolated single neutron star. We will present our observations and recent results.

  12. Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms

    Science.gov (United States)

    Egan, Raphael; Gibou, Frédéric

    2017-10-01

    We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

  13. Development of Constraint Force Equation Methodology for Application to Multi-Body Dynamics Including Launch Vehicle Stage Seperation

    Science.gov (United States)

    Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.

    2016-01-01

    The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.

  14. 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

  15. Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

    Science.gov (United States)

    Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.

    1990-01-01

    In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

  16. Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

    Science.gov (United States)

    Alsing, Justin; Silva, Hector O.; Berti, Emanuele

    2018-04-01

    We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2.0M⊙ sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support >2M⊙ neutron stars, our inference of mmax is able to distinguish between models at odds ratios of up to 12: 1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at 3 - 7 × the nuclear saturation density by ˜30 - 50% compared to simply requiring mmax > 2M⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c_s^max > 0.63c (99.8%), ruling out c_s^max c/√{3} at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

  17. Variational calculus with constraints on general algebroids

    Energy Technology Data Exchange (ETDEWEB)

    Grabowska, Katarzyna [Physics Department, Division of Mathematical Methods in Physics, University of Warsaw, Hoza 69, 00-681 Warszawa (Poland); Grabowski, Janusz [Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, PO Box 21, 00-956 Warszawa (Poland)], E-mail: konieczn@fuw.edu.pl, E-mail: jagrab@impan.gov.pl

    2008-05-02

    Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM.

  18. Variational calculus with constraints on general algebroids

    International Nuclear Information System (INIS)

    Grabowska, Katarzyna; Grabowski, Janusz

    2008-01-01

    Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM

  19. Geometric Liouville gravity

    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

  20. Geometric Rationalization for Freeform Architecture

    KAUST Repository

    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

  1. Path following control of planar snake robots using virtual holonomic constraints: theory and experiments.

    Science.gov (United States)

    Rezapour, Ehsan; Pettersen, Kristin Y; Liljebäck, Pål; Gravdahl, Jan T; Kelasidi, Eleni

    This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

  2. 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.

  3. 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

  4. Optimization of structures to satisfy a flutter velocity constraint by use of quadratic equation fitting. M.S. Thesis

    Science.gov (United States)

    Motiwalla, S. K.

    1973-01-01

    Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.

  5. (2+1)-维耦合的mKP方程的代数几何解%Algebro-Geometric Solutions to (2+1)-Dimensional Coupled Modified Kadomtsev-Petviashvili Equations

    Institute of Scientific and Technical Information of China (English)

    杜殿楼; 杨潇

    2012-01-01

    A (2+1)-dimensional coupled modified Kadomtsev-Petviashvili (CMKP) equation is proposed, and its decomposition is derived by its Lax pair. Based on the theory of algebraic curve, an algebro-geometric solution of the CMKP equation is obtained.%提出一个(2+1)-维耦合的mKP(CMKP)方程,通过其Lax对,实现了该方程的分解.进一步借助代数曲线理论,给出其代数几何解.

  6. 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

  7. Design with Nonlinear Constraints

    KAUST Repository

    Tang, Chengcheng

    2015-01-01

    . The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application

  8. Tissue-Mimicking Geometrical Constraints Stimulate Tissue-Like Constitution and Activity of Mouse Neonatal and Human-Induced Pluripotent Stem Cell-Derived Cardiac Myocytes

    Directory of Open Access Journals (Sweden)

    Götz Pilarczyk

    2016-01-01

    Full Text Available The present work addresses the question of to what extent a geometrical support acts as a physiological determining template in the setup of artificial cardiac tissue. Surface patterns with alternating concave to convex transitions of cell size dimensions were used to organize and orientate human-induced pluripotent stem cell (hIPSC-derived cardiac myocytes and mouse neonatal cardiac myocytes. The shape of the cells, as well as the organization of the contractile apparatus recapitulates the anisotropic line pattern geometry being derived from tissue geometry motives. The intracellular organization of the contractile apparatus and the cell coupling via gap junctions of cell assemblies growing in a random or organized pattern were examined. Cell spatial and temporal coordinated excitation and contraction has been compared on plain and patterned substrates. While the α-actinin cytoskeletal organization is comparable to terminally-developed native ventricular tissue, connexin-43 expression does not recapitulate gap junction distribution of heart muscle tissue. However, coordinated contractions could be observed. The results of tissue-like cell ensemble organization open new insights into geometry-dependent cell organization, the cultivation of artificial heart tissue from stem cells and the anisotropy-dependent activity of therapeutic compounds.

  9. Geometrical parton

    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.

  10. 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

  11. Constraints of the variation of fundamental couplings and sensitivity of the equation of state of dense matter

    Energy Technology Data Exchange (ETDEWEB)

    Perez-Garcia, M. Angeles, E-mail: mperezga@usal.es [Departamento de Fisica Fundamental and IUFFyM, Universidad de Salamanca, E-37008 Salamanca (Spain); Martins, C.J.A.P., E-mail: Carlos.Martins@astro.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal)

    2012-12-05

    We discuss the coupled variations of the gravitational, strong and electroweak coupling constants and the current knowledge of the nuclear equation of state based on heavy ion collision experiments and neutron star mass-radius relationship. In particular we focus in our description on phenomenological parameters, R, relating variations in the quantum chromodynamics scale {Lambda}{sub QCD} and the fine structure constant {alpha}, and S, relating variations of v, the Higgs vacuum expectation value and the Yukawa couplings, h, in the quark sector. This parametrization is valid for any model where gauge coupling unification occurs at some (unspecified) high energy scale. From a physically motivated set of equations of state for dense matter we obtain the constrained parameter phase space (R,S) in high density nuclear environments. This procedure is complementary to (although currently less powerful than) those used in low-density conditions. For variations of {Delta}{alpha}/{alpha}=0.005 we find that the obtained constrained parameter lies on a strip region in the (R,S) plane that partially overlaps some of the allowed values of parameters derived from primordial abundances. This may be of interest in the context of unification scenarios where a dense phase of the universe may have existed at early times.

  12. Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions

    International Nuclear Information System (INIS)

    Klaehn, T.; Blaschke, D.; Typel, S.; Dalen, E. N. E. van; Faessler, A.; Fuchs, C.; Gaitanos, T.; Wolter, H. H.; Grigorian, H.; Ho, A.; Weber, F.; Kolomeitsev, E. E.; Miller, M. C.; Roepke, G.; Truemper, J.; Voskresensky, D. N.

    2006-01-01

    A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below 1.5M · , and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1±0.2M · (1σ level) for PSR J0751+1807 and of 2.0±0.1M · from the innermost stable circular orbit for 4U 1636-536, the baryon mass--gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs

  13. Solution of Einstein's Geometrical Gravitational Field Equations Exterior to Astrophysically Real or Hypothetical Time Varying Distributions of Mass within Regions of Spherical Geometry

    Directory of Open Access Journals (Sweden)

    Chifu E. N.

    2009-07-01

    Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration

  14. Geometric metamorphosis.

    Science.gov (United States)

    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.

  15. 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

  16. Publisher Correction: Geometric constraints during epithelial jamming

    Science.gov (United States)

    Atia, Lior; Bi, Dapeng; Sharma, Yasha; Mitchel, Jennifer A.; Gweon, Bomi; Koehler, Stephan A.; DeCamp, Stephen J.; Lan, Bo; Kim, Jae Hun; Hirsch, Rebecca; Pegoraro, Adrian F.; Lee, Kyu Ha; Starr, Jacqueline R.; Weitz, David A.; Martin, Adam C.; Park, Jin-Ah; Butler, James P.; Fredberg, Jeffrey J.

    2018-06-01

    In the version of this Article originally published, the Supplementary Movies were linked to the wrong descriptions. These have now been corrected. Additionally, the authors would like to note that co-authors James P. Butler and Jeffrey J. Fredberg contributed equally to this Article; this change has now been made.

  17. A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2014-01-01

    Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145

  18. 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.)

  19. 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.)

  20. Initial singularity and pure geometric field theories

    Science.gov (United States)

    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.

  1. Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

    Science.gov (United States)

    Chatterjee, D.; Gulminelli, F.; Raduta, Ad. R.; Margueron, J.

    2017-12-01

    The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a Thomas-Fermi meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. An analytical approximation to the full Thomas-Fermi integrals is further proposed giving a fully analytical meta-model for nuclear masses. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction with Bayesian statistical tools. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full Hartree-Fock or extended Thomas-Fermi calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

  2. Geometric low-energy effective action in a doubled spacetime

    Science.gov (United States)

    Ma, Chen-Te; Pezzella, Franco

    2018-05-01

    The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing β functions. With d compact dimensions, an O (d , d ; Z) geometric structure can be added to it giving the supergravity theory with T-duality manifest. In this paper, this is constructed through the use of a suitable star product whose role is the one to implement the weak constraint on the fields and the gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for d ≥ 1. This orthogonality holds also for an arbitrary number of star products of fields for d = 1. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.

  3. Pragmatic geometric model evaluation

    Science.gov (United States)

    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

  4. Artificial dissipation models applied to Euler equations for analysis of supersonic flow of helium gas around a geometric configurations ramp and diffusor type

    Energy Technology Data Exchange (ETDEWEB)

    Rocha, Jussiê S., E-mail: jussie.soares@ifpi.edu.br [Instituto Federal do Piauí (IFPI), Valença, PI (Brazil); Maciel, Edisson Sávio de Góes, E-mail: edissonsavio@yahoo.com.br [Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos, SP (Brazil); Lira, Carlos A.B.O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil); Sousa, Pedro A.S.; Neto, Raimundo N.C., E-mail: augusto.96pedro@gmail.com, E-mail: r.correia17@hotmail.com [Instituto Federal do Piauí (IFPI), Teresina, PI (Brazil)

    2017-07-01

    Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D{sub E}ULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipation model linear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors. (author)

  5. Artificial dissipation models applied to Navier-Stokes equations for analysis of supersonic flow of helium gas around a geometric configuration ramp type

    International Nuclear Information System (INIS)

    Rocha, Jussie Soares da; Maciel, Edisson Savio de G.; Lira, Carlos A.B. de O.

    2015-01-01

    Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added safety. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in solving the Navier-Stokes equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic laminar flow of helium gas along a ramp configuration is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipations models linear and nonlinear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is to study the cited dissipation models and describe their characteristics in relation to the overall quality of the solution, aiming preliminary results for the development of computational tools of dynamic analysis of helium flow for the VHTGR core. (author)

  6. Artificial dissipation models applied to Euler equations for analysis of supersonic flow of helium gas around a geometric configurations ramp and diffusor type

    International Nuclear Information System (INIS)

    Rocha, Jussiê S.; Maciel, Edisson Sávio de Góes; Lira, Carlos A.B.O.; Sousa, Pedro A.S.; Neto, Raimundo N.C.

    2017-01-01

    Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D E ULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipation model linear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors. (author)

  7. Gravity, a geometrical course

    CERN Document Server

    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...

  8. Geometric recursion

    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...

  9. An efficient formulation for linear and geometric non-linear membrane elements

    Directory of Open Access Journals (Sweden)

    Mohammad Rezaiee-Pajand

    Full Text Available Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.

  10. Parametric FEM for geometric biomembranes

    Science.gov (United States)

    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.

  11. Structure of the space of solutions of Einstein's equations II: Several killing fields and the Einstein-Yang-Mills equations

    International Nuclear Information System (INIS)

    Arms, J.M.; Marsden, J.E.; Moncrief, V.

    1982-01-01

    The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members. Contents: Introduction 1. The Kuranishi map and its properties. 2. The momentum constraints. 3. The Hamiltonian constraints. 4. The Einstein-Yang-Mills system. 5. Discussion and examples

  12. 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.

