Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Connections and curvatures on complex Riemannian manifolds
International Nuclear Information System (INIS)
Ganchev, G.; Ivanov, S.
1991-05-01
Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs
On Riemannian manifolds (Mn, g) of quasi-constant curvature
International Nuclear Information System (INIS)
Rahman, M.S.
1995-07-01
A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature
Directory of Open Access Journals (Sweden)
Junya Takahashi
2018-05-01
Full Text Available We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.
Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory
International Nuclear Information System (INIS)
Velazquez, L
2013-01-01
Fluctuation geometry was recently proposed as a counterpart approach of the Riemannian geometry of inference theory (widely known as information geometry). This theory describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dp(x|θ). A main goal of this work is to clarify the statistical relevance of the Levi-Civita curvature tensor R ijkl (x|θ) of the statistical manifold M. For this purpose, the notion of irreducible statistical correlations is introduced. Specifically, a distribution dp(x|θ) exhibits irreducible statistical correlations if every distribution dp(x-check|θ) obtained from dp(x|θ) by considering a coordinate change x-check = φ(x) cannot be factorized into independent distributions as dp(x-check|θ) = prod i dp (i) (x-check i |θ). It is shown that the curvature tensor R ijkl (x|θ) arises as a direct indicator about the existence of irreducible statistical correlations. Moreover, the curvature scalar R(x|θ) allows us to introduce a criterium for the applicability of the Gaussian approximation of a given distribution function. This type of asymptotic result is obtained in the framework of the second-order geometric expansion of the distribution family dp(x|θ), which appears as a counterpart development of the high-order asymptotic theory of statistical estimation. In physics, fluctuation geometry represents the mathematical apparatus of a Riemannian extension for Einstein’s fluctuation theory of statistical mechanics. Some exact results of fluctuation geometry are now employed to derive the invariant fluctuation theorems. Moreover, the curvature scalar allows us to express some asymptotic formulae that account for the system fluctuating behavior beyond the Gaussian approximation, e.g.: it appears as a second-order correction of the Legendre transformation between thermodynamic potentials, P(θ)=θ i x-bar i -s( x-bar |θ)+k 2 R(x|θ)/6. (paper)
International Nuclear Information System (INIS)
Rasolofoson, N.G.
2014-01-01
The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
On the mean curvature of semi-Riemannian graphs in semi ...
Indian Academy of Sciences (India)
The study of the mean curvature of graph-like surfaces has a long history, but it is still a .... where, here and in the sequel, ∇h stands for the gradient of h on M, and ¯∇(¯h) the .... Then (1) follows by applying Proposition 17 of Chapter 4 in [12].
Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature
Directory of Open Access Journals (Sweden)
Francisco José Herranz
2006-01-01
Full Text Available A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed. Such systems admit three integrals of the motion (besides the Hamiltonian which are explicitly given in terms of ambient and geodesic polar coordinates. The resulting expressions cover the six spaces in a unified way as these are parametrized by two contraction parameters that govern the curvature and the signature of the metric on each space. Next two maximally superintegrable Hamiltonians are identified within the initial superintegrable family by finding the remaining constant of the motion. The former potential is the superposition of a (curved central harmonic oscillator with other three oscillators or centrifugal barriers (depending on each specific space, so that this generalizes the Smorodinsky-Winternitz system. The latter one is a superposition of the Kepler-Coulomb potential with another two oscillators or centrifugal barriers. As a byproduct, the Laplace-Runge-Lenz vector for these spaces is deduced. Furthermore both potentials are analysed in detail for each particular space. Some comments on their generalization to arbitrary dimension are also presented.
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
International Nuclear Information System (INIS)
Hervik, Sigbjoern; Coley, Alan
2011-01-01
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the S i - and N-properties, and show that if the curvature tensors of the space possess the N-property, then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null congruence. We also discuss the related Walker metrics.
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Energy Technology Data Exchange (ETDEWEB)
Hervik, Sigbjoern [Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger (Norway); Coley, Alan, E-mail: sigbjorn.hervik@uis.no, E-mail: aac@mathstat.dal.ca [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2011-01-07
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the S{sub i}- and N-properties, and show that if the curvature tensors of the space possess the N-property, then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null congruence. We also discuss the related Walker metrics.
On some hypersurfaces with time like normal bundle in pseudo Riemannian space forms
International Nuclear Information System (INIS)
Kashani, S.M.B.
1995-12-01
In this work we classify immersed hypersurfaces with constant sectional curvature in pseudo Riemannian space forms if the normal bundle is time like and the mean curvature is constant. (author). 9 refs
CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds
International Nuclear Information System (INIS)
Perdomo, Oscar M.
2012-01-01
In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h is an element of [-1,-(2√n-1/n can be realized as the constant curvature of a complete immersion of S 1 n-1 x R in the (n + 1)-dimensional de Sitter space S 1 n+1 . We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.
The three-body problem and equivariant Riemannian geometry
Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.
2017-08-01
We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.
Pseudo-Riemannian Novikov algebras
Energy Technology Data Exchange (ETDEWEB)
Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn
2008-08-08
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Hoelder continuity of energy minimizer maps between Riemannian polyhedra
International Nuclear Information System (INIS)
Bouziane, Taoufik
2004-10-01
The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the Hoelder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete our existence theorem obtained elsewhere, and consequently we generalize completely, to the case of target polyhedra without focal points (which is a weaker geometric condition than the nonpositivity of the curvature), the Eells-Fuglede's existence and regularity theorem which is the new version of the famous Eells-Sampson's theorem. (author)
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...
Introducing quantum Ricci curvature
Klitgaard, N.; Loll, R.
2018-02-01
Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by comparing the distance between pairs of spheres with that of their centers. The quantum Ricci curvature is designed for use on non-smooth and discrete metric spaces, and to satisfy the key criteria of scalability and computability. We test the prescription on a variety of regular and random piecewise flat spaces, mostly in two dimensions. This enables us to quantify its behavior for short lattices distances and compare its large-scale behavior with that of constantly curved model spaces. On the triangulated spaces considered, the quantum Ricci curvature has good averaging properties and reproduces classical characteristics on scales large compared to the discretization scale.
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
Riemannian geometry during the second half of the twentieth century
Berger, Marcel
1999-01-01
In the last fifty years of the twentieth century Riemannian geometry has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a truly remarkable survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. Berger's survey p...
Spherical-type hypersurfaces in a Riemannian manifold
International Nuclear Information System (INIS)
Ezin, J.P.; Rigoli, M.
1988-06-01
Let M be a compact hypersurface immersed in R n and let K and L be its mean curvature function and scalar curvature respectively. A classical global problem concerning these two geometrical quantities is to find out if assuming that either K or L is constant and under some additional assumptions M is a sphere. It was demonstrated that assuming the immersion to be an embedding, the consistency of K implies M to be spherical. It was also demonstrated that the sphere is the only compact hypersurface with constant scalar curvature embedded in Euclidean space. In this paper we give a generalization of these results when the ambient space is an appropriate Riemannian manifold (N, h). 17 refs
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...
Riemannian computing in computer vision
Srivastava, Anuj
2016-01-01
This book presents a comprehensive treatise on Riemannian geometric computations and related statistical inferences in several computer vision problems. This edited volume includes chapter contributions from leading figures in the field of computer vision who are applying Riemannian geometric approaches in problems such as face recognition, activity recognition, object detection, biomedical image analysis, and structure-from-motion. Some of the mathematical entities that necessitate a geometric analysis include rotation matrices (e.g. in modeling camera motion), stick figures (e.g. for activity recognition), subspace comparisons (e.g. in face recognition), symmetric positive-definite matrices (e.g. in diffusion tensor imaging), and function-spaces (e.g. in studying shapes of closed contours). · Illustrates Riemannian computing theory on applications in computer vision, machine learning, and robotics · Emphasis on algorithmic advances that will allow re-application in other...
Scattering theory for Riemannian Laplacians
DEFF Research Database (Denmark)
Ito, Kenichi; Skibsted, Erik
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another...... condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or hyperbolic...
Dynamic graphs, community detection, and Riemannian geometry
Energy Technology Data Exchange (ETDEWEB)
Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun
2018-03-29
A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.
Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes
International Nuclear Information System (INIS)
De Andrade, L.C.G.
2010-01-01
Recently Vishik anti-fast dynamo theorem has been tested against non-stretching flux tubes (Phys. Plasmas, 15 (2008)). In this paper, another anti dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusion less media. In the non-diffusive media Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res., 23 (1996) 857) in the context of geo dynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in the absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo.
Exact solutions for isometric embeddings of pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Amery, G; Moodley, J
2014-01-01
Embeddings into higher dimensions are of direct importance in the study of higher dimensional theories of our Universe, in high energy physics and in classical general relativity. Theorems have been established that guarantee the existence of local and global codimension-1 embeddings between pseudo-Riemannian manifolds, particularly for Einstein embedding spaces. A technique has been provided to determine solutions to such embeddings. However, general solutions have not yet been found and most known explicit solutions are for embedded spaces with relatively simple Ricci curvature. Motivated by this, we have considered isometric embeddings of 4-dimensional pseudo-Riemannian spacetimes into 5-dimensional Einstein manifolds. We have applied the technique to treat specific 4-dimensional cases of interest in astrophysics and cosmology (including the global monopole exterior and Vaidya-de Sitter-class solutions), and provided novel physical insights into, for example, Einstein-Gauss-Bonnet gravity. Since difficulties arise in solving the 5-dimensional equations for given 4-dimensional spaces, we have also investigated embedded spaces, which admit bulks with a particular metric form. These analyses help to provide insight to the general embedding problem
Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures
Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre
2002-01-01
Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...
Tomaschitz, R
1989-01-01
We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.
International Nuclear Information System (INIS)
Tomaschitz, R.
1989-01-01
We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...
Modern approaches to discrete curvature
Romon, Pascal
2017-01-01
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.
Absence of embedded eigenvalues for Riemannian Laplacians
DEFF Research Database (Denmark)
Ito, Kenichi; Skibsted, Erik
Schrödinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates are naturally defined. In this case one of our geometric conditions is a positive lower bound of the second fundamenta...
Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system
International Nuclear Information System (INIS)
Kawabe, Tetsuji
2003-01-01
Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Mao, Shasha; Xiong, Lin; Jiao, Licheng; Feng, Tian; Yeung, Sai-Kit
2017-05-01
Riemannian optimization has been widely used to deal with the fixed low-rank matrix completion problem, and Riemannian metric is a crucial factor of obtaining the search direction in Riemannian optimization. This paper proposes a new Riemannian metric via simultaneously considering the Riemannian geometry structure and the scaling information, which is smoothly varying and invariant along the equivalence class. The proposed metric can make a tradeoff between the Riemannian geometry structure and the scaling information effectively. Essentially, it can be viewed as a generalization of some existing metrics. Based on the proposed Riemanian metric, we also design a Riemannian nonlinear conjugate gradient algorithm, which can efficiently solve the fixed low-rank matrix completion problem. By experimenting on the fixed low-rank matrix completion, collaborative filtering, and image and video recovery, it illustrates that the proposed method is superior to the state-of-the-art methods on the convergence efficiency and the numerical performance.
Surface meshing with curvature convergence
Li, Huibin; Zeng, Wei; Morvan, Jean-Marie; Chen, Liming; Gu, Xianfengdavid
2014-01-01
Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.
Surface meshing with curvature convergence
Li, Huibin
2014-06-01
Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.
Sub-Riemannian geometry and optimal transport
Rifford, Ludovic
2014-01-01
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-12-01
A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.
Pseudo harmonic morphisms on Riemannian polyhedra
International Nuclear Information System (INIS)
Aprodu, M.A.; Bouziane, T.
2004-10-01
The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede and pseudo-horizontally weakly conformal in our sense. We characterize them by means of germs of harmonic functions on the source polyhedron, in the sense of Korevaar-Schoen, and germs of holomorphic functions on the Kaehler target manifold. (author)
Higher-order Jordan Osserman pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
Contour Propagation With Riemannian Elasticity Regularization
DEFF Research Database (Denmark)
Bjerre, Troels; Hansen, Mads Fogtmann; Sapru, W.
2011-01-01
Purpose/Objective(s): Adaptive techniques allow for correction of spatial changes during the time course of the fractionated radiotherapy. Spatial changes include tumor shrinkage and weight loss, causing tissue deformation and residual positional errors even after translational and rotational image...... the planning CT onto the rescans and correcting to reflect actual anatomical changes. For deformable registration, a free-form, multi-level, B-spline deformation model with Riemannian elasticity, penalizing non-rigid local deformations, and volumetric changes, was used. Regularization parameters was defined...... on the original delineation and tissue deformation in the time course between scans form a better starting point than rigid propagation. There was no significant difference of locally and globally defined regularization. The method used in the present study suggests that deformed contours need to be reviewed...
Transversal Dirac families in Riemannian foliations
International Nuclear Information System (INIS)
Glazebrook, J.F.; Kamber, F.W.
1991-01-01
We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation. (orig.)
Prescribed curvature tensor in locally conformally flat manifolds
Pina, Romildo; Pieterzack, Mauricio
2018-01-01
A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
Inverse curvature flows in asymptotically Robertson Walker spaces
Kröner, Heiko
2018-04-01
In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.