  13. Convex analysis and nonlinear geometric elliptic equations

    National Research Council Canada - National Science Library

    Bakelʹman, I. ︠I︡A; Bakelman, Ilya J

    1994-01-01

    ... provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the Germa...

  14. 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

  15. Geometrization of quantum physics

    Science.gov (United States)

    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.

  16. 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.

  17. 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.

  18. Visualizing the Geometric Series.

    Science.gov (United States)

    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)

  19. 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.)

  20. Geometrically constrained kinematic global navigation satellite systems positioning: Implementation and performance

    Science.gov (United States)

    Asgari, Jamal; Mohammadloo, Tannaz H.; Amiri-Simkooei, Ali Reza

    2015-09-01

    GNSS kinematic techniques are capable of providing precise coordinates in extremely short observation time-span. These methods usually determine the coordinates of an unknown station with respect to a reference one. To enhance the precision, accuracy, reliability and integrity of the estimated unknown parameters, GNSS kinematic equations are to be augmented by possible constraints. Such constraints could be derived from the geometric relation of the receiver positions in motion. This contribution presents the formulation of the constrained kinematic global navigation satellite systems positioning. Constraints effectively restrict the definition domain of the unknown parameters from the three-dimensional space to a subspace defined by the equation of motion. To test the concept of the constrained kinematic positioning method, the equation of a circle is employed as a constraint. A device capable of moving on a circle was made and the observations from 11 positions on the circle were analyzed. Relative positioning was conducted by considering the center of the circle as the reference station. The equation of the receiver's motion was rewritten in the ECEF coordinates system. A special attention is drawn onto how a constraint is applied to kinematic positioning. Implementing the constraint in the positioning process provides much more precise results compared to the unconstrained case. This has been verified based on the results obtained from the covariance matrix of the estimated parameters and the empirical results using kinematic positioning samples as well. The theoretical standard deviations of the horizontal components are reduced by a factor ranging from 1.24 to 2.64. The improvement on the empirical standard deviation of the horizontal components ranges from 1.08 to 2.2.

  1. Geometric Rationalization for Freeform Architecture

    KAUST Repository

    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

  2. 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)

  3. Constraint Differentiation

    DEFF Research Database (Denmark)

    Mödersheim, Sebastian Alexander; Basin, David; Viganò, Luca

    2010-01-01

    We introduce constraint differentiation, a powerful technique for reducing search when model-checking security protocols using constraint-based methods. Constraint differentiation works by eliminating certain kinds of redundancies that arise in the search space when using constraints to represent...... results show that constraint differentiation substantially reduces search and considerably improves the performance of OFMC, enabling its application to a wider class of problems....

  4. Toward making the constraint hypersurface an attractor in free evolution

    International Nuclear Information System (INIS)

    Fiske, David R.

    2004-01-01

    When constructing numerical solutions to systems of evolution equations subject to a constraint, one must decide what role the constraint equations will play in the evolution system. In one popular choice, known as free evolution, a simulation is treated as a Cauchy problem, with the initial data constructed to satisfy the constraint equations. This initial data are then evolved via the evolution equations with no further enforcement of the constraint equations. The evolution, however, via the discretized evolution equations introduce constraint violating modes at the level of truncation error, and these constraint violating modes will behave in a formalism dependent way. This paper presents a generic method for incorporating the constraint equations into the evolution equations so that the off-constraint dynamics are biased toward the constraint satisfying solutions

  5. Geometric Series and Computers--An Application.

    Science.gov (United States)

    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)

  6. Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms

    International Nuclear Information System (INIS)

    Gan, Dongming; Dias, Jorge; Seneviratne, Lakmal; Dai, Jian S.

    2014-01-01

    This paper investigates various topologies and mobility of a class of metamorphic parallel mechanisms synthesized with reconfigurable rTPS limbs. Based on the reconfigurable Hooke (rT) joint, the rTPS limb has two phases which result in parallel mechanisms having ability of mobility change. While in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane which is used to demonstrate different topologies of the nrTPS metamorphic parallel mechanisms by investigating various relations (parallel or intersecting) among the n constraint planes (n = 2,3,..,6). Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals mobility and redundant geometric conditions of the mechanism topologies. By altering the limbs into the non-constraint phase without constraint plane, new mechanism phases are deduced with mobility change based on each mechanism topology.

  7. Tentative purely geometrical Machian framework for describing gravity and inertia

    Energy Technology Data Exchange (ETDEWEB)

    Goldoni, R [Pisa Univ. (Italy). Ist. di Matematica

    1979-03-03

    The purely geometrical Machian approach to gravitation presented in this letter improves an already published one. In any non vacuum cosmos the gravitational equations in gravitational units are identical to Einstein's equations, while the equations describing the gravitational field in local atomic units are integrodifferential equations in agreement with the available experimental data.

  8. Geometric Design Laboratory

    Data.gov (United States)

    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...

  9. 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.

  10. Thomas Young's contributions to geometrical optics.

    Science.gov (United States)

    Atchison, David A; Charman, W Neil

    2011-07-01

    In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young's construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics. © 2011 The Authors. Clinical and Experimental Optometry © 2011 Optometrists Association Australia.

  11. Structure of the space of solutions of Einstein's equations II: Several killing fields and the Einstein-Yang-Mills equations

    Energy Technology Data Exchange (ETDEWEB)

    Arms, J.M.; Marsden, J.E.; Moncrief, V.

    1982-11-01

    The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members. Contents: Introduction 1. The Kuranishi map and its properties. 2. The momentum constraints. 3. The Hamiltonian constraints. 4. The Einstein-Yang-Mills system. 5. Discussion and examples.

  12. Momentum constraint relaxation

    International Nuclear Information System (INIS)

    Marronetti, Pedro

    2006-01-01

    Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature A ij -tilde, generated by a vector potential w i , as outlined by York. The components of w i are relaxed to solve approximately the momentum constraint equations, slowly pushing the evolution towards the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that it effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly

  13. Harmonic and geometric analysis

    CERN Document Server

    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...

  14. Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

    Directory of Open Access Journals (Sweden)

    Shaochong Yang

    2017-01-01

    Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

  15. The Evolution of Sulfide in Shallow Aquatic Ecosystem Sediments: An Analysis of the Roles of Sulfate, Organic Carbon, and Iron and Feedback Constraints Using Structural Equation Modeling

    Science.gov (United States)

    Pollman, C. D.; Swain, E. B.; Bael, D.; Myrbo, A.; Monson, P.; Shore, M. D.

    2017-11-01

    The generation of elevated concentrations of sulfide in sediment pore waters that are toxic to rooted macrophytes is problematic in both marine and freshwaters. In marine waters, biogeochemical conditions that lead to toxic levels of sulfide generally relate to factors that affect oxygen dynamics or the sediment iron concentration. In freshwaters, increases in surface water sulfate have been implicated in decline of Zizania palustris (wild rice), which is important in wetlands across the Great Lakes region of North America. We developed a structural equation (SE) model to elucidate key variables that govern the evolution of sulfide in pore waters in shallow aquatic habitats that are potentially capable of supporting wild rice. The conceptual basis for the model is the hypothesis that dissimilatory sulfate reduction is limited by the availability of both sulfate and total organic carbon (TOC) in the sediment. The conceptual model also assumes that pore water sulfide concentrations are constrained by the availability of pore water iron and that sediment iron supports the supply of dissolved iron to the pore water. A key result from the SE model is that variations in three external variables (sulfate, sediment TOC, and sediment iron) contribute nearly equally to the observed variations in pore water sulfide. As a result, management efforts to mitigate against the toxic effects of pore water sulfide on macrophytes such as wild rice should approach defining a protective sulfate threshold as an exercise tailored to the geochemistry of each site that quantitatively considers the effects of ambient concentrations of sediment Fe and TOC.

  16. Geometrical Aspects of non-gravitational interactions

    OpenAIRE

    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...

  17. Constraint elimination in dynamical systems

    Science.gov (United States)

    Singh, R. P.; Likins, P. W.

    1989-01-01

    Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

  18. 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)

  19. 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)

  20. On the stationary Einstein-Maxwell-Klein-Gordon equations

    International Nuclear Information System (INIS)

    Gegenberg, J.D.

    1981-05-01

    The stationary Einstein-Maxwell-Klein-Gordon (EMKG) equations for interacting gravitational, electromagnetic and meson fields are examined. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. The EMKG equations are shown to admit a Higgs-like mechanism for giving mass to the gauge field. A theorem specifying sufficient conditions for the stationarity of the spacetime metric to imply stationarity of the other fields is proved. By imposing additional constraints and symmetries, the EMKG equations are considerably simplified. An attempt is made to apply a solution-generation technique, and this meets with only partial success. Finally, a stationary but non-static solution is found, and the geometric and physical properties are discussed

  1. 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

  2. Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

    Science.gov (United States)

    Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

    2018-01-01

    Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

  3. On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations

    Directory of Open Access Journals (Sweden)

    Abbas Badakaya Ja'afaru

    2012-01-01

    Full Text Available We study pursuit and evasion differential game problems described by infinite number of first-order differential equations with function coefficients in Hilbert space l2. Problems involving integral, geometric, and mix constraints to the control functions of the players are considered. In each case, we give sufficient conditions for completion of pursuit and for which evasion is possible. Consequently, strategy of the pursuer and control function of the evader are constructed in an explicit form for every problem considered.

  4. The solution space of the unitary matrix model string equation and the Sato Grassmannian

    International Nuclear Information System (INIS)

    Anagnostopoulos, K.N.; Bowick, M.J.; Schwarz, A.

    1992-01-01

    The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equations is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P, 2 - ]=1, with P and 2 - 2x2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n≥0), where L n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model. (orig.)

  5. Geometric measure theory a beginner's guide

    CERN Document Server

    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.

  6. MM Algorithms for Geometric and Signomial Programming.

    Science.gov (United States)

    Lange, Kenneth; Zhou, Hua

    2014-02-01

    This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

  7. A fast method for linear waves based on geometrical optics

    NARCIS (Netherlands)

    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

  8. Geometrically Induced Interactions and Bifurcations

    Science.gov (United States)

    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.

  9. Some geometric properties of magneto-fluid flows

    OpenAIRE

    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.

  10. Geometric group theory

    CERN Document Server

    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...

  11. Geometric and engineering drawing

    CERN Document Server

    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.

  12. Differential geometric structures

    CERN Document Server

    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.

  13. 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

  14. Solar constraints

    International Nuclear Information System (INIS)

    Provost, J.

    1984-01-01

    Accurate tests of the theory of stellar structure and evolution are available from the Sun's observations. The solar constraints are reviewed, with a special attention to the recent progress in observing global solar oscillations. Each constraint is sensitive to a given region of the Sun. The present solar models (standard, low Z, mixed) are discussed with respect to neutrino flux, low and high degree five-minute oscillations and low degree internal gravity modes. It appears that actually there do not exist solar models able to fully account for all the observed quantities. (Auth.)

  15. 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.

  16. Diffusion equation and non-holonomy

    International Nuclear Information System (INIS)

    Gomes, Luiz Carlos; Lobo, R.; Simao, F.R.A.

    1980-01-01

    The diffusion equation for particles in a Riemannian space subject to a single constraint is discussed. The implications of the holonomy and non-holonomy of this single constraint is also discussed. (L.C.) [pt

  17. Geometric Programming Approach to an Interactive Fuzzy Inventory Problem

    Directory of Open Access Journals (Sweden)

    Nirmal Kumar Mandal

    2011-01-01

    Full Text Available An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric programming method. If the decision maker is not satisfied with this result, he/she may try to update the current solution to his/her satisfactory solution. In this way we implement man-machine interactive procedure to solve the problem through geometric programming method.

  18. Geometric approximation algorithms

    CERN Document Server

    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.

  19. Geometrical optical illusionists.

    Science.gov (United States)

    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.

  20. Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics

    International Nuclear Information System (INIS)

    Vollick, Dan N.

    2004-01-01

    The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor R or μν , consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with R or μν =0 the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field

  1. Geometrical constraint on the localization of deep water formation

    Science.gov (United States)

    Ferreira, D.; Marshall, J.

    2008-12-01

    That deep water formation occurs in the North Atlantic and not North Pacific is one of the most notable features of the present climate. In an effort to build a system able to mimic such basic aspects of climate using a minimal description, we study here the influence of ocean geometry on the localization of deep water formation. Using the MIT GCM, two idealized configurations of an ocean-atmosphere-sea ice climate system are studied: Drake and Double-Drake. In Drake, one narrow barrier extends from the North Pole to 35°S while, in Double-Drake, two such barriers set 90° apart join at the North Pole to delimit a Small and a Large basin. Despite the different continental configurations, the two climates are strikingly similar in the zonal average (almost identical heat and fresh water transports, and meridional overturning circulation). However, regional circulations in the Small and Large basins exhibit distinctive Atlantic-like and Pacific-like characteristics: the Small basin is warmer and saltier than the Large one, concentrates dense water formation and deep overturning circulation and achieve the largest fraction of the northward ocean heat transport. We show that the warmer temperature and higher evaporation over the Small basin is not its distinguishing factor. Rather, it is the width of the basin in relation to the zonal fetch of the precipitation pattern. This generates a deficit/excess of precipitation over the Small/Large basin: a fraction of the moisture evaporated from the Small basin is transported zonally and rains out over the Large basin. This creates a salt contrast between the 2 basins, leading to the localization of deep convection in the salty Small basin. Finally, given on the broad similarities between the Double-Drake and real World, we suggest that many gross features that define the present climate are a consequence of 2 asymmetries: a meridional asymmetry (a zonally unblocked southern/blocked northern ocean) and a zonal one (a small and a large basin in the northern hemisphere).

  2. Modulation of collective cell behaviour by geometrical constraints

    Czech Academy of Sciences Publication Activity Database

    Lunova, M.; Zablotskyy, V.; Dempsey, N.M.; Devillers, T.; Jirsa, M.; Syková, Eva; Kubinová, Šárka; Lunov, O.; Dejneka, A.

    2016-01-01

    Roč. 8, č. 11 (2016), s. 1099-1110 ISSN 1757-9694 R&D Projects: GA MŠk(CZ) LO1309 Institutional support: RVO:68378041 Keywords : mesenchymal stem-cells * biophysical regulation * nuclear-structure Subject RIV: FP - Other Medical Disciplines Impact factor: 3.252, year: 2016

  3. Shaping tissues by balancing active forces and geometric constraints

    NARCIS (Netherlands)

    Foolen, J.; Yamashi, T.; Kollmannsberger, P.

    2015-01-01

    The self-organization of cells into complex tissues during growth and regeneration is a combination of physical–mechanical events and biochemical signal processing. Cells actively generate forces at all stages in this process, and according to the laws of mechanics, these forces result in stress

  4. Geometric methods in PDE’s

    CERN Document Server

    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. .

  5. A user friendly method for image based acquisition of constraint information during constrained motion of servo manipulator in hot-cells

    International Nuclear Information System (INIS)

    Saini, Surendra Singh; Sarkar, Ushnish; Swaroop, Tumapala Teja; Panjikkal, Sreejith; Ray, Debasish Datta

    2016-01-01

    In master slave manipulator, slave arm is controlled by an operator to manipulate the objects in remote environment using an iso-kinematic master arm which is located in the control room. In such a scenario, where the actual work environment is separated from the operator, formulation of techniques for assisting the operator to execute constrained motion (preferential inclusion or preferential exclusion of workspace zones) in the slave environment are not only helpful, but also essential. We had earlier demonstrated the efficacy of constraint motion with predefined geometrical constraints of various types. However, in a hot-cell scenario the generation of the constraint equations is difficult since we shall not have access to the cell for taking measurements. In this paper, a user friendly method is proposed for image based acquisition of the various constraint geometries thus eliminating the need to take in-cell measurements. For this purpose various hot cell tasks and required geometrical primitives pertaining to these tasks have been surveyed and an algorithm has been developed for generating the constraint geometry for each primitive. This methodology shall increase the efficiency and ease of use of the hot cell Telemanipulator by providing real time constraint acquisition and subsequent assistive force based constrained motion. (author)

  6. The constraints

    International Nuclear Information System (INIS)

    Jones, P.M.S.

    1987-01-01

    There are considerable incentives for the use of nuclear in preference to other sources for base load electricity generation in most of the developed world. These are economic, strategic, environmental and climatic. However, there are two potential constraints which could hinder the development of nuclear power to its full economic potential. These are public opinion and financial regulations which distort the nuclear economic advantage. The concerns of the anti-nuclear lobby are over safety, (especially following the Chernobyl accident), the management of radioactive waste, the potential effects of large scale exposure of the population to radiation and weapons proliferation. These are discussed. The financial constraint is over two factors, the availability of funds and the perception of cost, both of which are discussed. (U.K.)

  7. 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

  8. Portfolios with nonlinear constraints and spin glasses

    Science.gov (United States)

    Gábor, Adrienn; Kondor, I.

    1999-12-01

    In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

  9. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  10. 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.

  11. 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

  12. Geometric Series via Probability

    Science.gov (United States)

    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…

  13. Geometric mechanics of periodic pleated origami.

    Science.gov (United States)

    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.

  14. Design with Nonlinear Constraints

    KAUST Repository

    Tang, Chengcheng

    2015-12-10

    Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.

  15. Geometric Reasoning for Automated Planning

    Science.gov (United States)

    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.

  16. 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.

  17. Dynamics in geometrical confinement

    CERN Document Server

    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...

  18. Geometric group theory

    CERN Document Server

    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...

  19. Lectures in geometric combinatorics

    CERN Document Server

    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...

  20. 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.

  1. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  2. Geometric homology revisited

    OpenAIRE

    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...

  3. Geometric measure theory

    CERN Document Server

    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.

  4. Developing geometrical reasoning

    OpenAIRE

    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...

  5. Geometrically Consistent Mesh Modification

    KAUST Repository

    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.

  6. Geometric theory of information

    CERN Document Server

    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.

  7. 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

  8. 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

  9. Constraints on the CP-Violating MSSM

    CERN Document Server

    Arbey, A; Godbole, R M; Mahmoudi, F

    2016-01-01

    We discuss the prospects for observing CP violation in the MSSM with six CP-violating phases, using a geometric approach to maximise CP-violating observables subject to the experimental upper bounds on electric dipole moments. We consider constraints from Higgs physics, flavour physics, the dark matter relic density and spin-independent scattering cross section with matter.

  10. Freedom and constraint analysis and optimization

    NARCIS (Netherlands)

    Brouwer, Dannis Michel; Boer, Steven; Aarts, Ronald G.K.M.; Meijaard, Jacob Philippus; Jonker, Jan B.

    2011-01-01

    Many mathematical and intuitive methods for constraint analysis of mechanisms have been proposed. In this article we compare three methods. Method one is based on Grüblers equation. Method two uses an intuitive analysis method based on opening kinematic loops and evaluating the constraints at the

  11. 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.

  12. 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

  13. Geometric Computing for Freeform Architecture

    KAUST Repository

    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

  14. Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis

    Science.gov (United States)

    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.

  15. Geometric Constructions with the Computer.

    Science.gov (United States)

    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…

  16. Optimizing clinical performance and geometrical robustness of a new electrode device for intracranial tumor electroporation

    DEFF Research Database (Denmark)

    Mahmood, Faisal; Gehl, Julie

    2011-01-01

    and genes to intracranial tumors in humans, and demonstrate a method to optimize the design (i.e. geometry) of the electrode device prototype to improve both clinical performance and geometrical tolerance (robustness). We have employed a semiempirical objective function based on constraints similar to those...... sensitive to random geometrical deviations. The method is readily applicable to other electrode configurations....

  17. Geometric Algebra Computing

    CERN Document Server

    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

  18. 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

  19. 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

  20. 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.)

  1. 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

  2. Entropy Measures as Geometrical Tools in the Study of Cosmology

    Directory of Open Access Journals (Sweden)

    Gilbert Weinstein

    2017-12-01

    Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.

  3. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

    International Nuclear Information System (INIS)

    He, Ji-Huan; Elagan, S.K.; Li, Z.B.

    2012-01-01

    The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

  4. Renormgroup symmetries in problems of nonlinear geometrical optics

    International Nuclear Information System (INIS)

    Kovalev, V.F.

    1996-01-01

    Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

  5. 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.

  6. Partial Differential Equations in General Relativity

    International Nuclear Information System (INIS)

    Choquet-Bruhat, Yvonne

    2008-01-01

    General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

  7. Partial Differential Equations in General Relativity

    Energy Technology Data Exchange (ETDEWEB)

    Choquet-Bruhat, Yvonne

    2008-09-07

    General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

  8. Geometric constraints on the space of N = 2 SCFTs. Part I: physical constraints on relevant deformations

    Science.gov (United States)

    Argyres, Philip; Lotito, Matteo; Lü, Yongchao; Martone, Mario

    2018-02-01

    We initiate a systematic study of four dimensional N = 2 superconformal field theories (SCFTs) based on the analysis of their Coulomb branch geometries. Because these SCFTs are not uniquely characterized by their scale-invariant Coulomb branch geometries we also need information on their deformations. We construct all inequivalent such deformations preserving N = 2 supersymmetry and additional physical consistency conditions in the rank 1 case. These not only include all the ones previously predicted by S-duality, but also 16 additional deformations satisfying all the known N = 2 low energy consistency conditions. All but two of these additonal deformations have recently been identified with new rank 1 SCFTs; these identifications are briefly reviewed. Some novel ingredients which are important for this study include: a discussion of RG-flows in the presence of a moduli space of vacua; a classification of local N = 2 supersymmetry-preserving deformations of unitary N = 2 SCFTs; and an analysis of charge normalizations and the Dirac quantization condition on Coulomb branches. This paper is the first in a series of three. The second paper [1] gives the details of the explicit construction of the Coulomb branch geometries discussed here, while the third [2] discusses the computation of central charges of the associated SCFTs.

  9. Geometric theory on the elasticity of bio-membranes

    OpenAIRE

    Tu, Z. C.; Ou-Yang, Z. C.

    2004-01-01

    The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membrane...

  10. Fast geometric algorithms

    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

  11. Geometrical Image Transforms

    OpenAIRE

    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...

  12. 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)

  13. 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

  14. Geometrization of the electromagnetic field and dark matter

    International Nuclear Information System (INIS)

    Pestov, I.B.

    2005-01-01

    A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent local symmetry. The equations of dark matter field are derived that are invariant with respect to the local transformations. It is shown how to reduce these equations to the Maxwell equations. Thus, the dark matter field may be considered as generalized electromagnetic field and a simple solution of the old problem is given to connect electromagnetic field with geometrical properties of the physical manifold itself. It is shown that gauge fixing renders generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopical level (and to recognize the fundamental role of internal symmetry) the general covariant Dirac equation is derived in the Minkowski space-time which describes the interactions of spinor field with dark matter field

  15. Geometrization of the Electromagnetic Field and Dark Matter

    CERN Document Server

    Pestov, I B

    2005-01-01

    A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent local symmetry. The equations of dark matter field are derived that are invariant with respect to the local transformations. It is shown how to reduce these equations to the Maxwell equations. Thus, the dark matter field may be considered as generalized lectromagnetic field and a simple solution of the old problem is given to connect electromagnetic field with geometrical properties of the physical manifold itself. It is shown that gauge fixing renders generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopical level (and to recognize the fundamental role of internal symmetry) the general covariant Dirac equation is derived in the Minkowski space--time which des...

  16. Geometric construction of extended supergravity

    International Nuclear Information System (INIS)

    Kostelecky, V.A.