International Nuclear Information System (INIS)
Catoni, Francesco; Cannata, Roberto; Zampetti, Paolo
2005-08-01
The Riemann and Lorentz constant curvature surfaces are investigated from an Euclidean point of view. The four surfaces (constant positive and constant negative curvatures with definite and non-definite fine elements) are represented as surfaces in a Riemannian or in a particular semi-Riemannian flat space and it is shown that the complex and the hyperbolic numbers allow to obtain the same equations for the corresponding Riemann and Lorentz surfaces, respectively. Moreover it is shown that the geodesics on the Lorentz surfaces states, from a physical point of view, a link between curvature and fields. This result is obtained just as a consequence of the space-time geometrical symmetry, without invoking the famous Einstein general relativity postulate [it
Riemannian multi-manifold modeling and clustering in brain networks
Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.
2017-08-01
This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.
Embedded positive constant r-mean curvature hypersurfaces in Mm × R
Directory of Open Access Journals (Sweden)
Cheng Xu
2005-01-01
Full Text Available Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1-dimensional product manifold M x R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M x R with boundary in M x {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² x R of positive constant 2-mean curvature.
Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
Directory of Open Access Journals (Sweden)
Xiaoqiang Hua
2018-03-01
Full Text Available This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.
Straight-line string with curvature
International Nuclear Information System (INIS)
Solov'ev, L.D.
1995-01-01
Classical and quantum solutions for the relativistic straight-line string with arbitrary dependence on the world surface curvature are obtained. They differ from the case of the usual Nambu-Goto interaction by the behaviour of the Regge trajectory which in general can be non-linear. A regularization of the action is considered and a comparison with relativistic point with curvature is made. 5 refs
On the stability of the Lp -norm of the Riemannian curvature tensor
Indian Academy of Sciences (India)
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India .... the differential Bianchi identity simplifies the expression for the gradient of R2. ... it is a strict local minimizer for Rp. Applying Hölder inequality one can prove ...
On integrability of certain rank 2 sub-Riemannian structures
Czech Academy of Sciences Publication Activity Database
Kruglikov, B.S.; Vollmer, A.; Lukes-Gerakopoulos, Georgios
2017-01-01
Roč. 22, č. 5 (2017), s. 502-519 ISSN 1560-3547 R&D Projects: GA ČR(CZ) GJ17-06962Y Institutional support: RVO:67985815 Keywords : sub-Riemannian geodesic flow * Killing tensor * integral Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics OBOR OECD: Astronomy (including astrophysics,space science) Impact factor: 1.562, year: 2016
Geometric calculus: a new computational tool for Riemannian geometry
International Nuclear Information System (INIS)
Moussiaux, A.; Tombal, P.
1988-01-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus
Classification of non-Riemannian doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)
2017-10-15
Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)
A Random Riemannian Metric for Probabilistic Shortest-Path Tractography
DEFF Research Database (Denmark)
Hauberg, Søren; Schober, Michael; Liptrot, Matthew George
2015-01-01
of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We approximate this distribution with a Gaussian process and present a probabilistic numerics algorithm for computing the geodesic distribution. We demonstrate SPT improvements on data from the Human Connectome...
Aspects of quasi-Riemannian Kaluza-Klein theory
International Nuclear Information System (INIS)
Viswanathan, K.S.; Wong, B.
1985-01-01
We consider the applications of quasi-Riemannian geometry in Kaluza-Klein theories. We find that such theories cannot be implemented for all choices of the tangent group G/sub T/ and internal space G/H for reasons of gauge invariance. Coupling of fermions to gravity poses further problems in these theories
A Riemannian scalar measure for diffusion tensor images
Astola, L.J.; Fuster, A.; Florack, L.M.J.
2010-01-01
We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of Diffusion Tensor Imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI.
On determining the isometry group of a Riemannian space
International Nuclear Information System (INIS)
Karlhede, A.; Maccallum, M.A.H.
1982-01-01
An extension of the recently discussed algorithm for deciding the equivalence problem for Riemannian metrics is presented. The extension determines the structure constants of the isometry group and enables us to obtain some information about its orbits, including the form of the Killing vectors in canonical coordinates. (author)
An existence result of energy minimizer maps between Riemannian polyhedra
International Nuclear Information System (INIS)
Bouziane, T.
2004-06-01
In this paper, we prove the existence of energy minimizers in each free homotopy class of maps between polyhedra with target space without focal points. Our proof involves a careful study of some geometric properties of Riemannian polyhedra without focal points. Among other things, we show that on the relevant polyhedra, there exists a convex supporting function. (author)
Transformation optics, isotropic chiral media and non-Riemannian geometry
International Nuclear Information System (INIS)
Horsley, S A R
2011-01-01
The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include chiral media that are isotropic but inhomogeneous. It was found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and it is shown how such an interpretation may be applied to the design of optical devices.
The curvature coordinate system
DEFF Research Database (Denmark)
Almegaard, Henrik
2007-01-01
The paper describes a concept for a curvature coordinate system on regular curved surfaces from which faceted surfaces with plane quadrangular facets can be designed. The lines of curvature are used as parametric lines for the curvature coordinate system on the surface. A new conjugate set of lin...
Conservation laws in quantum mechanics on a Riemannian manifold
International Nuclear Information System (INIS)
Chepilko, N.M.
1992-01-01
In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n
Isometric C1-immersions for pairs of Riemannian metrics
International Nuclear Information System (INIS)
D'Ambra, Giuseppina; Datta, Mahuya
2001-08-01
Let h 1 , h 2 be two Euclidean metrics on R q , and let V be a C ∞ -manifold endowed with two Riemannian metrics g 1 and g 2 . We study the existence of C 1 -immersions f:(V,g 1 ,g 2 )→(R q ,h 1 ,h 2 ) such that f*(h i )=g i for i=1,2. (author)
Curvature properties of four-dimensional Walker metrics
International Nuclear Information System (INIS)
Chaichi, M; Garcia-Rio, E; Matsushita, Y
2005-01-01
A Walker n-manifold is a semi-Riemannian manifold, which admits a field of parallel null r-planes, r ≤ n/2. In the present paper we study curvature properties of a Walker 4-manifold (M, g) which admits a field of parallel null 2-planes. The metric g is necessarily of neutral signature (+ + - -). Such a Walker 4-manifold is the lowest dimensional example not of Lorentz type. There are three functions of coordinates which define a Walker metric. Some recent work shows that a Walker 4-manifold of restricted type whose metric is characterized by two functions exhibits a large variety of symplectic structures, Hermitian structures, Kaehler structures, etc. For such a restricted Walker 4-manifold, we shall study mainly curvature properties, e.g., conditions for a Walker metric to be Einstein, Osserman, or locally conformally flat, etc. One of our main results is the exact solutions to the Einstein equations for a restricted Walker 4-manifold
Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
Directory of Open Access Journals (Sweden)
Orlando Ragnisco
2007-02-01
Full Text Available An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3 integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.
New Riemannian Priors on the Univariate Normal Model
Directory of Open Access Journals (Sweden)
Salem Said
2014-07-01
Full Text Available The current paper introduces new prior distributions on the univariate normal model, with the aim of applying them to the classification of univariate normal populations. These new prior distributions are entirely based on the Riemannian geometry of the univariate normal model, so that they can be thought of as “Riemannian priors”. Precisely, if {pθ ; θ ∈ Θ} is any parametrization of the univariate normal model, the paper considers prior distributions G( θ - , γ with hyperparameters θ - ∈ Θ and γ > 0, whose density with respect to Riemannian volume is proportional to exp(−d2(θ, θ - /2γ2, where d2(θ, θ - is the square of Rao’s Riemannian distance. The distributions G( θ - , γ are termed Gaussian distributions on the univariate normal model. The motivation for considering a distribution G( θ - , γ is that this distribution gives a geometric representation of a class or cluster of univariate normal populations. Indeed, G( θ - , γ has a unique mode θ - (precisely, θ - is the unique Riemannian center of mass of G( θ - , γ, as shown in the paper, and its dispersion away from θ - is given by γ. Therefore, one thinks of members of the class represented by G( θ - , γ as being centered around θ - and lying within a typical distance determined by γ. The paper defines rigorously the Gaussian distributions G( θ - , γ and describes an algorithm for computing maximum likelihood estimates of their hyperparameters. Based on this algorithm and on the Laplace approximation, it describes how the distributions G( θ - , γ can be used as prior distributions for Bayesian classification of large univariate normal populations. In a concrete application to texture image classification, it is shown that this leads to an improvement in performance over the use of conjugate priors.
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.
a Super Voxel-Based Riemannian Graph for Multi Scale Segmentation of LIDAR Point Clouds
Li, Minglei
2018-04-01
Automatically segmenting LiDAR points into respective independent partitions has become a topic of great importance in photogrammetry, remote sensing and computer vision. In this paper, we cast the problem of point cloud segmentation as a graph optimization problem by constructing a Riemannian graph. The scale space of the observed scene is explored by an octree-based over-segmentation with different depths. The over-segmentation produces many super voxels which restrict the structure of the scene and will be used as nodes of the graph. The Kruskal coordinates are used to compute edge weights that are proportional to the geodesic distance between nodes. Then we compute the edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between super voxel nodes on the scene surface. The final segmentation results are generated by clustering similar super voxels and cutting off the weak edges in the graph. The performance of this method was evaluated on LiDAR point clouds for both indoor and outdoor scenes. Additionally, extensive comparisons to state of the art techniques show that our algorithm outperforms on many metrics.
Discrimination of curvature from motion during smooth pursuit eye movements and fixation.
Ross, Nicholas M; Goettker, Alexander; Schütz, Alexander C; Braun, Doris I; Gegenfurtner, Karl R
2017-09-01
Smooth pursuit and motion perception have mainly been investigated with stimuli moving along linear trajectories. Here we studied the quality of pursuit movements to curved motion trajectories in human observers and examined whether the pursuit responses would be sensitive enough to discriminate various degrees of curvature. In a two-interval forced-choice task subjects pursued a Gaussian blob moving along a curved trajectory and then indicated in which interval the curve was flatter. We also measured discrimination thresholds for the same curvatures during fixation. Motion curvature had some specific effects on smooth pursuit properties: trajectories with larger amounts of curvature elicited lower open-loop acceleration, lower pursuit gain, and larger catch-up saccades compared with less curved trajectories. Initially, target motion curvatures were underestimated; however, ∼300 ms after pursuit onset pursuit responses closely matched the actual curved trajectory. We calculated perceptual thresholds for curvature discrimination, which were on the order of 1.5 degrees of visual angle (°) for a 7.9° curvature standard. Oculometric sensitivity to curvature discrimination based on the whole pursuit trajectory was quite similar to perceptual performance. Oculometric thresholds based on smaller time windows were higher. Thus smooth pursuit can quite accurately follow moving targets with curved trajectories, but temporal integration over longer periods is necessary to reach perceptual thresholds for curvature discrimination. NEW & NOTEWORTHY Even though motion trajectories in the real world are frequently curved, most studies of smooth pursuit and motion perception have investigated linear motion. We show that pursuit initially underestimates the curvature of target motion and is able to reproduce the target curvature ∼300 ms after pursuit onset. Temporal integration of target motion over longer periods is necessary for pursuit to reach the level of precision found
On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature
Hu, Xue
2018-06-01
In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.
Implementing quantum Ricci curvature
Klitgaard, N.; Loll, R.
2018-05-01
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.
Energy Technology Data Exchange (ETDEWEB)
Rintoul, Mark Daniel [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Wilson, Andrew T. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Valicka, Christopher G. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Kegelmeyer, W. Philip [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Shead, Timothy M. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Newton, Benjamin D. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Czuchlewski, Kristina Rodriguez [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-09-01
We want to organize a body of trajectories in order to identify, search for, classify and predict behavior among objects such as aircraft and ships. Existing compari- son functions such as the Fr'echet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as total distance traveled and distance be- tween start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generally be mapped easily to behaviors of interest to humans that are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to iden- tify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories, predict destination and apply unsupervised machine learning algorithms.
On the de Rham–Wu decomposition for Riemannian and Lorentzian manifolds
International Nuclear Information System (INIS)
Galaev, Anton S
2014-01-01
It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold. (paper)
Quantum Riemannian geometry of phase space and nonassociativity
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Beggs Edwin J.
2017-04-01
Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
International Nuclear Information System (INIS)
Audretsch, J.; Gaehler, F.; Straumann, N.
1984-01-01
Previous axiomatic approaches to general relativity which led to a Weylian structure of space-time are supplemented by a physical condition which implies the existence of a preferred pseudo-Riemannian structure. It is stipulated that the trajectories of the short wave limit of classical massive fields agree with the geodesics of the Weyl connection and it is shown that this is equivalent to the vanishing of the covariant derivative of a ''mass function'' of nontrivial Weyl type.This in turn is proven to be equivalent to the existence of a preferred metric of the conformal structure such that the Weyl connection is reducible to a connection of the bundle of orthonormal frames belonging to this distinguished metric. (orig.)
Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II
International Nuclear Information System (INIS)
Chepilko, N.M.; Romanenko, A.V.
2001-01-01
The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. (orig.)
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
International Nuclear Information System (INIS)
Lawn, Marie-Amélie; Roth, Julien
2011-01-01
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.