    1982-01-01

    This work describes the explict construction of the locally SO(4)-invariant, on-shell de Sitter supergravity. First, aspects of classical differential geometry used in the construction of local gauge theories are reviewed. Emphasis is placed on fiber bundles and their uses in Yang-Mills and Einstein theories. Next, the extension of the formalism to differential supergeometry is outlined. Applications to extended supergravities are discussed. Finally, the O(4) deSitter supergravity is obtained by considering a bundle of frames constructed using the orthosymplectic superalgebra osp(4/4). The structure group of this bundle is Sl(2C) x SO(4) and the tangent space to the base supermanifold is homeomorphic to the coset osp(4/4)/sl(2C) x so(4). Constraints taken into the Bianchi identifies yield a realization of the superalgebra in the function space of connections, vielbeins, curvatures and torsions of the bundle. Auxiliary fields, transformation laws and equations of motion are determined. Consistency of the realization is verified, proving closure of the algebra. The associated Poincare supergravity is obtained by a contraction

  17. Calculation of the geometric buckling for reactors of various shapes

    Energy Technology Data Exchange (ETDEWEB)

    Sjoestrand, N E

    1958-05-15

    A systematic investigation is made of the eleven coordinate systems in which the reactor equation {nabla}{sup 2}{phi} + B{sup 2}{phi} = 0 is separable. The fundamental solution and geometric buckling are given for those cases where the separated equations lead to known functions. It is especially shown that reactors of prolate and oblate spheroidal shape can be calculated in detail, and the results are given in extensive tables.

  18. ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY

    OpenAIRE

    Enrique Gonzalo Reyes Garcia

    2004-01-01

    ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...

  19. 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

  20. Geometrical meaning of Baecklund transformation for Ernst equation

    International Nuclear Information System (INIS)

    Hou Boyu; Hou Boyuan; Wang Pei

    1983-01-01

    An Einstein spacetime E admitting a two-parameter Abelian group G 2 of isometries may be described covariantly on a two dimensional manifold S. From the two independent Killing vector fields that generate the group G 2 a 2x2 matrix is obtained. For simplicity the authors stick to the assumption that both Killing vectors are spacelike, but the case that one of Killing vectors is timelike can be discussed similarly. So in this case the base space S is a 2-dimensional Minkowski space. (Auth.)

  1. 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.)

  2. 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

  3. 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'

  4. 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)

  5. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  6. Diffusion Processes Satisfying a Conservation Law Constraint

    Directory of Open Access Journals (Sweden)

    J. Bakosi

    2014-01-01

    Full Text Available We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the nonnegativity and the unit-sum conservation law constraints are satisfied as the variables evolve in time. We investigate the consequences of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.

  7. A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

    CERN Document Server

    Vacaru, Sergiu I.; Yazici, Enis

    2014-01-01

    We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.

  8. Space-time-matter analytic and geometric structures

    CERN Document Server

    Brüning, Jochen

    2018-01-01

    At the boundary of mathematics and mathematical physics, this monograph explores recent advances in the mathematical foundations of string theory and cosmology. The geometry of matter and the evolution of geometric structures as well as special solutions, singularities and stability properties of the underlying partial differential equations are discussed.

  9. Some geometric properties of magneto-fluid flows

    Directory of Open Access Journals (Sweden)

    S. S. Gangwar

    1982-01-01

    Full Text Available 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.

  10. A geometrical approach to free-field quantization

    International Nuclear Information System (INIS)

    Tabensky, R.; Valle, J.W.F.

    1977-01-01

    A geometrical approach to the quantization of free relativistic fields is given. Complex probability amplitudes are assigned to the solutions of the classical evolution equation. It is assumed that the evolution is stricly classical, according to the scalar unitary representation of the Poincare group in a functional space. The theory is equivalent to canonical quantization [pt

  11. A geometric model for magnetizable bodies with internal variables

    Directory of Open Access Journals (Sweden)

    Restuccia, L

    2005-11-01

    Full Text Available In a geometrical framework for thermo-elasticity of continua with internal variables we consider a model of magnetizable media previously discussed and investigated by Maugin. We assume as state variables the magnetization together with its space gradient, subjected to evolution equations depending on both internal and external magnetic fields. We calculate the entropy function and necessary conditions for its existence.

  12. Geometric and Algebraic Approaches in the Concept of Complex Numbers

    Science.gov (United States)

    Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.

    2006-01-01

    This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

  13. Life Science-Related Physics Laboratory on Geometrical Optics

    Science.gov (United States)

    Edwards, T. H.; And Others

    1975-01-01

    Describes a laboratory experiment on geometrical optics designed for life science majors in a noncalculus introductory physics course. The thin lens equation is used by the students to calculate the focal length of the lens necessary to correct a myopic condition in an optical bench simulation of a human eye. (Author/MLH)

  14. Geometrical description of fields

    International Nuclear Information System (INIS)

    Sokolik, H.

    1979-01-01

    The author suggests a purely algebraic interpretation of interaction. The main idea is to consider interaction as a deformation of an inhomogeneous algebra composed of momentum operators and an arbitrary group admitting the equation of the theory. The only difference between this approach and the conventional one is that the generalized momentum operators do not commute with aech other, due not merely to the introduction of some external interaction field, but to the change of the structure of the algebra from which the theory stems

  15. Thermomechanical constraints and constitutive formulations in thermoelasticity

    Directory of Open Access Journals (Sweden)

    Baek S.

    2003-01-01

    Full Text Available We investigate three classes of constraints in a thermoelastic body: (i a deformation-temperature constraint, (ii a deformation-entropy constraint, and (iii a deformation-energy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii and (iii are equivalent. By using a limiting procedure, we show that for the constraint (i, the entropy plays the role of a Lagrange multiplier while for (ii and (iii, the absolute temperature plays the role of Lagrange multiplier. We further demonstrate that the governing equations for materials subject to constraint (i are identical to those of an unconstrained material whose internal energy is an affine function of the entropy, while those for materials subject to constraints (ii and (iii are identical to those of an unstrained material whose Helmholtz potential is affine in the absolute temperature. Finally, we model the thermoelastic response of a peroxide-cured vulcanizate of natural rubber and show that imposing the constraint in which the volume change depends only on the internal energy leads to very good predictions (compared to experimental results of the stress and temperature response under isothermal and isentropic conditions.

  16. Regular Polygons and Geometric Series.

    Science.gov (United States)

    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)

  17. Geometric Invariants and Object Recognition.

    Science.gov (United States)

    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

  18. 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.

  19. On the constraints violation in forward dynamics of multibody systems

    Energy Technology Data Exchange (ETDEWEB)

    Marques, Filipe [University of Minho, Department of Mechanical Engineering (Portugal); Souto, António P. [University of Minho, Department of Textile Engineering (Portugal); Flores, Paulo, E-mail: pflores@dem.uminho.pt [University of Minho, Department of Mechanical Engineering (Portugal)

    2017-04-15

    It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method.

  20. Rayleigh's hypothesis and the geometrical optics limit.

    Science.gov (United States)

    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.

  1. The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

    OpenAIRE

    Maj, Omar

    2004-01-01

    The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...

  2. Mathematics and Maxwell's equations

    International Nuclear Information System (INIS)

    Boozer, Allen H

    2010-01-01

    The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.

  3. 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

  4. On the geometrical approach to the relativistic string theory

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Nesterenko, V.V.

    1978-01-01

    In a geometrical approach to the string theory in the four-dimensional Minkowski space the relativistic invariant gauge proposed earlier for the string moving in three-dimensional space-time is used. In contrast to the results of previous paper the system of equations for the coefficients of the fundamental forms of the string model world sheet can be reduced now to one nonlinear Lionville equation again but for a complex valued function u. It is shown that in the case of space-time with arbitrary dimension there are such string motions which are described by one non-linear equation with a real function u. And as a consequence the soliton solutions investigated earlier take place in a geometrical approach to the string theory in any dimensional space-time

  5. Polarization ellipse and Stokes parameters in geometric algebra.

    Science.gov (United States)

    Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

    2012-01-01

    In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

  6. Quantum no-singularity theorem from geometric flows

    Science.gov (United States)

    Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

    2018-04-01

    In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

  7. 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)

  8. Geometric Computing for Freeform Architecture

    KAUST Repository

    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.

  9. 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

  10. 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)

  11. Multiscale geometric modeling of macromolecules II: Lagrangian representation

    Science.gov (United States)

    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

  12. On the motion of matter in the geometrical gauge field theory

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2005-01-01

    In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. The problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries

  13. Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load.

    Science.gov (United States)

    Huang, Yonghui; Yang, Zhicheng; Liu, Airong; Fu, Jiyang

    2018-05-28

    The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL's dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

  14. Discrete geometric structures for architecture

    KAUST Repository

    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

  15. Geometrical optics in general relativity

    OpenAIRE

    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.

  16. 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.

  17. Geometric inequalities methods of proving

    CERN Document Server

    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. .

  18. 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.

  19. 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.

  20. A note on the geometric unification of gravity and electromagnetism

    International Nuclear Information System (INIS)

    Coley, A.

    1984-01-01

    In recent years there have been many authors that have sought a geometrically unified theory of gravity and electromagnetism. It will be argued that the motivation behind the search for such a unified theory on geometric grounds alone is both erroneous and misleading. It is felt that any new unified theory of gravity and electromagnetism must include an explanation of why the existing theory is inadequate, and should provide clear physical reasons for introducing new fields (or field equations) that appear in the theory. (author)

  1. Geometric scalar theory of gravity beyond spherical symmetry

    Science.gov (United States)

    Moschella, U.; Novello, M.

    2017-04-01

    We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

  2. Large-scale block adjustment without use of ground control points based on the compensation of geometric calibration for ZY-3 images

    Science.gov (United States)

    Yang, Bo; Wang, Mi; Xu, Wen; Li, Deren; Gong, Jianya; Pi, Yingdong

    2017-12-01

    The potential of large-scale block adjustment (BA) without ground control points (GCPs) has long been a concern among photogrammetric researchers, which is of effective guiding significance for global mapping. However, significant problems with the accuracy and efficiency of this method remain to be solved. In this study, we analyzed the effects of geometric errors on BA, and then developed a step-wise BA method to conduct integrated processing of large-scale ZY-3 satellite images without GCPs. We first pre-processed the BA data, by adopting a geometric calibration (GC) method based on the viewing-angle model to compensate for systematic errors, such that the BA input images were of good initial geometric quality. The second step was integrated BA without GCPs, in which a series of technical methods were used to solve bottleneck problems and ensure accuracy and efficiency. The BA model, based on virtual control points (VCPs), was constructed to address the rank deficiency problem caused by lack of absolute constraints. We then developed a parallel matching strategy to improve the efficiency of tie points (TPs) matching, and adopted a three-array data structure based on sparsity to relieve the storage and calculation burden of the high-order modified equation. Finally, we used the conjugate gradient method to improve the speed of solving the high-order equations. To evaluate the feasibility of the presented large-scale BA method, we conducted three experiments on real data collected by the ZY-3 satellite. The experimental results indicate that the presented method can effectively improve the geometric accuracies of ZY-3 satellite images. This study demonstrates the feasibility of large-scale mapping without GCPs.

  3. Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

    Science.gov (United States)

    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.

  4. 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.

  5. 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

  6. Geometric flows in Horava-Lifshitz gravity

    CERN Document Server

    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...

  7. Fluid mechanics a geometrical point of view

    CERN Document Server

    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...

  8. 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)

  9. An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics

    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

  10. 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.

  11. Auto-focusing accelerating hyper-geometric laser beams

    International Nuclear Information System (INIS)

    Kovalev, A A; Kotlyar, V V; Porfirev, A P

    2016-01-01

    We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory. (paper)

  12. Geometrical theory of nonlinear phase distortion of intense laser beams

    International Nuclear Information System (INIS)

    Glaze, J.A.; Hunt, J.T.; Speck, D.R.