The metric and curvature properties of H-space
International Nuclear Information System (INIS)
Hansen, R.O.; Newman, E.T.; Penrose, R.; Tod, K.P.
1978-01-01
The space H of asymptotically (left-) shear-free cuts of the future null infinity (good cuts) of an asymptotically flat space-time M is defined. The connection between this space and the asymptotic projective twistor space of M is discussed, and this relation is used to prove that H is four-complex-dimensional for sufficiently 'calm' gravitational radiation in M. The metric on H-space is defined by a simple contour integral expression and is found to be complex Riemannian. The good cut equation governing H-space is solved to three orders by a Taylor series and the solution is used to demonstrate that the curvature of H-space is always a self dual (left flat) solution of the Einstein vacuum equations. (author)
Curvature in mathematics and physics
Sternberg, Shlomo
2012-01-01
This original Dover textbook is based on an advanced undergraduate course taught by the author for more than 50 years. It introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Directory of Open Access Journals (Sweden)
Feng Qi
2014-10-01
Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS
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Jesus Angulo
2014-06-01
Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.
Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms
Lawn , Marie-Amélie; Roth , Julien
2011-01-01
9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well ...
Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds
Chikin, V. M.
2017-07-01
In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n≥ 7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.
Signed zeros of Gaussian vector fields - density, correlation functions and curvature
Foltin, G
2003-01-01
We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.
Advanced Curvature Deformable Mirrors
2010-09-01
ORGANIZATION NAME(S) AND ADDRESS(ES) University of Hawaii ,Institute for Astronomy,640 North A‘ohoku Place, #209 , Hilo ,HI,96720-2700 8. PERFORMING...Advanced Curvature Deformable Mirrors Christ Ftaclas1,2, Aglae Kellerer2 and Mark Chun2 Institute for Astronomy, University of Hawaii
Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry
International Nuclear Information System (INIS)
Pan, Yiwen
2014-01-01
In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S 1 ×M 4 , which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S 3 or T 3 -fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation
Introduction to global analysis minimal surfaces in Riemannian manifolds
Moore, John Douglas
2017-01-01
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...
Point interactions in two- and three-dimensional Riemannian manifolds
International Nuclear Information System (INIS)
Erman, Fatih; Turgut, O Teoman
2010-01-01
We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two- and three-dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator Φ(E). In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for a general class of manifolds, e.g. for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by the Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the β function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by Rajeev.
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
Commutative curvature operators over four-dimensional generalized symmetric
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Ali Haji-Badali
2014-12-01
Full Text Available Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary
International Nuclear Information System (INIS)
Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.
2005-08-01
We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)
Regularized strings with extrinsic curvature
International Nuclear Information System (INIS)
Ambjoern, J.; Durhuus, B.
1987-07-01
We analyze models of discretized string theories, where the path integral over world sheet variables is regularized by summing over triangulated surfaces. The inclusion of curvature in the action is a necessity for the scaling of the string tension. We discuss the physical properties of models with extrinsic curvature terms in the action and show that the string tension vanishes at the critical point where the bare extrinsic curvature coupling tends to infinity. Similar results are derived for models with intrinsic curvature. (orig.)
Haptic perception of object curvature in Parkinson's disease.
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Jürgen Konczak
2008-07-01
Full Text Available The haptic perception of the curvature of an object is essential for adequate object manipulation and critical for our guidance of actions. This study investigated how the ability to perceive the curvature of an object is altered by Parkinson's disease (PD.Eight healthy subjects and 11 patients with mild to moderate PD had to judge, without vision, the curvature of a virtual "box" created by a robotic manipulandum. Their hands were either moved passively along a defined curved path or they actively explored the curved curvature of a virtual wall. The curvature was either concave or convex (bulging to the left or right and was judged in two locations of the hand workspace--a left workspace location, where the curved hand path was associated with curved shoulder and elbow joint paths, and a right workspace location in which these joint paths were nearly linear. After exploring the curvature of the virtual object, subjects had to judge whether the curvature was concave or convex. Based on these data, thresholds for curvature sensitivity were established. The main findings of the study are: First, 9 out 11 PD patients (82% showed elevated thresholds for detecting convex curvatures in at least one test condition. The respective median threshold for the PD group was increased by 343% when compared to the control group. Second, when distal hand paths became less associated with proximal joint paths (right workspace, haptic acuity was reduced substantially in both groups. Third, sensitivity to hand trajectory curvature was not improved during active exploration in either group.Our data demonstrate that PD is associated with a decreased acuity of the haptic sense, which may occur already at an early stage of the disease.
Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.
Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing
2018-03-01
In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.
Brane cosmology with curvature corrections
International Nuclear Information System (INIS)
Kofinas, Georgios; Maartens, Roy; Papantonopoulos, Eleftherios
2003-01-01
We study the cosmology of the Randall-Sundrum brane-world where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. The combined effect of these curvature corrections to the action removes the infinite-density big bang singularity, although the curvature can still diverge for some parameter values. A radiation brane undergoes accelerated expansion near the minimal scale factor, for a range of parameters. This acceleration is driven by the geometric effects, without an inflation field or negative pressures. At late times, conventional cosmology is recovered. (author)
Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds
Liu, Yang
2017-11-01
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.
Quantum theory of spinor field in four-dimensional Riemannian space-time
International Nuclear Information System (INIS)
Shavokhina, N.S.
1996-01-01
The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs
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Mohammed Larbi Labbi
2007-12-01
Full Text Available The $(2k$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Construction of harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces
International Nuclear Information System (INIS)
Konderak, J.
1988-09-01
Defined here is an orthogonal multiplication for vector spaces with indefinite nondegenerate scalar product. This is then used, via the Hopf construction, to obtain harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces. Examples of harmonic maps are constructed using Clifford algebras. (author). 6 refs
Manifolds of positive scalar curvature
Energy Technology Data Exchange (ETDEWEB)
Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)
2002-08-15
This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.
Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework
Miolane, Nina; Pennec, Xavier
2015-01-01
Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ's shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis of diseases, one needs to perform statistics on Lie groups. A Lie group G is a manifold that carries an additional group structure. Statistics on Riemannian manifolds have been well studied with the pioneer work of Fréchet, Karcher and Kendall [1, 2, 3, 4] followed by others [5, 6, 7, 8, 9]. In order to use such a Riemannian structure for statistics on Lie groups, one needs to define a Riemannian metric that is compatible with the group structure, i.e a bi-invariant metric. However, it is well known that general Lie groups which cannot be decomposed into the direct product of compact and abelian groups do not admit a bi-invariant metric. One may wonder if removing the positivity of the metric, thus asking only for a bi-invariant pseudo-Riemannian metric, would be sufficient for most of the groups used in Computational Anatomy. In this paper, we provide an algorithmic procedure that constructs bi-invariant pseudo-metrics on a given Lie group G. The procedure relies on a classification theorem of Medina and Revoy. However in doing so, we prove that most Lie groups do not admit any bi-invariant (pseudo-) metric. We conclude that the (pseudo-) Riemannian setting is not the richest setting if one wants to perform statistics on Lie groups. One may have to rely on another framework, such as affine connection space.
Some Inequalities for the -Curvature Image
Directory of Open Access Journals (Sweden)
Daijun Wei
2009-01-01
Full Text Available Lutwak introduced the notion of -curvature image and proved an inequality for the volumes of convex body and its -curvature image. In this paper, we first give an monotonic property of -curvature image. Further, we establish two inequalities for the -curvature image and its polar, respectively. Finally, an inequality for the volumes of -projection body and -curvature image is obtained.
Tachyonless models of relativistic particles with curvature and torsion
International Nuclear Information System (INIS)
Kuznetsov, Yu.A.; Plyushchaj, M.S.
1992-01-01
The problem of construction (2+1)-dimensional tachyonless models of relativistic particles with an action depending on the world-trajectory curvature and torsion is investigated. The special class of models, described by maximum symmetric action and comprising only spin internal degrees of freedom is found. The examples of systems from the special class are given, whose classical and quantum spectra contain only massive states. 23 refs
Lectures on mean curvature flows
Zhu, Xi-Ping
2002-01-01
"Mean curvature flow" is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals \\pi, the curve tends to the unit circle. In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential ...
Curvature radiation by bunches of particles
International Nuclear Information System (INIS)
Saggion, A.
1975-01-01
A bunch of relativistic particles moving on a curved trajectory is considered. The coherent emission of curvature radiation is described with particular regard to the role played by the 'shape' of the bunch as a function of its dimensions. It is found that the length of the bunch strongly affects the spectrum of the radiation emitted, with no effect on its polarization. For wavelengths shorter than the length of the bunch, the emitted intensity as a function of frequency shows recurrent maxima and minima, the height of the maxima being proportional to νsup(-5/3). The bunch dimensions perpendicular to the plane of the orbit affect both the spectral intensity and the polarization of the radiation. (orig./BJ) [de
Environmental influences on DNA curvature
DEFF Research Database (Denmark)
Ussery, David; Higgins, C.F.; Bolshoy, A.
1999-01-01
DNA curvature plays an important role in many biological processes. To study environmentalinfluences on DNA curvature we compared the anomalous migration on polyacrylamide gels ofligation ladders of 11 specifically-designed oligonucleotides. At low temperatures (25 degreesC and below) most......, whilst spermine enhanced theanomalous migration of a different set of sequences. Sequences with a GGC motif exhibitedgreater curvature than predicted by the presently-used angles for the nearest-neighbour wedgemodel and are especially sensitive to Mg2+. The data have implications for models...... for DNAcurvature and for environmentally-sensitive DNA conformations in the regulation of geneexpression....
Curvature force and dark energy
International Nuclear Information System (INIS)
Balakin, Alexander B; Pavon, Diego; Schwarz, Dominik J; Zimdahl, Winfried
2003-01-01
A curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy, such as a rolling tachyon condensate or a Chaplygin gas. Any given Hubble rate and deceleration parameter can be traced back to the action of an effective curvature force on the gas particles. This force self-consistently reacts back on the cosmological dynamics. The links between an imperfect fluid description, a kinetic description with effective antifriction forces and curvature forces, which represent a non-minimal coupling of gravity to matter, are established
Existence of parallel spinors on non-simply-connected Riemannian manifolds
International Nuclear Information System (INIS)
McInnes, B.
1997-04-01
It is well known, and important for applications, that Ricci-flat Riemannian manifolds of non-generic holonomy always admit a parallel [covariant constant] spinor if they are simply connected. The non-simply-connected case is much more subtle, however. We show that a parallel spinor can still be found in this case provided that the [real] dimension is not a multiple of four, and provided that the spin structure is carefully chosen. (author). 10 refs
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group
Ardentov, Andrei A.; Sachkov, Yuri L.
2017-12-01
We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.
Directory of Open Access Journals (Sweden)
Fan Yang
2015-07-01
Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.
The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations
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.
Curvature bound from gravitational catalysis
Gies, Holger; Martini, Riccardo
2018-04-01
We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic...
A prescribing geodesic curvature problem
International Nuclear Information System (INIS)
Chang, K.C.; Liu, J.Q.
1993-09-01
Let D be the unit disk and k be a function on S 1 = δD. Find a flat metric which is pointwise conformal to the standard metric and has k as the geodesic curvature of S 1 . A sufficient condition for the existence of such a metric is that the harmonic extension of k in D has saddle points. (author). 11 refs
Seeley-Gilkey coefficients for the fourth-order operators on a Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1989-01-01
A new covariant method for computing the coefficients in the heat kernel expansion is suggested. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a Riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimension of the space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method suggested allows one to calculate coefficients by computer using the analytical calculation system. 19 refs.; 1 fig
Control of nonholonomic systems from sub-Riemannian geometry to motion planning
Jean, Frédéric
2014-01-01
Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.
Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures
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Ishikawa Goo
2015-06-01
Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.
On the model of the relativistic particle with curvature and torsion
International Nuclear Information System (INIS)
Nesterenko, V.V.
1992-01-01
Two integrals along the world trajectory of its curvature and torsion are added to the standard action for the point-like spinless relativistic particle. This enables one to quantize the model canonically and to derive exactly the relation between the spin and mass of the states. 10 refs
Cosmic curvature tested directly from observations
Denissenya, Mikhail; Linder, Eric V.; Shafieloo, Arman
2018-03-01
Cosmic spatial curvature is a fundamental geometric quantity of the Universe. We investigate a model independent, geometric approach to measure spatial curvature directly from observations, without any derivatives of data. This employs strong lensing time delays and supernova distance measurements to measure the curvature itself, rather than just testing consistency with flatness. We define two curvature estimators, with differing error propagation characteristics, that can crosscheck each other, and also show how they can be used to map the curvature in redshift slices, to test constancy of curvature as required by the Robertson-Walker metric. Simulating realizations of redshift distributions and distance measurements of lenses and sources, we estimate uncertainties on the curvature enabled by next generation measurements. The results indicate that the model independent methods, using only geometry without assuming forms for the energy density constituents, can determine the curvature at the ~6×10‑3 level.
Curvature Entropy for Curved Profile Generation
Ujiie, Yoshiki; Kato, Takeo; Sato, Koichiro; Matsuoka, Yoshiyuki
2012-01-01
In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribu...
A remark about the mean curvature
International Nuclear Information System (INIS)
Zhang Weitao.
1992-11-01
In this paper, we give an integral identity about the mean curvature in Sobolev space H 0 1 (Ω) intersection H 2 (Ω). Suppose the mean curvature on Γ=δΩ is positive, we prove some inequalities of the positive mean curvature and propose some open problems. (author). 4 refs
International Nuclear Information System (INIS)
Barenboim, Gabriela; Martínez, Enrique Fernández; Mena, Olga; Verde, Licia
2010-01-01
Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d A (z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Ω k in a direct, model-independent way. In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z). Combining measurements of both H(z) and d A (z) up to sufficiently high redshifts z ∼ 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z)−Ω k degeneracy
Segmentation of High Angular Resolution Diffusion MRI using Sparse Riemannian Manifold Clustering
Wright, Margaret J.; Thompson, Paul M.; Vidal, René
2015-01-01
We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to represent HARDI data and cast the problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and the presence of complex fiber configurations, and show its superior performance compared to alternative segmentation methods. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers, as well as white matter fiber tracts of clinical importance in the human brain. PMID:24108748
Curvature Entropy for Curved Profile Generation
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Koichiro Sato
2012-03-01
Full Text Available In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features. The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.
Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form
Energy Technology Data Exchange (ETDEWEB)
Guendelman, Eduardo [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); Nissimov, Emil; Pacheva, Svetlana [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)
2015-10-15
We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold - one standard Riemannian given by √(-g) (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless ''dust'' fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe's epoch without evolution pathologies. (orig.)
A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
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Qiang Ru
2013-01-01
Full Text Available We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.
Zimmermann, Ralf
2016-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.
DEFF Research Database (Denmark)
Zimmermann, Ralf
2017-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...... converges locally and exhibits a linear rate of convergence....
Dynamic Double Curvature Mould System
DEFF Research Database (Denmark)
Jepsen, Christian Raun; Kristensen, Mathias Kræmmergaard; Kirkegaard, Poul Henning
2011-01-01
The present paper describes a concept for a reconfigurable mould surface which is designed to fit the needs of contemporary architecture. The core of the concept presented is a dynamic surface manipulated into a given shape using a digital signal created directly from the CAD drawing of the design....... This happens fast, automatic and without production of waste, and the manipulated surface is fair and robust, eliminating the need for additional, manual treatment. Limitations to the possibilities of the flexible form are limited curvature and limited level of detail, making it especially suited for larger...
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
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Sheng-lan Chen
2014-01-01
Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Svane, Anne Marie
2017-01-01
distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition......We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed...... in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal...
Differential calculus on the space of Steiner minimal trees in Riemannian manifolds
International Nuclear Information System (INIS)
Ivanov, A O; Tuzhilin, A A
2001-01-01
It is proved that the length of a minimal spanning tree, the length of a Steiner minimal tree, and the Steiner ratio regarded as functions of finite subsets of a connected complete Riemannian manifold have directional derivatives in all directions. The derivatives of these functions are calculated and some properties of their critical points are found. In particular, a geometric criterion for a finite set to be critical for the Steiner ratio is found. This criterion imposes essential restrictions on the geometry of the sets for which the Steiner ratio attains its minimum, that is, the sets on which the Steiner ratio of the boundary set is equal to the Steiner ratio of the ambient space
Seeley-Gilkey coefficients for fourth-order operators on Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1990-01-01
The covariant pseudodifferential-operator method of Widom is developed for computing the coefficients in the heat kernel expansion. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimensions of space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method allows one to calculate the coefficients by computer using an analytical calculation system. The method also permits a simple generalization to manifolds with torsion and supermanifolds. (orig.)
Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
Energy Technology Data Exchange (ETDEWEB)
De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2017-09-15
We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
Do extended bodies move alon.o the geodesics of the Riemannian space-time
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.
1980-01-01
Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8
Curvature-Controlled Topological Defects
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Luka Mesarec
2017-05-01
Full Text Available Effectively, two-dimensional (2D closed films exhibiting in-plane orientational ordering (ordered shells might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.
Higher curvature supergravity and cosmology
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio [Th-Ph Department, CERN, Geneva (Switzerland); U.C.L.A., Los Angeles, CA (United States); INFN - LNF, Frascati (Italy); Sagnotti, Augusto [Scuola Normale Superiore, Pisa (Italy); INFN, Pisa (Italy)
2016-04-15
In this contribution we describe dual higher-derivative formulations of some cosmological models based on supergravity. Work in this direction started with the R + R{sup 2} Starobinsky model, whose supersymmetric extension was derived in the late 80's and was recently revived in view of new CMB data. Models dual to higher-derivative theories are subject to more restrictions than their bosonic counterparts or standard supergravity. The three sections are devoted to a brief description of R + R{sup 2} supergravity, to a scale invariant R{sup 2} supergravity and to theories with a nilpotent curvature, whose duals describe non-linear realizations (in the form of a Volkov-Akulov constrained superfield) coupled to supergravity. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
SLED phenomenology: curvature vs. volume
International Nuclear Information System (INIS)
Niedermann, Florian; Schneider, Robert
2016-01-01
We assess the question whether the SLED (Supersymmetric Large Extra Dimensions) model admits phenomenologically viable solutions with 4D maximal symmetry. We take into account a finite brane width and a scale invariance (SI) breaking dilaton-brane coupling, both of which should be included in a realistic setup. Provided that the brane tension and the microscopic size of the brane take generic values set by the fundamental bulk Planck scale, we find that either the 4D curvature or the size of the extra dimensions is unacceptably large. Since this result is independent of the dilaton-brane couplings, it provides the biggest challenge to the SLED program. In addition, to quantify its potential with respect to the cosmological constant problem, we infer the amount of tuning on model parameters required to obtain a sufficiently small 4D curvature. A first answer was recently given in http://dx.doi.org/10.1007/JHEP02(2016)025, showing that 4D flat solutions are only ensured in the SI case by imposing a tuning relation, even if a brane-localized flux is included. In this companion paper, we find that the tuning can in fact be avoided for certain SI breaking brane-dilaton couplings, but only at the price of worsening the phenomenological problem. Our results are obtained by solving the full coupled Einstein-dilaton system in a completely consistent way. The brane width is implemented using a well-known ring regularization. In passing, we note that for the couplings considered here the results of http://dx.doi.org/10.1007/JHEP02(2016)025 (which only treated infinitely thin branes) are all consistently recovered in the thin brane limit, and how this can be reconciled with the concerns about their correctness, recently brought up in http://dx.doi.org/10.1007/JHEP01(2016)017.
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
The curvature function in general relativity
International Nuclear Information System (INIS)
Hall, G S; MacNay, Lucy
2006-01-01
A function, here called the curvature function, is defined and which is constructed explicitly from the type (0, 4) curvature tensor. Although such a function may be defined for any manifold admitting a metric, attention is here concentrated on this function on a spacetime. Some properties of this function are explored and compared with a previous discussion of it given by Petrov
Güler, Fatma; Kasap, Emin
Using the curvature theory for the ruled surfaces a technique for robot trajectory planning is presented. This technique ensures the calculation of robot’s next path. The positional variation of the Tool Center Point (TCP), linear velocity, angular velocity are required in the work area of the robot. In some circumstances, it may not be physically achievable and a re-computation of the robot trajectory might be necessary. This technique is suitable for re-computation of the robot trajectory. We obtain different robot trajectories which change depending on the darboux angle function and define trajectory ruled surface family with a common trajectory curve with the rotation trihedron. Also, the motion of robot end effector is illustrated with examples.
Energy Technology Data Exchange (ETDEWEB)
Gao, Dengliang
2013-03-01
In 3D seismic interpretation, curvature is a popular attribute that depicts the geometry of seismic reflectors and has been widely used to detect faults in the subsurface; however, it provides only part of the solutions to subsurface structure analysis. This study extends the curvature algorithm to a new curvature gradient algorithm, and integrates both algorithms for fracture detection using a 3D seismic test data set over Teapot Dome (Wyoming). In fractured reservoirs at Teapot Dome known to be formed by tectonic folding and faulting, curvature helps define the crestal portion of the reservoirs that is associated with strong seismic amplitude and high oil productivity. In contrast, curvature gradient helps better define the regional northwest-trending and the cross-regional northeast-trending lineaments that are associated with weak seismic amplitude and low oil productivity. In concert with previous reports from image logs, cores, and outcrops, the current study based on an integrated seismic curvature and curvature gradient analysis suggests that curvature might help define areas of enhanced potential to form tensile fractures, whereas curvature gradient might help define zones of enhanced potential to develop shear fractures. In certain fractured reservoirs such as at Teapot Dome where faulting and fault-related folding contribute dominantly to the formation and evolution of fractures, curvature and curvature gradient attributes can be potentially applied to differentiate fracture mode, to predict fracture intensity and orientation, to detect fracture volume and connectivity, and to model fracture networks.
Gahm, Jin Kyu; Shi, Yonggang
2018-05-01
Surface mapping methods play an important role in various brain imaging studies from tracking the maturation of adolescent brains to mapping gray matter atrophy patterns in Alzheimer's disease. Popular surface mapping approaches based on spherical registration, however, have inherent numerical limitations when severe metric distortions are present during the spherical parameterization step. In this paper, we propose a novel computational framework for intrinsic surface mapping in the Laplace-Beltrami (LB) embedding space based on Riemannian metric optimization on surfaces (RMOS). Given a diffeomorphism between two surfaces, an isometry can be defined using the pullback metric, which in turn results in identical LB embeddings from the two surfaces. The proposed RMOS approach builds upon this mathematical foundation and achieves general feature-driven surface mapping in the LB embedding space by iteratively optimizing the Riemannian metric defined on the edges of triangular meshes. At the core of our framework is an optimization engine that converts an energy function for surface mapping into a distance measure in the LB embedding space, which can be effectively optimized using gradients of the LB eigen-system with respect to the Riemannian metrics. In the experimental results, we compare the RMOS algorithm with spherical registration using large-scale brain imaging data, and show that RMOS achieves superior performance in the prediction of hippocampal subfields and cortical gyral labels, and the holistic mapping of striatal surfaces for the construction of a striatal connectivity atlas from substantia nigra. Copyright © 2018 Elsevier B.V. All rights reserved.
Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei
2012-12-01
Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.
Curvature function and coarse graining
International Nuclear Information System (INIS)
Diaz-Marin, Homero; Zapata, Jose A.
2010-01-01
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions have encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to ''local details'' ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function F S (A) defined below. It covers the holonomy function in the sense that expF S (A)=Hol(l=∂S,A).
Curvature and torsion in growing actin networks
International Nuclear Information System (INIS)
Shaevitz, Joshua W; Fletcher, Daniel A
2008-01-01
Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque
Inferring imagined speech using EEG signals: a new approach using Riemannian manifold features
Nguyen, Chuong H.; Karavas, George K.; Artemiadis, Panagiotis
2018-02-01
Objective. In this paper, we investigate the suitability of imagined speech for brain-computer interface (BCI) applications. Approach. A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the relevance vector machines classifier is proposed. The method is applied on electroencephalographic (EEG) signals and tested in multiple subjects. Main results. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. Significance. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published.
Color Texture Image Retrieval Based on Local Extrema Features and Riemannian Distance
Directory of Open Access Journals (Sweden)
Minh-Tan Pham
2017-10-01
Full Text Available A novel efficient method for content-based image retrieval (CBIR is developed in this paper using both texture and color features. Our motivation is to represent and characterize an input image by a set of local descriptors extracted from characteristic points (i.e., keypoints within the image. Then, dissimilarity measure between images is calculated based on the geometric distance between the topological feature spaces (i.e., manifolds formed by the sets of local descriptors generated from each image of the database. In this work, we propose to extract and use the local extrema pixels as our feature points. Then, the so-called local extrema-based descriptor (LED is generated for each keypoint by integrating all color, spatial as well as gradient information captured by its nearest local extrema. Hence, each image is encoded by an LED feature point cloud and Riemannian distances between these point clouds enable us to tackle CBIR. Experiments performed on several color texture databases including Vistex, STex, color Brodazt, USPtex and Outex TC-00013 using the proposed approach provide very efficient and competitive results compared to the state-of-the-art methods.
Canonical quantization of a relativistic particle with curvature and torsion
International Nuclear Information System (INIS)
Nesterenko, V.V.