    1975-01-01

    Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier

  13. High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3D surface-shape measurement.

    Science.gov (United States)

    Liu, Xinran; Kofman, Jonathan

    2017-07-10

    A new fringe projection method for surface-shape measurement was developed using four high-frequency phase-shifted background modulation fringe patterns. The pattern frequency is determined using a new fringe-wavelength geometry-constraint model that allows only two corresponding-point candidates in the measurement volume. The correct corresponding point is selected with high reliability using a binary pattern computed from intensity background encoded in the fringe patterns. Equations of geometry-constraint parameters permit parameter calculation prior to measurement, thus reducing measurement computational cost. Experiments demonstrated the ability of the method to perform 3D shape measurement for a surface with geometric discontinuity, and for spatially isolated objects.

  14. Robust Utility Maximization Under Convex Portfolio Constraints

    International Nuclear Information System (INIS)

    Matoussi, Anis; Mezghani, Hanen; Mnif, Mohamed

    2015-01-01

    We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle

  15. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  16. Geometric group theory an introduction

    CERN Document Server

    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.

  17. Geometric procedures for civil engineers

    CERN Document Server

    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.

  18. Geometrization and Generalization of the Kowalevski Top

    Science.gov (United States)

    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.

  19. An introduction to geometrical physics

    CERN Document Server

    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

  20. Asymptotic geometric analysis, part I

    CERN Document Server

    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

  1. 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

  2. Geometric integration for particle accelerators

    Science.gov (United States)

    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.

  3. 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.)

  4. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  5. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    Science.gov (United States)

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  6. L∞ Variational Problems with Running Costs and Constraints

    International Nuclear Information System (INIS)

    Aronsson, G.; Barron, E. N.

    2012-01-01

    Various approaches are used to derive the Aronsson–Euler equations for L ∞ calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson–Euler equation for the basic L ∞ problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.

  7. Optimal portfolio strategies under a shortfall constraint | Akume ...

    African Journals Online (AJOL)

    We impose dynamically, a shortfall constraint in terms of Tail Conditional Expectation on the portfolio selection problem in continuous time, in order to obtain optimal strategies. The nancial market is assumed to comprise n risky assets driven by geometric Brownian motion and one risk-free asset. The method of Lagrange ...

  8. Origin of constraints in relativistic classical Hamiltonian dynamics

    International Nuclear Information System (INIS)

    Mallik, S.; Hugentobler, E.

    1979-01-01

    We investigate the null-plane or the front form of relativistic classical Hamiltonian dynamics as proposed by Dirac and developed by Leutwyler and Stern. For systems of two spinless particles we show that the algebra of Poincare generators is equivalent to describing dynamics in terms of two covariant constraint equations, the Poisson bracket of the two constraints being weakly zero. The latter condition is solved for certain simple forms of constraints

  9. 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.

  10. Time evolution in a geometric model of a particle

    International Nuclear Information System (INIS)

    Atiyah, M.F.; Franchetti, G.; Schroers, B.J.

    2015-01-01

    We analyse the properties of a (4+1)-dimensional Ricci-flat spacetime which may be viewed as an evolving Taub-NUT geometry, and give exact solutions of the Maxwell and gauged Dirac equation on this background. We interpret these solutions in terms of a geometric model of the electron and its spin, and discuss links between the resulting picture and Dirac’s Large Number Hypothesis.

  11. Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

    Directory of Open Access Journals (Sweden)

    Gloria Marí Beffa

    2008-03-01

    Full Text Available In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998, 161-213; 55 (1999, 127-208]. The paper discusses the close connection between different types of geometries and the type of equations they realize. In particular, we describe the direct relation between symmetric spaces and equations of KdV-type, and the possible geometric origins of this connection.

  12. Constraints from jet calculus on quark recombination

    International Nuclear Information System (INIS)

    Jones, L.M.; Lassila, K.E.; Willen, D.

    1979-01-01

    Within the QCD jet calculus formalism, we deduce an equation describing recombination of quarks and antiquarks into mesons within a quark or gluon jet. This equation relates the recombination function R(x 1 ,x 2 ,x) used in current literature to the fragmentation function for producing that same meson out of the parton initiating the jet. We submit currently used recombination functions to our consistency test, taking as input mainly the u-quark fragmentation data into π + mesons, but also s-quark fragmentation into K - mesons. The constraint is well satisfied at large Q 2 for large moments. Our results depend on one parameter, Q 0 2 , the constraint equation being satisfied for small values of this parameter

  13. A geometric theory on the elasticity of bio-membranes

    International Nuclear Information System (INIS)

    Tu, Z C; Ou-Yang, Z C

    2004-01-01

    The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status of theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on surfaces embedded in three-dimensional Euclidean space by using exterior differential forms

  14. 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...

  15. In Defence of Geometrical Algebra

    NARCIS (Netherlands)

    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

  16. 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.)

  17. 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.)

  18. 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)

  19. Vergence, Vision, and Geometric Optics

    Science.gov (United States)

    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…

  20. 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)

  1. 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)

  2. Future Cosmological Constraints From Fast Radio Bursts

    Science.gov (United States)

    Walters, Anthony; Weltman, Amanda; Gaensler, B. M.; Ma, Yin-Zhe; Witzemann, Amadeus

    2018-03-01

    We consider the possible observation of fast radio bursts (FRBs) with planned future radio telescopes, and investigate how well the dispersions and redshifts of these signals might constrain cosmological parameters. We construct mock catalogs of FRB dispersion measure (DM) data and employ Markov Chain Monte Carlo analysis, with which we forecast and compare with existing constraints in the flat ΛCDM model, as well as some popular extensions that include dark energy equation of state and curvature parameters. We find that the scatter in DM observations caused by inhomogeneities in the intergalactic medium (IGM) poses a big challenge to the utility of FRBs as a cosmic probe. Only in the most optimistic case, with a high number of events and low IGM variance, do FRBs aid in improving current constraints. In particular, when FRBs are combined with CMB+BAO+SNe+H 0 data, we find the biggest improvement comes in the {{{Ω }}}{{b}}{h}2 constraint. Also, we find that the dark energy equation of state is poorly constrained, while the constraint on the curvature parameter, Ω k , shows some improvement when combined with current constraints. When FRBs are combined with future baryon acoustic oscillation (BAO) data from 21 cm Intensity Mapping, we find little improvement over the constraints from BAOs alone. However, the inclusion of FRBs introduces an additional parameter constraint, {{{Ω }}}{{b}}{h}2, which turns out to be comparable to existing constraints. This suggests that FRBs provide valuable information about the cosmological baryon density in the intermediate redshift universe, independent of high-redshift CMB data.

  3. Faddeev-Jackiw quantization and constraints

    International Nuclear Information System (INIS)

    Barcelos-Neto, J.; Wotzasek, C.

    1992-01-01

    In a recent Letter, Faddeev and Jackiw have shown that the reduction of constrained systems into its canonical, first-order form, can bring some new insight into the research of this field. For sympletic manifolds the geometrical structure, called Dirac or generalized bracket, is obtained directly from the inverse of the nonsingular sympletic two-form matrix. In the cases of nonsympletic manifolds, this two-form is degenerated and cannot be inverted to provide the generalized brackets. This singular behavior of the sympletic matrix is indicative of the presence of constraints that have to be carefully considered to yield to consistent results. One has two possible routes to treat this problem: Dirac has taught us how to implement the constraints into the potential part (Hamiltonian) of the canonical Lagrangian, leading to the well-known Dirac brackets, which are consistent with the constraints and can be mapped into quantum commutators (modulo ordering terms). The second route, suggested by Faddeev and Jackiw, and followed in this paper, is to implement the constraints directly into the canonical part of the first order Lagrangian, using the fact that the consistence condition for the stability of the constrained manifold is linear in the time derivative. This algorithm may lead to an invertible two-form sympletic matrix from where the Dirac brackets are readily obtained. This algorithm is used in this paper to investigate some aspects of the quantization of constrained systems with first- and second-class constraints in the sympletic approach

  4. Geometrical themes inspired by the n-body problem

    CERN Document Server

    Herrera, Haydeé; Herrera, Rafael

    2018-01-01

    Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions.   R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...

  5. Geometrical shock dynamics for magnetohydrodynamic fast shocks

    KAUST Repository

    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

  6. 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

  7. Geometrical shock dynamics for magnetohydrodynamic fast shocks

    KAUST Repository

    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

  8. 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

  9. Monomial geometric programming with an arbitrary fuzzy relational inequality

    Directory of Open Access Journals (Sweden)

    E. Shivanian

    2015-11-01

    Full Text Available In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.

  10. Integrable systems of partial differential equations determined by structure equations and Lax pair

    International Nuclear Information System (INIS)

    Bracken, Paul

    2010-01-01

    It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

  11. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  12. Financing Constraints and Entrepreneurship

    OpenAIRE

    William R. Kerr; Ramana Nanda

    2009-01-01

    Financing constraints are one of the biggest concerns impacting potential entrepreneurs around the world. Given the important role that entrepreneurship is believed to play in the process of economic growth, alleviating financing constraints for would-be entrepreneurs is also an important goal for policymakers worldwide. We review two major streams of research examining the relevance of financing constraints for entrepreneurship. We then introduce a framework that provides a unified perspecti...

  13. Temporal Concurrent Constraint Programming

    DEFF Research Database (Denmark)

    Nielsen, Mogens; Valencia Posso, Frank Dan

    2002-01-01

    The ntcc calculus is a model of non-deterministic temporal concurrent constraint programming. In this paper we study behavioral notions for this calculus. In the underlying computational model, concurrent constraint processes are executed in discrete time intervals. The behavioral notions studied...... reflect the reactive interactions between concurrent constraint processes and their environment, as well as internal interactions between individual processes. Relationships between the suggested notions are studied, and they are all proved to be decidable for a substantial fragment of the calculus...

  14. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  15. Generalized reduced magnetohydrodynamic equations

    International Nuclear Information System (INIS)

    Kruger, S.E.

    1999-01-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

  16. On a Linear Equation Arising in Isometric Embedding of Torus-like Surface

    Institute of Scientific and Technical Information of China (English)

    Chunhe LI

    2009-01-01

    The solvability of a linear equation and the regularity of the solution are discussed.The equation is arising in a geometric problem which is concerned with the realization of Alexandroff's positive annul in R3.

  17. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    Science.gov (United States)

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  18. 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

  19. Geometric Model of a Coronal Cavity

    Science.gov (United States)

    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.; hide

    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

  20. 3D geometrically isotropic metamaterial for telecom wavelengths

    DEFF Research Database (Denmark)

    Malureanu, Radu; Andryieuski, Andrei; Lavrinenko, Andrei

    2009-01-01

    of the unit cell is not infinitely small, certain geometrical constraints have to be fulfilled to obtain an isotropic response of the material [3]. These conditions and the metal behaviour close to the plasma frequency increase the design complexity. Our unit cell is composed of two main parts. The first part...... is obtained in a certain bandwidth. The proposed unit cell has the cubic point group of symmetry and being repeatedly placed in space can effectively reveal isotropic optical properties. We use the CST commercial software to characterise the “cube-in-cage” structure. Reflection and transmission spectra...

  1. Multiterminal Estimation - Extensions and a Geometric Interpretation

    National Research Council Canada - National Science Library

    Jornsten, Rebecka

    2002-01-01

    ... constraints, and a test channel constraint referred to as the solvability condition. Han and Amari tightened the upper bound under weaker constraints on both the rates and the test channel distributions...

  2. 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...

  3. 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.

  4. 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

  5. Riemannian geometry and geometric analysis

    CERN Document Server

    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...

  6. Geometric mean for subspace selection.

    Science.gov (United States)

    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.

  7. Temporal Concurrent Constraint Programming

    DEFF Research Database (Denmark)

    Nielsen, Mogens; Palamidessi, Catuscia; Valencia, Frank Dan

    2002-01-01

    The ntcc calculus is a model of non-deterministic temporal concurrent constraint programming. In this paper we study behavioral notions for this calculus. In the underlying computational model, concurrent constraint processes are executed in discrete time intervals. The behavioral notions studied...

  8. Evaluating Distributed Timing Constraints

    DEFF Research Database (Denmark)

    Kristensen, C.H.; Drejer, N.

    1994-01-01

    In this paper we describe a solution to the problem of implementing time-optimal evaluation of timing constraints in distributed real-time systems.......In this paper we describe a solution to the problem of implementing time-optimal evaluation of timing constraints in distributed real-time systems....

  9. Theory of Constraints (TOC)

    DEFF Research Database (Denmark)

    Michelsen, Aage U.

    2004-01-01

    Tankegangen bag Theory of Constraints samt planlægningsprincippet Drum-Buffer-Rope. Endvidere skitse af The Thinking Process.......Tankegangen bag Theory of Constraints samt planlægningsprincippet Drum-Buffer-Rope. Endvidere skitse af The Thinking Process....

  10. A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

    Science.gov (United States)

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

  11. Influence of part orientation on the geometric accuracy in robot-based incremental sheet metal forming

    Science.gov (United States)

    Störkle, Denis Daniel; Seim, Patrick; Thyssen, Lars; Kuhlenkötter, Bernd

    2016-10-01

    This article describes new developments in an incremental, robot-based sheet metal forming process (`Roboforming') for the production of sheet metal components for small lot sizes and prototypes. The dieless kinematic-based generation of the shape is implemented by means of two industrial robots, which are interconnected to a cooperating robot system. Compared to other incremental sheet metal forming (ISF) machines, this system offers high geometrical form flexibility without the need of any part-dependent tools. The industrial application of ISF is still limited by certain constraints, e.g. the low geometrical accuracy. Responding to these constraints, the authors present the influence of the part orientation and the forming sequence on the geometric accuracy. Their influence is illustrated with the help of various experimental results shown and interpreted within this article.

  12. Multiscale geometric modeling of macromolecules I: Cartesian representation

    Science.gov (United States)

    Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

    2014-01-01

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  13. Multiscale geometric modeling of macromolecules I: Cartesian representation

    Energy Technology Data Exchange (ETDEWEB)

    Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)

    2014-01-15

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  14. Partial differential equations mathematical techniques for engineers

    CERN Document Server

    Epstein, Marcelo

    2017-01-01

    This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...

  15. On the Langevin equation for stochastic quantization of gravity

    International Nuclear Information System (INIS)

    Nakazawa, Naohito.

    1989-10-01

    We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations leads to stochastic quantization of gravity including an unique superspace metric. (author)

  16. Operator-assisted planning and execution of proximity operations subject to operational constraints

    Science.gov (United States)

    Grunwald, Arthur J.; Ellis, Stephen R.

    1991-01-01

    Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

  17. Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

    International Nuclear Information System (INIS)

    Mori, N.; Kobayashi, K.

    1996-01-01

    A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

  18. Geometrical properties of systems with spiral trajectories in R^3

    Directory of Open Access Journals (Sweden)

    Luka Korkut

    2015-10-01

    Full Text Available We study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the geometrical point of view. The oscillatory behavior of solutions at infinity is measured by oscillatory and phase dimensions, The oscillatory dimension is defined as the box dimension of the reflected solution near the origin, while the phase dimension is defined as the box dimension of a trajectory of the planar system in the phase plane. Using the phase dimension of the second-order equation we compute the box dimension of a spiral trajectory of the spatial system. This phase dimension of the second-order equation is connected to the asymptotic of the associated Poincare map. Also, the box dimension of a trajectory of the reduced normal form with one eigenvalue equals zero, and a pair of pure imaginary eigenvalues is computed when limit cycles bifurcate from the origin.

  19. Stabilization of wave equations with variable coefficient and delay in the dynamical boundary feedback

    Directory of Open Access Journals (Sweden)

    Dandan Guo

    2017-08-01

    Full Text Available In this article we consider the boundary stabilization of a wave equation with variable coefficients. This equation has an acceleration term and a delayed velocity term on the boundary. Under suitable geometric conditions, we obtain the exponential decay for the solutions. Our proof relies on the geometric multiplier method and the Lyapunov approach.

  20. Constraint-based reachability

    Directory of Open Access Journals (Sweden)

    Arnaud Gotlieb

    2013-02-01

    Full Text Available Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with standard backward or forward exploration strategies. An approach that we call Constraint-based reachability, is proposed to address reachability problems by exploring program states using a constraint model of the whole program. The keypoint of the approach is to interpret imperative constructions such as conditionals, loops, array and memory manipulations with the fundamental notion of constraint over a computational domain. By combining constraint filtering and abstraction techniques, Constraint-based reachability is able to solve reachability problems which are usually outside the scope of backward or forward exploration strategies. This paper proposes an interpretation of classical filtering consistencies used in Constraint Programming as abstract domain computations, and shows how this approach can be used to produce a constraint solver that efficiently generates solutions for reachability problems that are unsolvable by other approaches.

  1. The respiratory system in equations

    CERN Document Server

    Maury, Bertrand

    2013-01-01

    The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

  2. Quasisymmetry equations for conventional stellarators

    International Nuclear Information System (INIS)

    Pustovitov, V.D.

    1994-11-01

    General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)

  3. Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

    Institute of Scientific and Technical Information of China (English)

    WANG ShunJin; ZHANG Hua

    2007-01-01

    Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

  4. Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

  5. Bernoulli's Equation

    Indian Academy of Sciences (India)

    regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.

  6. Relativistic equations

    International Nuclear Information System (INIS)

    Gross, F.

    1986-01-01

    Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs

  7. 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.

  8. Geometric Topology and Shape Theory

    CERN Document Server

    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.

  9. Field guide to geometrical optics

    CERN Document Server

    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.

  10. 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)

  11. A history of geometrical methods

    CERN Document Server

    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

  12. Geometrical optics and optimal transport.

    Science.gov (United States)

    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.

  13. Metric approach to quantum constraints

    International Nuclear Information System (INIS)

    Brody, Dorje C; Hughston, Lane P; Gustavsson, Anna C T

    2009-01-01

    A framework for deriving equations of motion for constrained quantum systems is introduced and a procedure for its implementation is outlined. In special cases, the proposed new method, which takes advantage of the fact that the space of pure states in quantum mechanics has both a symplectic structure and a metric structure, reduces to a quantum analogue of the Dirac theory of constraints in classical mechanics. Explicit examples involving spin-1/2 particles are worked out in detail: in the first example, our approach coincides with a quantum version of the Dirac formalism, while the second example illustrates how a situation that cannot be treated by Dirac's approach can nevertheless be dealt with in the present scheme.

  14. Constraints on the braneworld from compact stars

    Energy Technology Data Exchange (ETDEWEB)

    Felipe, R.G. [Instituto Politecnico de Lisboa, ISEL, Instituto Superior de Engenharia de Lisboa, Lisboa (Portugal); Instituto Superior Tecnico, Universidade de Lisboa, Departamento de Fisica, Centro de Fisica Teorica de Particulas, CFTP, Lisboa (Portugal); Paret, D.M. [Universidad de la Habana, Departamento de Fisica General, Facultad de Fisica, La Habana (Cuba); Martinez, A.P. [Instituto de Cibernetica, Matematica y Fisica (ICIMAF), La Habana (Cuba); Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico, Distrito Federal (Mexico)

    2016-06-15

    According to the braneworld idea, ordinary matter is confined on a three-dimensional space (brane) that is embedded in a higher-dimensional space-time where gravity propagates. In this work, after reviewing the limits coming from general relativity, finiteness of pressure and causality on the brane, we derive observational constraints on the braneworld parameters from the existence of stable compact stars. The analysis is carried out by solving numerically the brane-modified Tolman-Oppenheimer-Volkoff equations, using different representative equations of state to describe matter in the star interior. The cases of normal dense matter, pure quark matter and hybrid matter are considered. (orig.)

  15. Power Series Solution to the Pendulum Equation

    Science.gov (United States)

    Benacka, Jan

    2009-01-01

    This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

  16. Generalized reduced MHD equations

    International Nuclear Information System (INIS)

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

  17. Optimal Stopping with Information Constraint

    International Nuclear Information System (INIS)

    Lempa, Jukka

    2012-01-01

    We study the optimal stopping problem proposed by Dupuis and Wang (Adv. Appl. Probab. 34:141–157, 2002). In this maximization problem of the expected present value of the exercise payoff, the underlying dynamics follow a linear diffusion. The decision maker is not allowed to stop at any time she chooses but rather on the jump times of an independent Poisson process. Dupuis and Wang (Adv. Appl. Probab. 34:141–157, 2002), solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we propose a mild set of conditions (covering the setup of Dupuis and Wang in Adv. Appl. Probab. 34:141–157, 2002) on both the underlying and the payoff and build and use a Markovian apparatus based on the Bellman principle of optimality to solve the problem under these conditions. We also discuss the interpretation of this model as optimal timing of an irreversible investment decision under an exogenous information constraint.

  18. Hamilton's equations for a fluid membrane

    International Nuclear Information System (INIS)

    Capovilla, R; Guven, J; Rojas, E

    2005-01-01

    Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations

  19. Constraints on backreaction in dust universes

    International Nuclear Information System (INIS)

    Raesaenen, Syksy

    2006-01-01

    We study backreaction in dust universes using exact equations which do not rely on perturbation theory, concentrating on theoretical and observational constraints. In particular, we discuss the recent suggestion (Kolb et al 2005 Preprint hep-th/0503117) that superhorizon perturbations could explain present-day accelerated expansion as a useful example which can be ruled out. We note that a backreaction explanation of late-time acceleration will have to involve spatial curvature and subhorizon perturbations

  20. Resources, constraints and capabilities

    NARCIS (Netherlands)

    Dhondt, S.; Oeij, P.R.A.; Schröder, A.

    2018-01-01

    Human and financial resources as well as organisational capabilities are needed to overcome the manifold constraints social innovators are facing. To unlock the potential of social innovation for the whole society new (social) innovation friendly environments and new governance structures

  1. 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

  2. Soliton solutions of some nonlinear evolution equations with time ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...

  3. Geometric Filtering Effect of Vertical Vibrations in Railway Vehicles

    Directory of Open Access Journals (Sweden)

    Mădălina Dumitriu

    2012-09-01

    Full Text Available The paper herein examines the geometric filtering effect coming from the axle base of a railway vehicle upon the vertical vibrations behavior, due to the random irregularities of the track. For this purpose, the complete model of a two-level suspension and flexible carbody vehicle has been taken into account. Following the modal analysis, the movement equations have been treated in an original manner and brought to a structure that points out at the symmetrical and anti-symmetrical decoupled movements of vehicle and their excitation modes. There has been shown that the geometric filtering has a selective behavior in decreasing the level of vibrations, and its contribution is affected by the axle base magnitude, rolling speed and frequency range.

  4. An algebraic geometric approach to separation of variables

    CERN Document Server

    Schöbel, Konrad

    2015-01-01

    Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.”   (Jim Stasheff)   Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3-Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations   Target Groups Scientists in the fie...

  5. Image understanding using geometric context

    Science.gov (United States)

    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.

  6. Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

    Science.gov (United States)

    Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

    2018-01-01

    In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

  7. Selection of new constraints

    International Nuclear Information System (INIS)

    Sugier, A.