1991-01-01
A generalization of the relativistic particle action is considered. It contain, in addition to the length of the world trajectory, the integrals along the world curve of its curvature and torsion. The generalized Hamiltonian formalism for this model in the D-dimensional space-time is constructed. A complete set of the constraints in the phase space is obtained and their division into the first-class and the second-class constraints is accomplished. On this basis the canonical quantization of the model is fulfilled. For D=3 the mass spectrum is obtained in the sector without tachyonic states, the mass of the state being dependent on its spin. It is shown that in the framework of this model when D=3 the possibility to describe the states with integral, half-odd-integral and continuous spins is derived. Interaction with an external Abelian gauge field introduced in the geometrical way. 21 refs
Right thoracic curvature in the normal spine
Directory of Open Access Journals (Sweden)
Masuda Keigo
2011-01-01
Full Text Available Abstract Background Trunk asymmetry and vertebral rotation, at times observed in the normal spine, resemble the characteristics of adolescent idiopathic scoliosis (AIS. Right thoracic curvature has also been reported in the normal spine. If it is determined that the features of right thoracic side curvature in the normal spine are the same as those observed in AIS, these findings might provide a basis for elucidating the etiology of this condition. For this reason, we investigated right thoracic curvature in the normal spine. Methods For normal spinal measurements, 1,200 patients who underwent a posteroanterior chest radiographs were evaluated. These consisted of 400 children (ages 4-9, 400 adolescents (ages 10-19 and 400 adults (ages 20-29, with each group comprised of both genders. The exclusion criteria were obvious chest and spinal diseases. As side curvature is minimal in normal spines and the range at which curvature is measured is difficult to ascertain, first the typical curvature range in scoliosis patients was determined and then the Cobb angle in normal spines was measured using the same range as the scoliosis curve, from T5 to T12. Right thoracic curvature was given a positive value. The curve pattern was organized in each collective three groups: neutral (from -1 degree to 1 degree, right (> +1 degree, and left ( Results In child group, Cobb angle in left was 120, in neutral was 125 and in right was 155. In adolescent group, Cobb angle in left was 70, in neutral was 114 and in right was 216. In adult group, Cobb angle in left was 46, in neutral was 102 and in right was 252. The curvature pattern shifts to the right side in the adolescent group (p Conclusions Based on standing chest radiographic measurements, a right thoracic curvature was observed in normal spines after adolescence.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-01-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads
Higher Curvature Supergravity, Supersymmetry Breaking and Inflation
Ferrara, Sergio
2017-01-01
In these lectures, after a short introduction to cosmology, we discuss the supergravity embedding of higher curvature models of inflation. The supergravity description of such models is presented for the two different formulations of minimal supergravity.
Curvature of Indoor Sensor Network: Clustering Coefficient
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We investigate the geometric properties of the communication graph in realistic low-power wireless networks. In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient. Clustering coefficient analysis is a computationally simplified, semilocal approach, which nevertheless captures such a large-scale feature as congestion in the underlying network. The clustering coefficient concept is applied to three cases of indoor sensor networks, under varying thresholds on the link packet reception rate (PRR. A transition from positive curvature (“meshed” network to negative curvature (“core concentric” network is observed by increasing the threshold. Even though this paper deals with network curvature per se, we nevertheless expand on the underlying congestion motivation, propose several new concepts (network inertia and centroid, and finally we argue that greedy routing on a virtual positively curved network achieves load balancing on the physical network.
The spinning particle with extrinsic curvature
International Nuclear Information System (INIS)
Dhar, A.
1988-01-01
We construct and analyse an action for the spinning particle which contains an extrinsic curvature term. A possible generalization of this construction to the case of the spinning string is also discussed. (orig.)
GDP growth and the yield curvature
DEFF Research Database (Denmark)
Møller, Stig Vinther
2014-01-01
This paper examines the forecastability of GDP growth using information from the term structure of yields. In contrast to previous studies, the paper shows that the curvature of the yield curve contributes with much more forecasting power than the slope of yield curve. The yield curvature also...... predicts bond returns, implying a common element to time-variation in expected bond returns and expected GDP growth....
Curvature-Induced Instabilities of Shells
Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.
2018-01-01
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.
Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics
Energy Technology Data Exchange (ETDEWEB)
Novello, Mario [Centro Brasileiro de Pesquisas Fisicas (ICRA/CBPF), Rio de Janeiro, RJ (Brazil). Instituto de Cosmologia Relatividade e Astrofisica; Bittencourt, Eduardo, E-mail: eduardo.bittencourt@icranet.org [Physics Department, La Sapienza University of Rome (Italy)
2015-12-15
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric ĝ μ υ which is responsible to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associatedĝ geometry. Only recently, the method introduced by Einstein in general relativity was used beyond the domain of gravitational forces to map arbitrary accelerated bodies submitted to non-Newtonian attractions onto geodesics of a modified geometry. This process has its roots in the very ancient idea to treat any dynamical problem in Classical Mechanics as nothing but a problem of static where all forces acting on a body annihilates themselves including the inertial ones. This general procedure, that concerns arbitrary forces - beyond the uses of General Relativity that is limited only to gravitational processes - is nothing but the relativistic version of the d'Alembert method in classical mechanics and consists in the principle of Metric Relativity. The main difference between gravitational interaction and all other forces concerns the universality of gravity which added to the interpretation of the equivalence principle allows all associated geometries-one for each different body in the case of non-gravitational forces-to be unified into a unique Riemannian space-time structure. The same geometrical description appears for electromagnetic waves in the optical limit within the context of nonlinear theories or material medium. Once it is largely discussed in the literature, the so-called analogue models of gravity, we will dedicate few sections on this emphasizing their relation with the new concepts introduced here. Then, we pass to the description of the Dynamical Bridge formalism
The speed-curvature power law in Drosophila larval locomotion.
Zago, Myrka; Lacquaniti, Francesco; Gomez-Marin, Alex
2016-10-01
We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. © 2016 The Authors.
Management by Trajectory: Trajectory Management Study Report
Leiden, Kenneth; Atkins, Stephen; Fernandes, Alicia D.; Kaler, Curt; Bell, Alan; Kilbourne, Todd; Evans, Mark
2017-01-01
In order to realize the full potential of the Next Generation Air Transportation System (NextGen), improved management along planned trajectories between air navigation service providers (ANSPs) and system users (e.g., pilots and airline dispatchers) is needed. Future automation improvements and increased data communications between aircraft and ground automation would make the concept of Management by Trajectory (MBT) possible.
Congedo, Marco; Barachant, Alexandre
2015-01-01
Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In
National Aeronautics and Space Administration — Adaptive Trajectory Design (ATD) is an original concept for quick and efficient end-to-end trajectory designs using proven piece-wise dynamical methods. With ongoing...
Curvature constraints from the causal entropic principle
International Nuclear Information System (INIS)
Bozek, Brandon; Albrecht, Andreas; Phillips, Daniel
2009-01-01
Current cosmological observations indicate a preference for a cosmological constant that is drastically smaller than what can be explained by conventional particle physics. The causal entropic principle (Bousso et al.) provides an alternative approach to anthropic attempts to predict our observed value of the cosmological constant by calculating the entropy created within a causal diamond. We have extended this work to use the causal entropic principle to predict the preferred curvature within the 'multiverse'. We have found that values larger than ρ k =40ρ m are disfavored by more than 99.99% peak value at ρ Λ =7.9x10 -123 and ρ k =4.3ρ m for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending on the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work.
Some Inequalities for the Lp-Curvature Image
Directory of Open Access Journals (Sweden)
Xiang Yu
2009-01-01
Full Text Available Lutwak introduced the notion of Lp-curvature image and proved an inequality for the volumes of convex body and its Lp-curvature image. In this paper, we first give an monotonic property of Lp-curvature image. Further, we establish two inequalities for the Lp-curvature image and its polar, respectively. Finally, an inequality for the volumes of Lp-projection body and Lp-curvature image is obtained.
Quantifying the quality of hand movement in stroke patients through three-dimensional curvature
Directory of Open Access Journals (Sweden)
Osu Rieko
2011-10-01
Full Text Available Abstract Background To more accurately evaluate rehabilitation outcomes in stroke patients, movement irregularities should be quantified. Previous work in stroke patients has revealed a reduction in the trajectory smoothness and segmentation of continuous movements. Clinically, the Stroke Impairment Assessment Set (SIAS evaluates the clumsiness of arm movements using an ordinal scale based on the examiner's observations. In this study, we focused on three-dimensional curvature of hand trajectory to quantify movement, and aimed to establish a novel measurement that is independent of movement duration. We compared the proposed measurement with the SIAS score and the jerk measure representing temporal smoothness. Methods Sixteen stroke patients with SIAS upper limb proximal motor function (Knee-Mouth test scores ranging from 2 (incomplete performance to 4 (mild clumsiness were recruited. Nine healthy participant with a SIAS score of 5 (normal also participated. Participants were asked to grasp a plastic glass and repetitively move it from the lap to the mouth and back at a conformable speed for 30 s, during which the hand movement was measured using OPTOTRAK. The position data was numerically differentiated and the three-dimensional curvature was computed. To compare against a previously proposed measure, the mean squared jerk normalized by its minimum value was computed. Age-matched healthy participants were instructed to move the glass at three different movement speeds. Results There was an inverse relationship between the curvature of the movement trajectory and the patient's SIAS score. The median of the -log of curvature (MedianLC correlated well with the SIAS score, upper extremity subsection of Fugl-Meyer Assessment, and the jerk measure in the paretic arm. When the healthy participants moved slowly, the increase in the jerk measure was comparable to the paretic movements with a SIAS score of 2 to 4, while the MedianLC was distinguishable
Computing with spatial trajectories
2011-01-01
Covers the fundamentals and the state-of-the-art research inspired by the spatial trajectory data Readers are provided with tutorial-style chapters, case studies and references to other relevant research work This is the first book that presents the foundation dealing with spatial trajectories and state-of-the-art research and practices enabled by trajectories
Extrinsic and intrinsic curvatures in thermodynamic geometry
Energy Technology Data Exchange (ETDEWEB)
Hosseini Mansoori, Seyed Ali, E-mail: shossein@bu.edu [Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215 (United States); Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Sharifian, Elham, E-mail: e.sharifian@ph.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of)
2016-08-10
We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner–Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.
Extrinsic and intrinsic curvatures in thermodynamic geometry
International Nuclear Information System (INIS)
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz; Sharifian, Elham
2016-01-01
We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner–Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.
Substrate curvature gradient drives rapid droplet motion.
Lv, Cunjing; Chen, Chao; Chuang, Yin-Chuan; Tseng, Fan-Gang; Yin, Yajun; Grey, Francois; Zheng, Quanshui
2014-07-11
Making small liquid droplets move spontaneously on solid surfaces is a key challenge in lab-on-chip and heat exchanger technologies. Here, we report that a substrate curvature gradient can accelerate micro- and nanodroplets to high speeds on both hydrophilic and hydrophobic substrates. Experiments for microscale water droplets on tapered surfaces show a maximum speed of 0.42 m/s, 2 orders of magnitude higher than with a wettability gradient. We show that the total free energy and driving force exerted on a droplet are determined by the substrate curvature and substrate curvature gradient, respectively. Using molecular dynamics simulations, we predict nanoscale droplets moving spontaneously at over 100 m/s on tapered surfaces.
Cosmic curvature from de Sitter equilibrium cosmology.
Albrecht, Andreas
2011-10-07
I show that the de Sitter equilibrium cosmology generically predicts observable levels of curvature in the Universe today. The predicted value of the curvature, Ω(k), depends only on the ratio of the density of nonrelativistic matter to cosmological constant density ρ(m)(0)/ρ(Λ) and the value of the curvature from the initial bubble that starts the inflation, Ω(k)(B). The result is independent of the scale of inflation, the shape of the potential during inflation, and many other details of the cosmology. Future cosmological measurements of ρ(m)(0)/ρ(Λ) and Ω(k) will open up a window on the very beginning of our Universe and offer an opportunity to support or falsify the de Sitter equilibrium cosmology.
Radion stabilization in higher curvature warped spacetime
Energy Technology Data Exchange (ETDEWEB)
Das, Ashmita [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India); Mukherjee, Hiya; Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2018-02-15
We consider a five dimensional AdS spacetime in presence of higher curvature term like F(R) = R + αR{sup 2} in the bulk. In this model, we examine the possibility of modulus stabilization from the scalar degrees of freedom of higher curvature gravity free of ghosts. Our result reveals that the model stabilizes itself and the mechanism of modulus stabilization can be argued from a geometric point of view. We determine the region of the parametric space for which the modulus (or radion) can to be stabilized. We also show how the mass and coupling parameters of radion field are modified due to higher curvature term leading to modifications of its phenomenological implications on the visible 3-brane. (orig.)
Longitudinal surface curvature effect in magnetohydrodynamics
International Nuclear Information System (INIS)
Bodas, N.G.
1975-01-01
The two-dimensional motion of an incompressible and electrically conducting fluid past an electrically insulated body surface (having curvature) is studied for a given O(1) basic flow and magnetic field, when (i) the applied magnetic field is aligned with the velocity in the basic flow, and (ii) the applied magnetic field is within the body surface. 01 and 0(Re sup(1/2)) mean the first and second order approximations respectively in an exansion scheme in powers of Resup(-1/2), Re being the Reynolds number). The technique of matched asymptotic expansions is used to solve the problem. The governing partial differential equations to 0(Resup(-1/2)) boundary layer approximation are found to give similarity solutions for a family of surface curvature and pressure gradient distributions in case (i), and for uniform basic flow with analytic surface curvature distributions in case (ii). The equations are solved numerically. In case (i) it is seen that the effect of the magnetic field on the skin-friction- correction due to the curvature is very small. Also the magnetic field at the wall is reduced by the curvature on the convex side. In case (ii) the magnetic field significantly increases the skin-friction-correction due to the curvature. The effect of the magnetic field on the O(1) and O(Resup(-1/2)) skin friction coefficients increases with the increase of the electrical conductivity of the fluid. Also, at higher values of the magnetic pressure, moderate changes in the electrical conductivity do not influence the correction to the skin-friction significantly. (Auth.)