    2003-01-01

    The selected new constraints should be consistent with the scale of concern i.e. be expressed roughly as fractions or multiples of the average annual background. They should take into account risk considerations and include the values of the currents limits, constraints and other action levels. The recommendation is to select four leading values for the new constraints: 500 mSv ( single event or in a decade) as a maximum value, 0.01 mSv/year as a minimum value; and two intermediate values: 20 mSv/year and 0.3 mSv/year. This new set of dose constraints, representing basic minimum standards of protection for the individuals taking into account the specificity of the exposure situations are thus coherent with the current values which can be found in ICRP Publications. A few warning need however to be noticed: There is no more multi sources limit set by ICRP. The coherence between the proposed value of dose constraint (20 mSv/year) and the current occupational dose limit of 20 mSv/year is valid only if the workers are exposed to one single source. When there is more than one source, it will be necessary to apportion. The value of 1000 mSv lifetimes used for relocation can be expressed into annual dose, which gives approximately 10 mSv/year and is coherent with the proposed dose constraint. (N.C.)

  8. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem

    DEFF Research Database (Denmark)

    Delbary, Fabrice; Knudsen, Kim

    2014-01-01

    to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...

  9. Geometrical approach to the dynamics of the relativistic string

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Koshkarov, A.L.

    1979-01-01

    The dynamics of the relativistic string is considered from the point of view of the gaussian theory of two-dimensional surfaces in the three-dimensional pseudoeuclidean space-epsilon 3 1 according to which the surface is characterized by its first and second quadratic forms. The geometrical approach possesses an advantage which gives the possibility to solve manifestly additional conditions on the vector describing the coordinates of the string world surface. The equations of motion and boundary conditions are written out for the cases of a string with massive ends and a closed string. The basic equations are formulated for the coefficients of the first and second quadratic forms of the string world surface, which represent the known geometric conditions of integration of Gauss and Weingarten derivation formulas. By means of integration of the derivation formulas the representation is obtained for the form of the string world surface in a certain basis, which satisfies the equations of motion as well as additional conditions. A new relativistic invariant gauge is suggested which fixes the second quadratic form of the surface. This representation can be extended to the case of arbitrary dimensional space

  10. Constitutive equations for discrete electromagnetic problems over polyhedral grids

    International Nuclear Information System (INIS)

    Codecasa, Lorenzo; Trevisan, Francesco

    2007-01-01

    In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field problem. The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations. In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual grid. Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations of the electromagnetic field

  11. Geometrical model for the electron

    International Nuclear Information System (INIS)

    El-Sherbini, T.M.

    1985-07-01

    A model for an electron of finite dimensions is proposed. This model disregards the concept of electronic charge and leads to Bohr's frequency formula for the hydrogen atom and to Maxwell's equations for electromagnetic fields. The stability of a free electron under the action of centrifugal and transverse forces is discussed. (author)

  12. Misconceptions and constraints

    International Nuclear Information System (INIS)

    Whitten, M.; Mahon, R.

    2005-01-01

    In theory, the sterile insect technique (SIT) is applicable to a wide variety of invertebrate pests. However, in practice, the approach has been successfully applied to only a few major pests. Chapters in this volume address possible reasons for this discrepancy, e.g. Klassen, Lance and McInnis, and Robinson and Hendrichs. The shortfall between theory and practice is partly due to the persistence of some common misconceptions, but it is mainly due to one constraint, or a combination of constraints, that are biological, financial, social or political in nature. This chapter's goal is to dispel some major misconceptions, and view the constraints as challenges to overcome, seeing them as opportunities to exploit. Some of the common misconceptions include: (1) released insects retain residual radiation, (2) females must be monogamous, (3) released males must be fully sterile, (4) eradication is the only goal, (5) the SIT is too sophisticated for developing countries, and (6) the SIT is not a component of an area-wide integrated pest management (AW-IPM) strategy. The more obvious constraints are the perceived high costs of the SIT, and the low competitiveness of released sterile males. The perceived high up-front costs of the SIT, their visibility, and the lack of private investment (compared with alternative suppression measures) emerge as serious constraints. Failure to appreciate the true nature of genetic approaches, such as the SIT, may pose a significant constraint to the wider adoption of the SIT and other genetically-based tactics, e.g. transgenic genetically modified organisms (GMOs). Lack of support for the necessary underpinning strategic research also appears to be an important constraint. Hence the case for extensive strategic research in ecology, population dynamics, genetics, and insect behaviour and nutrition is a compelling one. Raising the competitiveness of released sterile males remains the major research objective of the SIT. (author)

  13. Geometrical and topological formulation of local gauge and supergauge theories

    International Nuclear Information System (INIS)

    Macrae, K.I.

    1976-01-01

    A geometrical and topological formulation of local gauge and supergauge invariance is presented. Analysis of experiments of the type described by Bohm and Aharanov and in the attempt to understand immersed submanifolds such as the string with internal symmetry, in a geometric setting, are led to the introduction of fiber bundles, superspaces. Many exact classical solutions to the equations of motion were considered for these gauge theories with specific choices of gauge group such as SU 4 . We describe some exact soliton solutions to these theories which have linear Regge trajectories, i.e., their angular momentum is a linear function of their mass squared. Next one discusses the actions and equations of motion for gauge theories whose base manifolds can have arbitrarily dimensioned submanifolds excised from them, manifolds with holes were discussed. These holes can have fractional quark charges when the structure group is, for example, SU 3 or SU 4 . By extending the concept of conservation of energy to include the excised submanifolds, their actions, and their equations of motion were derived showing that they can act as charged particles. Using the fractionality of the quark charges, are led to suggest a topological confinement mechanism for these particles. One also derives the actions and equations of motion for the string from this viewpoint. Some new Lie algebras which have anticommuting elements are introduced. Their gauge theories are described, and the possibility of fermionic actions for the anticommuting pieces is examined. Supersymmetric strings and their supergauge transformations were discussed and an extension was suggested of supersymmetry to immersed minimal submanifolds other than the string. Both quarklike and vectorlike fermions are included. Finally the invariance of both the equations of motion and the gauge conditions under supersymmetry transformations for these submanifolds were described

  14. Geometrical charged-particle optics

    CERN Document Server

    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...

  15. Geometric Methods in Physics XXXV

    CERN Document Server

    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.

  16. 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...

  17. 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

  18. The Langevin equation

    Science.gov (United States)

    Pomeau, Yves; Piasecki, Jarosław

    2017-11-01

    The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.

  19. Real solutions to equations from geometry

    CERN Document Server

    Sottile, Frank

    2011-01-01

    Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all ...

  20. Revised predictive equations for salt intrusion modelling in estuaries

    NARCIS (Netherlands)

    Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.

    2015-01-01

    For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion

  1. Perfect fluid cosmological Universes: One equation of state and the ...

    Indian Academy of Sciences (India)

    Anadijiban Das

    2018-01-04

    Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...

  2. Type II Superstring Field Theory: Geometric Approach and Operadic Description

    CERN Document Server

    Jurco, Branislav

    2013-01-01

    We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a $\\mathcal{N}=1$ generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.

  3. Geometric function theory: a modern view of a classical subject

    International Nuclear Information System (INIS)

    Crowdy, Darren

    2008-01-01

    Geometric function theory is a classical subject. Yet it continues to find new applications in an ever-growing variety of areas such as modern mathematical physics, more traditional fields of physics such as fluid dynamics, nonlinear integrable systems theory and the theory of partial differential equations. This paper surveys, with a view to modern applications, open problems and challenges in this subject. Here we advocate an approach based on the use of the Schottky–Klein prime function within a Schottky model of compact Riemann surfaces. (open problem)

  4. Geometric theory of fundamental interactions. Foundations of unified physics

    International Nuclear Information System (INIS)

    Pestov, A.B.

    2012-01-01

    We put forward an idea that regularities of unified physics are in a simple relation: everything in the concept of space and the concept of space in everything. With this hypothesis as a ground, a conceptual structure of a unified geometrical theory of fundamental interactions is created and deductive derivation of its main equations is produced. The formulated theory gives solution of the actual problems, provides opportunity to understand the origin and nature of physical fields, local internal symmetry, time, energy, spin, charge, confinement, dark energy and dark matter, thus conforming the existence of new physics in its unity

  5. Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD

    International Nuclear Information System (INIS)

    Machado, Magno V.T.

    2011-01-01

    The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization. (author)

  6. Pattern control and suppression of spatiotemporal chaos using geometrical resonance

    International Nuclear Information System (INIS)

    Gonzalez, J.A.; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E.

    2004-01-01

    We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek 4 , and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743

  7. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  8. 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)

  9. 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....

  10. Diffusion equations and the time evolution of foreign exchange rates

    Energy Technology Data Exchange (ETDEWEB)

    Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)

    2013-10-01

    We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

  11. Diffusion equations and the time evolution of foreign exchange rates

    Science.gov (United States)

    Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

    2013-10-01

    We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

  12. Diffusion equations and the time evolution of foreign exchange rates

    International Nuclear Information System (INIS)

    Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram

    2013-01-01

    We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

  13. On the Motion of Matter in the Geometrical Gauge Field Theory

    CERN Document Server

    Konopleva, N P

    2005-01-01

    In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. In the talk, the problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries.

  14. Guide to Geometric Algebra in Practice

    CERN Document Server

    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

  15. The electromagnetic field equations for moving media

    International Nuclear Information System (INIS)

    Ivezić, T

    2017-01-01

    In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)

  16. Occupational dose constraint

    International Nuclear Information System (INIS)

    Heilbron Filho, Paulo Fernando Lavalle; Xavier, Ana Maria

    2005-01-01

    The revision process of the international radiological protection regulations has resulted in the adoption of new concepts, such as practice, intervention, avoidable and restriction of dose (dose constraint). The latter deserving of special mention since it may involve reducing a priori of the dose limits established both for the public and to individuals occupationally exposed, values that can be further reduced, depending on the application of the principle of optimization. This article aims to present, with clarity, from the criteria adopted to define dose constraint values to the public, a methodology to establish the dose constraint values for occupationally exposed individuals, as well as an example of the application of this methodology to the practice of industrial radiography

  17. Psychological constraints on egalitarianism

    DEFF Research Database (Denmark)

    Kasperbauer, Tyler Joshua

    2015-01-01

    processes motivating people to resist various aspects of egalitarianism. I argue for two theses, one normative and one descriptive. The normative thesis holds that egalitarians must take psychological constraints into account when constructing egalitarian ideals. I draw from non-ideal theories in political...... philosophy, which aim to construct moral goals with current social and political constraints in mind, to argue that human psychology must be part of a non-ideal theory of egalitarianism. The descriptive thesis holds that the most fundamental psychological challenge to egalitarian ideals comes from what......Debates over egalitarianism for the most part are not concerned with constraints on achieving an egalitarian society, beyond discussions of the deficiencies of egalitarian theory itself. This paper looks beyond objections to egalitarianism as such and investigates the relevant psychological...

  18. Linearization: Geometric, Complex, and Conditional

    Directory of Open Access Journals (Sweden)

    Asghar Qadir

    2012-01-01

    Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.

  19. Integration rules for scattering equations

    International Nuclear Information System (INIS)

    Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.

    2015-01-01

    As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.

  20. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  1. Geometry and dynamics with time-dependent constraints

    CERN Document Server

    Evans, Jonathan M.; Jonathan M Evans; Philip A Tuckey

    1995-01-01

    We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.

  2. Analysis of entropy models with equality and inequality constraints

    Energy Technology Data Exchange (ETDEWEB)

    Jefferson, T R; Scott, C H

    1979-06-01

    Entropy models are emerging as valuable tools in the study of various social problems of spatial interaction. With the development of the modeling has come diversity. Increased flexibility in the model can be obtained by allowing certain constraints to be relaxed from equality to inequality. To provide a better understanding of these entropy models they are analyzed by geometric programming. Dual mathematical programs and algorithms are obtained. 7 references.

  3. Discrete geometric structures for architecture

    KAUST Repository

    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

  4. Geometric asymmetry driven Janus micromotors

    Science.gov (United States)

    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

  5. Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology

    Science.gov (United States)

    Cartailler, J.; Schuss, Z.; Holcman, D.