Singh, Harkirat; Wahi, Pankaj
2017-08-01
The motion of a string in the presence of a doubly curved obstacle is investigated. A mathematical model has been developed for a general shape of the obstacle. However, detailed analysis has been performed for a shape relevant to the Indian stringed musical instruments like Tanpura and Sitar. In particular, we explore the effect of obstacle's curvature in the plane perpendicular to the string axis on its motion. This geometrical feature of the obstacle introduces a coupling between motions in mutually perpendicular directions over and above the coupling due to the stretching nonlinearity. We find that only one planar motion is possible for our system. Small amplitude planar motions are stable to perturbations in the perpendicular direction resulting in non-whirling motions while large amplitude oscillations lead to whirling motions. The critical amplitude of oscillations, across which there is a transition in the qualitative behavior of the non-planar trajectories, is determined using Floquet theory. Our analysis reveals that a small obstacle curvature in a direction perpendicular to the string axis leads to a considerable reduction in the critical amplitudes required for initiation of whirling motions. Hence, this obstacle curvature has a destabilizing effect on the planar motions in contrast to the curvature along the string axis which stabilizes planar motions.
Comprehensive Use of Curvature for Robust and Accurate Online Surface Reconstruction.
Lefloch, Damien; Kluge, Markus; Sarbolandi, Hamed; Weyrich, Tim; Kolb, Andreas
2017-12-01
Interactive real-time scene acquisition from hand-held depth cameras has recently developed much momentum, enabling applications in ad-hoc object acquisition, augmented reality and other fields. A key challenge to online reconstruction remains error accumulation in the reconstructed camera trajectory, due to drift-inducing instabilities in the range scan alignments of the underlying iterative-closest-point (ICP) algorithm. Various strategies have been proposed to mitigate that drift, including SIFT-based pre-alignment, color-based weighting of ICP pairs, stronger weighting of edge features, and so on. In our work, we focus on surface curvature as a feature that is detectable on range scans alone and hence does not depend on accurate multi-sensor alignment. In contrast to previous work that took curvature into consideration, however, we treat curvature as an independent quantity that we consistently incorporate into every stage of the real-time reconstruction pipeline, including densely curvature-weighted ICP, range image fusion, local surface reconstruction, and rendering. Using multiple benchmark sequences, and in direct comparison to other state-of-the-art online acquisition systems, we show that our approach significantly reduces drift, both when analyzing individual pipeline stages in isolation, as well as seen across the online reconstruction pipeline as a whole.
Zero curvature conditions and conformal covariance
International Nuclear Information System (INIS)
Akemann, G.; Grimm, R.
1992-05-01
Two-dimensional zero curvature conditions were investigated in detail, with special emphasis on conformal properties, and the appearance of covariant higher order differential operators constructed in terms of a projective connection was elucidated. The analysis is based on the Kostant decomposition of simple Lie algebras in terms of representations with respect to their 'principal' SL(2) subalgebra. (author) 27 refs
Constraining inverse curvature gravity with supernovae
Energy Technology Data Exchange (ETDEWEB)
Mena, Olga; Santiago, Jose; /Fermilab; Weller, Jochen; /University Coll., London /Fermilab
2005-10-01
We show that the current accelerated expansion of the Universe can be explained without resorting to dark energy. Models of generalized modified gravity, with inverse powers of the curvature can have late time accelerating attractors without conflicting with solar system experiments. We have solved the Friedman equations for the full dynamical range of the evolution of the Universe. This allows us to perform a detailed analysis of Supernovae data in the context of such models that results in an excellent fit. Hence, inverse curvature gravity models represent an example of phenomenologically viable models in which the current acceleration of the Universe is driven by curvature instead of dark energy. If we further include constraints on the current expansion rate of the Universe from the Hubble Space Telescope and on the age of the Universe from globular clusters, we obtain that the matter content of the Universe is 0.07 {le} {omega}{sub m} {le} 0.21 (95% Confidence). Hence the inverse curvature gravity models considered can not explain the dynamics of the Universe just with a baryonic matter component.
On Mass, Spacetime Curvature, and Gravity
Janis, Allen I.
2018-01-01
The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Curvature driven instabilities in toroidal plasmas
International Nuclear Information System (INIS)
Andersson, P.
1986-11-01
The electromagnetic ballooning mode, the curvature driven trapped electron mode and the toroidally induced ion temperature gradient mode have been studies. Eigenvalue equations have been derived and solved both numerically and analytically. For electromagnetic ballooning modes the effects of convective damping, finite Larmor radius, higher order curvature terms, and temperature gradients have been investigated. A fully toroidal fluid ion model has been developed. It is shown that a necessary and sufficient condition for an instability below the MHD limit is the presence of an ion temperature gradient. Analytical dispersion relations giving results in good agreement with numerical solutions are also presented. The curvature driven trapped electron modes are found to be unstable for virtually all parameters with growth rates of the order of the diamagnetic drift frequency. Studies have been made, using both a gyrokinetic ion description and the fully toroidal ion model. Both analytical and numerical results are presented and are found to be in good agreement. The toroidally induced ion temperature gradients modes are found to have a behavior similar to that of the curvature driven trapped electron modes and can in the electrostatic limit be described by a simple quadratic dispersion equation. (author)
Random paths with curvature dependent action
International Nuclear Information System (INIS)
Ambjoern, J.; Durhuus, B.
1986-11-01
We study discretized random paths with a curvature dependent action. The scaling limits of the corresponding statistical mechanical models can be constructed explicitly and are either usual Brownian motion or a theory where the correlations of tangents are nonzero and described by diffusion on the unit sphere. In the latter case the two point function has an anomalous dimension η = 1. (orig.)
Trajectories of martian habitability.
Cockell, Charles S
2014-02-01
Beginning from two plausible starting points-an uninhabited or inhabited Mars-this paper discusses the possible trajectories of martian habitability over time. On an uninhabited Mars, the trajectories follow paths determined by the abundance of uninhabitable environments and uninhabited habitats. On an inhabited Mars, the addition of a third environment type, inhabited habitats, results in other trajectories, including ones where the planet remains inhabited today or others where planetary-scale life extinction occurs. By identifying different trajectories of habitability, corresponding hypotheses can be described that allow for the various trajectories to be disentangled and ultimately a determination of which trajectory Mars has taken and the changing relative abundance of its constituent environments.
Lunar and interplanetary trajectories
Biesbroek, Robin
2016-01-01
This book provides readers with a clear description of the types of lunar and interplanetary trajectories, and how they influence satellite-system design. The description follows an engineering rather than a mathematical approach and includes many examples of lunar trajectories, based on real missions. It helps readers gain an understanding of the driving subsystems of interplanetary and lunar satellites. The tables and graphs showing features of trajectories make the book easy to understand. .
Leal-Junior, Arnaldo G.; Frizera, Anselmo; José Pontes, Maria
2018-03-01
Polymer optical fibers (POFs) are suitable for applications such as curvature sensors, strain, temperature, liquid level, among others. However, for enhancing sensitivity, many polymer optical fiber curvature sensors based on intensity variation require a lateral section. Lateral section length, depth, and surface roughness have great influence on the sensor sensitivity, hysteresis, and linearity. Moreover, the sensor curvature radius increase the stress on the fiber, which leads on variation of the sensor behavior. This paper presents the analysis relating the curvature radius and lateral section length, depth and surface roughness with the sensor sensitivity, hysteresis and linearity for a POF curvature sensor. Results show a strong correlation between the decision parameters behavior and the performance for sensor applications based on intensity variation. Furthermore, there is a trade-off among the sensitive zone length, depth, surface roughness, and curvature radius with the sensor desired performance parameters, which are minimum hysteresis, maximum sensitivity, and maximum linearity. The optimization of these parameters is applied to obtain a sensor with sensitivity of 20.9 mV/°, linearity of 0.9992 and hysteresis below 1%, which represent a better performance of the sensor when compared with the sensor without the optimization.
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich; Pottmann, Helmut; Wallner, Johannes
2009-01-01
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable
From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos
Kuznetsov, Sergey P.
2016-12-01
Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Higher curvature self-interaction corrections to Hawking radiation
Fairoos, C.; Sarkar, Sudipta; Yogendran, K. P.
2017-07-01
The purely thermal nature of Hawking radiation from evaporating black holes leads to the information loss paradox. A possible route to its resolution could be if (enough) correlations are shown to be present in the radiation emitted from evaporating black holes. A reanalysis of Hawking's derivation including the effects of self-interactions in general relativity shows that the emitted radiation does deviate from pure thermality; however no correlations exist between successively emitted Hawking quanta. We extend the calculations to Einstein-Gauss-Bonnet gravity and investigate if higher curvature corrections to the action lead to some new correlations in the Hawking spectra. The effective trajectory of a massless shell is determined by solving the constraint equations and the semiclassical tunneling probability is calculated. As in the case of general relativity, the radiation is no longer thermal and there is no correlation between successive emissions. The absence of any extra correlations in the emitted radiations even in Gauss-Bonnet gravity suggests that the resolution of the paradox is beyond the scope of semiclassical gravity.
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
Translating solitons to symplectic and Lagrangian mean curvature flows
International Nuclear Information System (INIS)
Han Xiaoli; Li Jiayu
2007-05-01
In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study symplectic translating solitons. We prove that there is no translating solitons with vertical bar α vertical bar ≤ α 0 to the symplectic mean curvature flow or to the almost calibrated Lagrangian mean curvature flow for some α 0 . (author)
Integration of length and curvature in haptic perception
Panday, V.; Bergmann Tiest, W.M.; Kappers, A.M.L.
2014-01-01
We investigated if and how length and curvature information are integrated when an object is explored in one hand. Subjects were asked to explore four types of objects between thumb and index finger. Objects differed in either length, curvature, both length and curvature correlated as in a circle,
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
On a curvature-statistics theorem
International Nuclear Information System (INIS)
Calixto, M; Aldaya, V
2008-01-01
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
Cosmological signatures of anisotropic spatial curvature
International Nuclear Information System (INIS)
Pereira, Thiago S.; Marugán, Guillermo A. Mena; Carneiro, Saulo
2015-01-01
If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature
Cosmological signatures of anisotropic spatial curvature
Energy Technology Data Exchange (ETDEWEB)
Pereira, Thiago S. [Departamento de Física, Universidade Estadual de Londrina, 86057-970, Londrina – PR (Brazil); Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006, Madrid (Spain); Carneiro, Saulo, E-mail: tspereira@uel.br, E-mail: mena@iem.cfmac.csic.es, E-mail: saulo.carneiro@pq.cnpq.br [Instituto de Física, Universidade Federal da Bahia, 40210-340, Salvador – BA (Brazil)
2015-07-01
If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature.
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Harmonic curvatures and generalized helices in En
International Nuclear Information System (INIS)
Camci, Cetin; Ilarslan, Kazim; Kula, Levent; Hacisalihoglu, H. Hilmi
2009-01-01
In n-dimensional Euclidean space E n , harmonic curvatures of a non-degenerate curve defined by Ozdamar and Hacisalihoglu [Ozdamar E, Hacisalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A1 1975;24:15-23]. In this paper, we give some characterizations for a non-degenerate curve α to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve α in n-dimensional Euclidean space E n and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve α is a generalized helix in the sense of Hayden.
Gravitational curvature an introduction to Einstein's theory
Frankel, Theodore Thomas
1979-01-01
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence, replacing the often-tedious analytical computations with geometric arguments. Clearly presented and physically motivated derivations express the deflection of light, Schwarzchild's exterior and interior solutions, and the Oppenheimer-Volkoff equations. A perfect choice for advanced students of mathematics, this volume will also appeal to mathematicians interested in physics. It stresses
Curvature controlled wetting in two dimensions
DEFF Research Database (Denmark)
Gil, Tamir; Mikheev, Lev V.
1995-01-01
. As the radius of the substrate r0→∞, the leading effect of the curvature is adding the Laplace pressure ΠL∝r0-1 to the pressure balance in the film. At temperatures and pressures under which the wetting is complete in planar geometry, Laplace pressure suppresses divergence of the mean thickness of the wetting...... term reduces the thickness by the amount proportional to r0-1/3...
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
Inflationary scenario from higher curvature warped spacetime
International Nuclear Information System (INIS)
Banerjee, Narayan; Paul, Tanmoy
2017-01-01
We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR 2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n s ) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)
Inflationary scenario from higher curvature warped spacetime
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2017-10-15
We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR{sup 2} in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n{sub s}) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)
Codimension two branes and distributional curvature
International Nuclear Information System (INIS)
Traschen, Jennie
2009-01-01
In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. In contrast, there are obstacles to concentrating sources on surfaces that have a higher codimension, for example, a string in a spacetime with a dimension greater than or equal to four. Here it is shown that, by giving up some of the generality of the codimension one case, curvature can be concentrated on submanifolds that have codimension two. A class of metrics is identified such that (1) the scalar curvature and Ricci densities exist as distributions with support on a codimension two submanifold, and (2) using the Einstein equation, the distributional curvature corresponds to a concentrated stress-energy with equation of state p = -ρ, where p is the isotropic pressure tangent to the submanifold, and ρ is the energy density. This is the appropriate stress-energy to describe a self-gravitating brane that is governed by an area action, or a braneworld deSitter cosmology. The possibility of having a different equation of state arise from a wider class of metrics is discussed.
Distributed mean curvature on a discrete manifold for Regge calculus
International Nuclear Information System (INIS)
Conboye, Rory; Miller, Warner A; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Miller, Warner A.; Ray, Shannon
2015-09-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich
2009-12-18
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Integration of length and curvature in haptic perception.
Panday, Virjanand; Tiest, Wouter M Bergmann; Kappers, Astrid M L
2014-01-24
We investigated if and how length and curvature information are integrated when an object is explored in one hand. Subjects were asked to explore four types of objects between thumb and index finger. Objects differed in either length, curvature, both length and curvature correlated as in a circle, or anti-correlated. We found that when both length and curvature are present, performance is significantly better than when only one of the two cues is available. Therefore, we conclude that there is integration of length and curvature. Moreover, if the two cues are correlated in a circular cross-section instead of in an anti-correlated way, performance is better than predicted by a combination of two independent cues. We conclude that integration of curvature and length is highly efficient when the cues in the object are combined as in a circle, which is the most common combination of curvature and length in daily life.
Foster, Cyrus; Jaroux, Belgacem A.
2012-01-01
The Trajectory Browser is a web-based tool developed at the NASA Ames Research Center to be used for the preliminary assessment of trajectories to small-bodies and planets and for providing relevant launch date, time-of-flight and V requirements. The site hosts a database of transfer trajectories from Earth to asteroids and planets for various types of missions such as rendezvous, sample return or flybys. A search engine allows the user to find trajectories meeting desired constraints on the launch window, mission duration and delta V capability, while a trajectory viewer tool allows the visualization of the heliocentric trajectory and the detailed mission itinerary. The anticipated user base of this tool consists primarily of scientists and engineers designing interplanetary missions in the context of pre-phase A studies, particularly for performing accessibility surveys to large populations of small-bodies. The educational potential of the website is also recognized for academia and the public with regards to trajectory design, a field that has generally been poorly understood by the public. The website is currently hosted on NASA-internal URL http://trajbrowser.arc.nasa.gov/ with plans for a public release as soon as development is complete.
Energy Technology Data Exchange (ETDEWEB)
Allen, P. W.; Jessup, E. A.; White, R. E. [Air Resources Field Research Office, Las Vegas, Nevada (United States)
1967-07-01
A single air molecule can have a trajectory that can be described with a line, but most meteorologists use single lines to represent the trajectories of air parcels. A single line trajectory has the disadvantage that it is a categorical description of position. Like categorized forecasts it provides no qualification, and no provision for dispersion in case the parcel contains two or more molecules which may take vastly different paths. Diffusion technology has amply demonstrated that an initial aerosol cloud or volume of gas in the atmosphere not only grows larger, but sometimes divides into puffs, each having a different path or swath. Yet, the average meteorologist, faced with the problem of predicting the future motion of a cloud, usually falls back on the line trajectory approach with the explanation that he had no better tool for long range application. In his more rational moments, he may use some arbitrary device to spread his cloud with distance. One such technique has been to separate the trajectory into two or more trajectories, spaced about the endpoint of the original trajectory after a short period of travel, repeating this every so often like a chain reaction. This has the obvious disadvantage of involving a large amount of labor without much assurance of improved accuracy. Another approach is to draw a circle about the trajectory endpoint, to represent either diffusion or error. The problem then is to know what radius to give the circle and also whether to call it diffusion or error. Meteorologists at the Nevada Test Site (NTS) are asked frequently to provide advice which involves trajectory technology, such as prediction of an aerosol cloud path, reconstruction of the motion of a volume of air, indication of the dilution, and the possible trajectory prediction error over great distances. Therefore, we set out, nearly three years ago, to provide some statistical knowledge about the status of our trajectory technology. This report contains some of the
Zero curvature-surface driven small objects
Dou, Xiaoxiao; Li, Shanpeng; Liu, Jianlin
2017-08-01
In this study, we investigate the spontaneous migration of small objects driven by surface tension on a catenoid, formed by a layer of soap constrained by two rings. Although the average curvature of the catenoid is zero at each point, the small objects always migrate to the position near the ring. The force and energy analyses have been performed to uncover the mechanism, and it is found that the small objects distort the local shape of the liquid film, thus making the whole system energetically favorable. These findings provide some inspiration to design microfluidics, aquatic robotics, and miniature boats.
Spacetime Curvature and Higgs Stability after Inflation.
Herranen, M; Markkanen, T; Nurmi, S; Rajantie, A
2015-12-11
We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the standard model only through the nonminimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalization of the standard model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ≳1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.
Constraining inverse-curvature gravity with supernovae.
Mena, Olga; Santiago, José; Weller, Jochen
2006-02-03
We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07baryonic matter component.
Amplification of curvature perturbations in cyclic cosmology
International Nuclear Information System (INIS)
Zhang Jun; Liu Zhiguo; Piao Yunsong
2010-01-01
We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Curvature, zero modes and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de AstrofIsica de AndalucIa, Apartado Postal 3004, 18080 Granada (Spain)
2006-08-18
We explore an intriguing connection between the Fermi-Dirac and Bose-Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem. (letter to the editor)
Differential geometry bundles, connections, metrics and curvature
Taubes, Clifford Henry
2011-01-01
Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the
Curvature and temperature of complex networks.
Krioukov, Dmitri; Papadopoulos, Fragkiskos; Vahdat, Amin; Boguñá, Marián
2009-09-01
We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.
Directory of Open Access Journals (Sweden)
Natalie J. Forde
2017-04-01
Full Text Available Magnetic resonance imaging (MRI studies have highlighted subcortical, cortical, and structural connectivity abnormalities associated with attention-deficit/hyperactivity disorder (ADHD. Gyrification investigations of the cortex have been inconsistent and largely negative, potentially due to a lack of sensitivity of the previously used morphological parameters. The innovative approach of applying intrinsic curvature analysis, which is predictive of gyrification pattern, to the cortical surface applied herein allowed us greater sensitivity to determine whether the structural connectivity abnormalities thus far identified at a centimeter scale also occur at a millimeter scale within the cortical surface. This could help identify neurodevelopmental processes that contribute to ADHD. Structural MRI datasets from the NeuroIMAGE project were used [n = 306 ADHD, n = 164 controls, and n = 148 healthy siblings of individuals with ADHD (age in years, mean(sd; 17.2 (3.4, 16.8 (3.2, and 17.7 (3.8, respectively]. Reconstructions of the cortical surfaces were computed with FreeSurfer. Intrinsic curvature (taken as a marker of millimeter-scale surface connectivity and local gyrification index were calculated for each point on the surface (vertex with Caret and FreeSurfer, respectively. Intrinsic curvature skew and mean local gyrification index were extracted per region; frontal, parietal, temporal, occipital, cingulate, and insula. A generalized additive model was used to compare the trajectory of these measures between groups over age, with sex, scanner site, total surface area of hemisphere, and familiality accounted for. After correcting for sex, scanner site, and total surface area no group differences were found in the developmental trajectory of intrinsic curvature or local gyrification index. Despite the increased sensitivity of intrinsic curvature, compared to gyrification measures, to subtle morphological abnormalities of the cortical surface we found
Automated Cooperative Trajectories
Hanson, Curt; Pahle, Joseph; Brown, Nelson
2015-01-01
This presentation is an overview of the Automated Cooperative Trajectories project. An introduction to the phenomena of wake vortices is given, along with a summary of past research into the possibility of extracting energy from the wake by flying close parallel trajectories. Challenges and barriers to adoption of civilian automatic wake surfing technology are identified. A hardware-in-the-loop simulation is described that will support future research. Finally, a roadmap for future research and technology transition is proposed.
Branching trajectory continual integral
International Nuclear Information System (INIS)
Maslov, V.P.; Chebotarev, A.M.
1980-01-01
Heuristic definition of the Feynman continual integral over branching trajectories is suggested which makes it possible to obtain in the closed form the solution of the Cauchy problem for the model Hartree equation. A number of properties of the solution is derived from an integral representation. In particular, the quasiclassical asymptotics, exact solution in the gaussian case and perturbation theory series are described. The existence theorem for the simpliest continual integral over branching trajectories is proved [ru
Polarized curvature radiation in pulsar magnetosphere
Wang, P. F.; Wang, C.; Han, J. L.
2014-07-01
The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and corotating with the pulsar magnetosphere. Within the 1/γ emission cone, the waves can be divided into two natural wave-mode components, the ordinary (O) mode and the extraordinary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the corotation of relativistic particles with magnetosphere is not considered, the intensity distributions for the X-mode and O-mode components are quite similar within the pulsar beam, which causes serious depolarization. However, if the corotation of relativistic particles is considered, the intensity distributions of the two modes are very different, and the net polarization of outcoming emission should be significant. Our numerical results are compared with observations, and can naturally explain the orthogonal polarization modes of some pulsars. Strong linear polarizations of some parts of pulsar profile can be reproduced by curvature radiation and subsequent propagation effect.
Emergent gravity in spaces of constant curvature
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Orlando; Haddad, Matthew [Department of Physics, University of Miami,1320 Campo Sano Ave, Coral Gables, FL 33146 (United States)
2017-03-07
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.
Lecture notes on mean curvature flow, barriers and singular perturbations
Bellettini, Giovanni
2013-01-01
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
The curvature calculation mechanism based on simple cell model.
Yu, Haiyang; Fan, Xingyu; Song, Aiqi
2017-07-20
A conclusion has not yet been reached on how exactly the human visual system detects curvature. This paper demonstrates how orientation-selective simple cells can be used to construct curvature-detecting neural units. Through fixed arrangements, multiple plurality cells were constructed to simulate curvature cells with a proportional output to their curvature. In addition, this paper offers a solution to the problem of narrow detection range under fixed resolution by selecting an output value under multiple resolution. Curvature cells can be treated as concrete models of an end-stopped mechanism, and they can be used to further understand "curvature-selective" characteristics and to explain basic psychophysical findings and perceptual phenomena in current studies.
Statistical mechanics of paths with curvature dependent action
International Nuclear Information System (INIS)
Ambjoern, J.; Durhuus, B.; Jonsson, T.
1987-01-01
We analyze the scaling limit of discretized random paths with curvature dependent action. For finite values of the curvature coupling constant the theory belongs to the universality class of simple random walk. It is possible to define a non-trivial scaling limit if the curvature coupling tends to infinity. We compute exactly the two point function in this limit and discuss the relevance of our results for random surfaces and string theories. (orig.)
Evolution of the curvature perturbations during warm inflation
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
This paper considers warm inflation as an interesting application of multi-field inflation. Delta-N formalism is used for the calculation of the evolution of the curvature perturbations during warm inflation. Although the perturbations considered in this paper are decaying after the horizon exit, the corrections to the curvature perturbations sourced by these perturbations can remain and dominate the curvature perturbations at large scales. In addition to the typical evolution of the curvature perturbations, inhomogeneous diffusion rate is considered for warm inflation, which may lead to significant non-Gaussianity of the spectrum
3D face recognition with asymptotic cones based principal curvatures
Tang, Yinhang; Sun, Xiang; Huang, Di; Morvan, Jean-Marie; Wang, Yunhong; Chen, Liming
2015-01-01
The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.
Robust estimation of adaptive tensors of curvature by tensor voting.
Tong, Wai-Shun; Tang, Chi-Keung
2005-03-01
Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.
3D face recognition with asymptotic cones based principal curvatures
Tang, Yinhang
2015-05-01
The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.
Cholera toxin B subunit induces local curvature on lipid bilayers
DEFF Research Database (Denmark)
Pezeshkian, Weria; Nåbo, Lina J.; Ipsen, John H.
2017-01-01
B induces a local membrane curvature that is essential for its clathrin-independent uptake. Using all-atom molecular dynamics, we show that CTxB induces local curvature, with the radius of curvature around 36 nm. The main feature of the CTxB molecular structure that causes membrane bending is the protruding...... alpha helices in the middle of the protein. Our study points to a generic protein design principle for generating local membrane curvature through specific binding to their lipid anchors....
Hair curvature: a natural dialectic and review.
Nissimov, Joseph N; Das Chaudhuri, Asit Baran
2014-08-01
Although hair forms (straight, curly, wavy, etc.) are present in apparently infinite variations, each fibre can be reduced to a finite sequence of tandem segments of just three types: straight, bent/curly, or twisted. Hair forms can thus be regarded as resulting from genetic pathways that induce, reverse or modulate these basic curvature modes. However, physical interconversions between twists and curls demonstrate that strict one-to-one correspondences between them and their genetic causes do not exist. Current hair-curvature theories do not distinguish between bending and twisting mechanisms. We here introduce a multiple papillary centres (MPC) model which is particularly suitable to explain twisting. The model combines previously known features of hair cross-sectional morphology with partially/completely separated dermal papillae within single follicles, and requires such papillae to induce differential growth rates of hair cortical material in their immediate neighbourhoods. The MPC model can further help to explain other, poorly understood, aspects of hair growth and morphology. Separate bending and twisting mechanisms would be preferentially affected at the major or minor ellipsoidal sides of fibres, respectively, and together they exhaust the possibilities for influencing hair-form phenotypes. As such they suggest dialectic for hair-curvature development. We define a natural-dialectic (ND) which could take advantage of speculative aspects of dialectic, but would verify its input data and results by experimental methods. We use this as a top-down approach to first define routes by which hair bending or twisting may be brought about and then review evidence in support of such routes. In particular we consider the wingless (Wnt) and mammalian target of rapamycin (mTOR) pathways as paradigm pathways for molecular hair bending and twisting mechanisms, respectively. In addition to the Wnt canonical pathway, the Wnt/Ca(2+) and planar cell polarity (PCP) pathways
International Nuclear Information System (INIS)
Khaneja, Navin; Brockett, Roger; Glaser, Steffen J.