    2017-12-01

    We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck equations for charge concentration and electric potential as a model of electrodiffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nanopipettes and help to understand the local voltage changes inside dendrites and axons with heterogeneous local geometry.

  6. Constraint-based scheduling applying constraint programming to scheduling problems

    CERN Document Server

    Baptiste, Philippe; Nuijten, Wim

    2001-01-01

    Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem. It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study. The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts: The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems. Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsibl...

  7. Nonlinear elliptic equations of the second order

    CERN Document Server

    Han, Qing

    2016-01-01

    Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

  8. Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)

    2016-08-15

    This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

  9. 4th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s

    CERN Document Server

    Ishige, Kazuhiro; Nitsch, Carlo; Salani, Paolo

    2016-01-01

    This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions. .

  10. Constraints on Dbar uplifts

    International Nuclear Information System (INIS)

    Alwis, S.P. de

    2016-01-01

    We discuss constraints on KKLT/KKLMMT and LVS scenarios that use anti-branes to get an uplift to a deSitter vacuum, coming from requiring the validity of an effective field theory description of the physics. We find these are not always satisfied or are hard to satisfy.

  11. Ecosystems emerging. 5: Constraints

    Czech Academy of Sciences Publication Activity Database

    Patten, B. C.; Straškraba, Milan; Jorgensen, S. E.

    2011-01-01

    Roč. 222, č. 16 (2011), s. 2945-2972 ISSN 0304-3800 Institutional research plan: CEZ:AV0Z50070508 Keywords : constraint * epistemic * ontic Subject RIV: EH - Ecology, Behaviour Impact factor: 2.326, year: 2011 http://www.sciencedirect.com/science/article/pii/S0304380011002274

  12. Constraints and Ambiguity

    DEFF Research Database (Denmark)

    Dove, Graham; Biskjær, Michael Mose; Lundqvist, Caroline Emilie

    2017-01-01

    groups of students building three models each. We studied groups building with traditional plastic bricks and also using a digital environment. The building tasks students undertake, and our subsequent analysis, are informed by the role constraints and ambiguity play in creative processes. Based...

  13. Information geometric methods for complexity

    Science.gov (United States)

    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.

  14. 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

  15. 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.

  16. 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.

  17. Geometric structure of percolation clusters.

    Science.gov (United States)

    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).

  18. Geometric Phase Generated Optical Illusion.

    Science.gov (United States)

    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.

  19. Cosmographic Constraints and Cosmic Fluids

    Directory of Open Access Journals (Sweden)

    Salvatore Capozziello

    2013-12-01

    Full Text Available The problem of reproducing dark energy effects is reviewed here with particular interest devoted to cosmography. We summarize some of the most relevant cosmological models, based on the assumption that the corresponding barotropic equations of state evolve as the universe expands, giving rise to the accelerated expansion. We describe in detail the ΛCDM (Λ-Cold Dark Matter and ωCDM models, considering also some specific examples, e.g., Chevallier–Polarsky–Linder, the Chaplygin gas and the Dvali–Gabadadze–Porrati cosmological model. Finally, we consider the cosmological consequences of f(R and f(T gravities and their impact on the framework of cosmography. Keeping these considerations in mind, we point out the model-independent procedure related to cosmography, showing how to match the series of cosmological observables to the free parameters of each model. We critically discuss the role played by cosmography, as a selection criterion to check whether a particular model passes or does not present cosmological constraints. In so doing, we find out cosmological bounds by fitting the luminosity distance expansion of the redshift, z, adopting the recent Union 2.1 dataset of supernovae, combined with the baryonic acoustic oscillation and the cosmic microwave background measurements. We perform cosmographic analyses, imposing different priors on the Hubble rate present value. In addition, we compare our results with recent PLANCK limits, showing that the ΛCDM and ωCDM models seem to be the favorite with respect to other dark energy models. However, we show that cosmographic constraints on f(R and f(T cannot discriminate between extensions of General Relativity and dark energy models, leading to a disadvantageous degeneracy problem.

  20. Pitfalls of using the geometric-mean combining rule in the density gradient theory

    DEFF Research Database (Denmark)

    Liang, Xiaodong; Michelsen, Michael Locht; Kontogeorgis, Georgios

    2016-01-01

    It is popular and attractive to model the interfacial tension using the density gradient theory with the geometric-mean combining rule, in which the same equation of state is used for the interface and bulk phases. The computational efficiency is the most important advantage of this theory. In th...

  1. EFFECT OF GEOMETRIC CONFIGURATIONS ON HYDRODYNAMIC PERFORMANCE ASSESSMENT OF A MARINE PROPELLER

    Directory of Open Access Journals (Sweden)

    Samir. E. Belhenniche

    2016-12-01

    Full Text Available The present paper deals with the effect of the geometric characteristics on the propeller hydrodynamic performances. Several propeller configurations are created by changing number of blades, expanded area and pitch ratios. The Reynolds-Averaged Navier-Stokes (RANS equations are solved using the commercial code FLUENT 6.3.26. The standard

  2. A Spectral Geometrical Model for Compton Scatter Tomography Based on the SSS Approximation

    DEFF Research Database (Denmark)

    Kazantsev, Ivan G.; Olsen, Ulrik Lund; Poulsen, Henning Friis

    2016-01-01

    The forward model of single scatter in the Positron Emission Tomography for a detector system possessing an excellent spectral resolution under idealized geometrical assumptions is investigated. This model has the form of integral equations describing a flux of photons emanating from the same ann...

  3. Finsler-Geometric Continuum Mechanics

    Science.gov (United States)

    2016-05-01

    incremental boundary value problems. Crucial to deriving such equations is an extension of the divergence theorem for- warded in reference 56. Application of...to Ω in Eq. 16, as can spatial versions of the coordinate-free Stokes’ theorem in Eq. 18 and Rund’s horizontal divergence theo- rem in Eq. 19. 2.3... divergence theorem Eq. 19 and repeated integration by parts then gives the following equivalent integral form of Eq. 49: − ∫ M {[PAa|A + (PAa CCBC + ∂̄BPAa

  4. 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

  5. Geometric integrators for stochastic rigid body dynamics

    KAUST Repository

    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.

  6. Geometric integrators for stochastic rigid body dynamics

    KAUST Repository

    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.

  7. 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.

  8. 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)

  9. A geometric measure of dark energy with pairs of galaxies.

    Science.gov (United States)

    Marinoni, Christian; Buzzi, Adeline

    2010-11-25

    Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.

  10. Symbolic dynamics of the Lorenz equations

    International Nuclear Information System (INIS)

    Fang Hai-ping; Hao Bailin.

    1994-07-01

    The Lorenz equations are investigated in a wide range of parameters by using the method of symbolic dynamics. First, the systematics of stable periodic orbits in the Lorenz equations is compared with that of the one-dimensional cubic map, which shares the same discrete symmetry with the Lorenz model. The systematics is then ''corrected'' in such a way as to encompass all the known periodic windows of the Lorenz equations with only one exception. Second, in order to justify the above approach and to understand the exceptions, another 1D map with a discontinuity is extracted from an extension of the geometric Lorenz attractor and its symbolic dynamics is constructed. All this has to be done in light of symbolic dynamics of two-dimensional maps. Finally, symbolic dynamics for the actual Poincare return map of the Lorenz equations is constructed in a heuristic way. New periodic windows of the Lorenz equations and their parameters can be predicted from this symbolic dynamics in combination with the 1D cubic map. The extended geometric 2D Lorenz map and the 1D antisymmetric map with a discontinuity describe the topological aspects of the Lorenz equations to high accuracy. (author). 44 refs, 17 figs, 8 tabs

  11. Optimal design of geometrically nonlinear shells of revolution with using the mixed finite element method

    Science.gov (United States)

    Stupishin, L. U.; Nikitin, K. E.; Kolesnikov, A. G.

    2018-02-01

    The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.

  12. Demystifying the memory effect: A geometrical approach to understanding speckle correlations

    Science.gov (United States)

    Prunty, Aaron C.; Snieder, Roel K.

    2017-05-01

    The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.

  13. INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

    Directory of Open Access Journals (Sweden)

    Elena N. Kushner

    2018-01-01

    Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

  14. Shaping up: a geometric morphometric approach to assemblage ecomorphology.

    Science.gov (United States)

    Bower, L M; Piller, K R

    2015-09-01

    This study adopts an ecomorphological approach to test the utility of body shape as a predictor of niche relationships among a stream fish assemblage of the Tickfaw River (Lake Pontchartrain Basin) in southeastern Louisiana, U.S.A. To examine the potential influence of evolutionary constraints, analyses were performed with and without the influence of phylogeny. Fish assemblages were sampled throughout the year, and ecological data (habitat and tropic guild) and body shape (geometric morphometric) data were collected for each fish specimen. Multivariate analyses were performed to examine relationships and differences between body shape and ecological data. Results indicate that a relationship exists between body shape and trophic guild as well as flow regime, but no significant correlation between body shape and substratum was found. Body shape was a reliable indicator of position within assemblage niche space. © 2015 The Fisheries Society of the British Isles.

  15. Auxiliary fields in the geometrical relativistic particle dynamics

    International Nuclear Information System (INIS)

    Amador, A; Bagatella, N; Rojas, E; Cordero, R

    2008-01-01

    We describe how to construct the dynamics of relativistic particles, following either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles

  16. Auxiliary fields in the geometrical relativistic particle dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Amador, A; Bagatella, N; Rojas, E [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); Cordero, R [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N, Edificio 9, 07738 Mexico D.F (Mexico)], E-mail: aramador@gmail.com, E-mail: nbagatella@uv.mx, E-mail: cordero@esfm.ipn.mx, E-mail: efrojas@uv.mx

    2008-03-21

    We describe how to construct the dynamics of relativistic particles, following either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles.

  17. 'Footballs', conical singularities, and the Liouville equation

    International Nuclear Information System (INIS)

    Redi, Michele

    2005-01-01

    We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints

  18. On fictitious domain formulations for Maxwell's equations

    DEFF Research Database (Denmark)

    Dahmen, W.; Jensen, Torben Klint; Urban, K.

    2003-01-01

    We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...

  19. Optimal Route Searching with Multiple Dynamical Constraints—A Geometric Algebra Approach

    Directory of Open Access Journals (Sweden)

    Dongshuang Li

    2018-05-01

    Full Text Available The process of searching for a dynamic constrained optimal path has received increasing attention in traffic planning, evacuation, and personalized or collaborative traffic service. As most existing multiple constrained optimal path (MCOP methods cannot search for a path given various types of constraints that dynamically change during the search, few approaches for dynamic multiple constrained optimal path (DMCOP with type II dynamics are available for practical use. In this study, we develop a method to solve the DMCOP problem with type II dynamics based on the unification of various types of constraints under a geometric algebra (GA framework. In our method, the network topology and three different types of constraints are represented by using algebraic base coding. With a parameterized optimization of the MCOP algorithm based on a greedy search strategy under the generation-refinement paradigm, this algorithm is found to accurately support the discovery of optimal paths as the constraints of numerical values, nodes, and route structure types are dynamically added to the network. The algorithm was tested with simulated cases of optimal tourism route searches in China’s road networks with various combinations of constraints. The case study indicates that our algorithm can not only solve the DMCOP with different types of constraints but also use constraints to speed up the route filtering.

  20. Graphical constraints: a graphical user interface for constraint problems

    OpenAIRE

    Vieira, Nelson Manuel Marques

    2015-01-01

    A constraint satisfaction problem is a classical artificial intelligence paradigm characterized by a set of variables (each variable with an associated domain of possible values), and a set of constraints that specify relations among subsets of these variables. Solutions are assignments of values to all variables that satisfy all the constraints. Many real world problems may be modelled by means of constraints. The range of problems that can use this representation is very diverse and embrace...