2002-01-01
Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin decoupling to produce desired effective Hamiltonians. In this paper, we demonstrate that significant time can be saved in producing an effective Hamiltonian if spin decoupling is avoided. We provide time-optimal pulse sequences for producing an important class of effective Hamiltonians in three-spin networks. These effective Hamiltonians are useful for coherence-transfer experiments in three-spin systems and implementation of indirect swap and Λ 2 (U) gates in the context of NMR quantum computing. It is shown that computing these time-optimal pulses can be reduced to geometric problems that involve computing sub-Riemannian geodesics. Using these geometric ideas, explicit expressions for the minimum time required for producing these effective Hamiltonians, transfer of coherence, and implementation of indirect swap gates, in a three-spin network are derived (Theorems 1 and 2). It is demonstrated that geometric control techniques provide a systematic way of finding time-optimal pulse sequences for transferring coherence and synthesizing unitary transformations in quantum networks, with considerable time savings (e.g., 42.3% for constructing indirect swap gates)
Hawking temperature of constant curvature black holes
International Nuclear Information System (INIS)
Cai Ronggen; Myung, Yun Soo
2011-01-01
The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of M D-1 xS 1 , where D is the spacetime dimension and M D-1 stands for a conformal Minkowski spacetime in D-1 dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.
Differential geometry connections, curvature, and characteristic classes
Tu, Loring W
2017-01-01
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establ...
Natural curvature for manifest T-duality
International Nuclear Information System (INIS)
Poláček, Martin; Siegel, Warren
2014-01-01
We reformulate the manifestly T-dual description of the massless sector of the closed bosonic string, directly from the geometry associated with the (left and right) affine Lie algebra of the coset space Poincaré/Lorentz. This construction initially doubles not only the (spacetime) coordinates for translations but also those for Lorentz transformations (and their “dual”). As a result, the Lorentz connection couples directly to the string (as does the vielbein), rather than being introduced ad hoc to the covariant derivative as previously. This not only reproduces the old definition of T-dual torsion, but automatically gives a general, covariant definition of T-dual curvature (but still with some undetermined connections)
Nonminimal coupling of perfect fluids to curvature
International Nuclear Information System (INIS)
Bertolami, Orfeu; Lobo, Francisco S. N.; Paramos, Jorge
2008-01-01
In this work, we consider different forms of relativistic perfect fluid Lagrangian densities that yield the same gravitational field equations in general relativity (GR). A particularly intriguing example is the case with couplings of the form [1+f 2 (R)]L m , where R is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density L m =p, where p is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for L m do not imply the vanishing of the extra force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.
Topological photonic crystals with zero Berry curvature
Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori
2018-02-01
Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.
A Field Theory with Curvature and Anticurvature
Directory of Open Access Journals (Sweden)
M. I. Wanas
2014-01-01
Full Text Available The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.
Locus of the apices of projectile trajectories under constant drag
Hernández-Saldaña, H.
2017-11-01
Using the hodograph method, we present an analytical solution for projectile coplanar motion under constant drag, parametrised by the velocity angle. We find the locus formed by the apices of the projectile trajectories, and discuss its implementation for the motion of a particle on an inclined plane in presence of Coulomb friction. The range and time of flight are obtained numerically, and we find that the optimal launching angle is smaller than in the drag-free case. This is a good example of a problem with constant dissipation of energy that includes curvature; it is appropriate for intermediate courses of mechanics.
Escape trajectories of solar sails and general relativity
Energy Technology Data Exchange (ETDEWEB)
Kezerashvili, Roman Ya. [Physics Department, New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Vazquez-Poritz, Justin F., E-mail: jvazquez-poritz@citytech.cuny.ed [Physics Department, New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States)
2009-11-16
General relativity can have a significant impact on the long-range escape trajectories of solar sails deployed near the sun. For example, spacetime curvature in the vicinity of the sun can cause a solar sail traveling from about 4 solar radii to 2550 AU to be deflected by on the order of a million kilometers, and should therefore be taken into account at the beginning of the mission. There are a number of smaller general relativistic effects, such as frame dragging due to the slow rotation of the sun which can cause a deflection of more than one thousand kilometers.
Trajectory Calculator for Finite-Radius Cutter on a Lathe
Savchenkov, Anatoliy; Strekalov, Dmitry; Yu, Nan
2009-01-01
A computer program calculates the two-dimensional trajectory (radial vs. axial position) of a finite-radius-of-curvature cutting tool on a lathe so as to cut a workpiece to a piecewise-continuous, analytically defined surface of revolution. (In the original intended application, the tool is a diamond cutter, and the workpiece is made of a crystalline material and is to be formed into an optical resonator disk.) The program also calculates an optimum cutting speed as F/L, where F is a material-dependent empirical factor and L is the effective instantaneous length of the cutting edge.
Escape trajectories of solar sails and general relativity
International Nuclear Information System (INIS)
Kezerashvili, Roman Ya.; Vazquez-Poritz, Justin F.
2009-01-01
General relativity can have a significant impact on the long-range escape trajectories of solar sails deployed near the sun. For example, spacetime curvature in the vicinity of the sun can cause a solar sail traveling from about 4 solar radii to 2550 AU to be deflected by on the order of a million kilometers, and should therefore be taken into account at the beginning of the mission. There are a number of smaller general relativistic effects, such as frame dragging due to the slow rotation of the sun which can cause a deflection of more than one thousand kilometers.
On harmonic curvatures of a Frenet curve in Lorentzian space
International Nuclear Information System (INIS)
Kuelahci, Mihriban; Bektas, Mehmet; Erguet, Mahmut
2009-01-01
In this paper, we consider curves of AW(k)-type, 1 ≤ k ≤ 3, in Lorentzian space. We give curvature conditions of these kind of curves. Furthermore, we study harmonic curvatures of curves of AW(k)-type. We investigate that under what conditions AW(k)-type curves are helix. Some related theorems and corollaries are also proved.
The scalar curvature problem on the four dimensional half sphere
Ben-Ayed, M; El-Mehdi, K
2003-01-01
In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature for some metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.
Statistical mechanics of surfaces with curvature dependent action
International Nuclear Information System (INIS)
Jonsson, T.
1987-01-01
We review recent results about discretized random surfaces whose action (energy) depends on the extrinsic curvature. The surface tension scales to zero at an appropriate critical point if the coupling constant of the curvature term is taken to infinity. At this critical point one expects to be able to construct a continuum theory of smooth surfaces. (orig.)
Curvature of random walks and random polygons in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2013-01-01
The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to π. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. (paper)
Curvature collineations for the field of gravitational waves
International Nuclear Information System (INIS)
Singh, K.P.; Singh, Gulab
1981-01-01
It has been shown that the space-times formed from a plane-fronted gravity wave and from a plane sandwich wave with constant polarisation admit proper curvature collineation in general. The curvature collineation vectors have been determined explicitly. (author)
Interpreting Early Career Trajectories
Barnatt, Joan; Gahlsdorf Terrell, Dianna; D'Souza, Lisa Andries; Jong, Cindy; Cochran-Smith, Marilyn; Viesca, Kara Mitchell; Gleeson, Ann Marie; McQuillan, Patrick; Shakman, Karen
2017-01-01
Career decisions of four teachers are explored through the concept of figured worlds in this qualitative, longitudinal case study. Participants were purposefully chosen for similarity at entry, with a range of career trajectories over time. Teacher career paths included remaining in one school, repeated changes in schools, attrition after…
Trajectory structures and transport
International Nuclear Information System (INIS)
Vlad, Madalina; Spineanu, Florin
2004-01-01
The special problem of transport in two-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport
Robust modal curvature features for identifying multiple damage in beams
Ostachowicz, Wiesław; Xu, Wei; Bai, Runbo; Radzieński, Maciej; Cao, Maosen
2014-03-01
Curvature mode shape is an effective feature for damage detection in beams. However, it is susceptible to measurement noise, easily impairing its advantage of sensitivity to damage. To deal with this deficiency, this study formulates an improved curvature mode shape for multiple damage detection in beams based on integrating a wavelet transform (WT) and a Teager energy operator (TEO). The improved curvature mode shape, termed the WT - TEO curvature mode shape, has inherent capabilities of immunity to noise and sensitivity to damage. The proposed method is experimentally validated by identifying multiple cracks in cantilever steel beams with the mode shapes acquired using a scanning laser vibrometer. The results demonstrate that the improved curvature mode shape can identify multiple damage accurately and reliably, and it is fairly robust to measurement noise.
Directory of Open Access Journals (Sweden)
Maike Buchin
2015-03-01
Full Text Available The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity inter-distance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial,algorithmic, and experimental results.
INVESTIGATION OF CURVES SET BY CUBIC DISTRIBUTION OF CURVATURE
Directory of Open Access Journals (Sweden)
S. A. Ustenko
2014-03-01
Full Text Available Purpose. Further development of the geometric modeling of curvelinear contours of different objects based on the specified cubic curvature distribution and setpoints of curvature in the boundary points. Methodology. We investigate the flat section of the curvilinear contour generating under condition that cubic curvature distribution is set. Curve begins and ends at the given points, where angles of tangent slope and curvature are also determined. It was obtained the curvature equation of this curve, depending on the section length and coefficient c of cubic curvature distribution. The analysis of obtained equation was carried out. As well as, it was investigated the conditions, in which the inflection points of the curve are appearing. One should find such an interval of parameter change (depending on the input data and the section length, in order to place the inflection point of the curvature graph outside the curve section borders. It was determined the dependence of tangent slope of angle to the curve at its arbitrary point, as well as it was given the recommendations to solve a system of integral equations that allow finding the length of the curve section and the coefficient c of curvature cubic distribution. Findings. As the result of curves research, it is found that the criterion for their selection one can consider the absence of inflection points of the curvature on the observed section. Influence analysis of the parameter c on the graph of tangent slope angle to the curve showed that regardless of its value, it is provided the same rate of angle increase of tangent slope to the curve. Originality. It is improved the approach to geometric modeling of curves based on cubic curvature distribution with its given values at the boundary points by eliminating the inflection points from the observed section of curvilinear contours. Practical value. Curves obtained using the proposed method can be used for geometric modeling of curvilinear
Magnetic vortices in nanocaps induced by curvature
Abdelgawad, Ahmed M.; Nambiar, Nikhil; Bapna, Mukund; Chen, Hao; Majetich, Sara A.
2018-05-01
Magnetic nanoparticles with room temperature remanent magnetic vortices stabilized by their curvature are very intriguing due to their potential use in biomedicine. In the present study, we investigate room temperature magnetic chirality in 100 nm diameter permalloy spherical caps with 10 nm and 30 nm thicknesses. Micromagnetic OOMMF simulations predict the equilibrium spin structure for these caps to form a vortex state. We fabricate the permalloy caps by sputtering permalloy on both close-packed and sparse arrays of polystyrene nanoparticles. Magnetic force microscopy scans show a clear signature of a vortex state in close-packed caps of both 10 nm and 30 nm thicknesses. Alternating gradient magnetometry measurements of the caps are consistent with a remnant vortex state in 30 nm thick caps and a transition to an onion state followed by a vortex state in 10 nm thick caps. Out-of-plane measurements supported by micromagnetic simulations shows that an out-of-plane field can stabilize a vortex state down to a diameter of 15 nm.
Semantic Enrichment of GPS Trajectories
de Graaff, V.; van Keulen, Maurice; de By, R.A.
2012-01-01
Semantic annotation of GPS trajectories helps us to recognize the interests of the creator of the GPS trajectories. Automating this trajectory annotation circumvents the requirement of additional user input. To annotate the GPS traces automatically, two types of automated input are required: 1) a
Face recognition based on depth maps and surface curvature
Gordon, Gaile G.
1991-09-01
This paper explores the representation of the human face by features based on the curvature of the face surface. Curature captures many features necessary to accurately describe the face, such as the shape of the forehead, jawline, and cheeks, which are not easily detected from standard intensity images. Moreover, the value of curvature at a point on the surface is also viewpoint invariant. Until recently range data of high enough resolution and accuracy to perform useful curvature calculations on the scale of the human face had been unavailable. Although several researchers have worked on the problem of interpreting range data from curved (although usually highly geometrically structured) surfaces, the main approaches have centered on segmentation by signs of mean and Gaussian curvature which have not proved sufficient in themselves for the case of the human face. This paper details the calculation of principal curvature for a particular data set, the calculation of general surface descriptors based on curvature, and the calculation of face specific descriptors based both on curvature features and a priori knowledge about the structure of the face. These face specific descriptors can be incorporated into many different recognition strategies. A system that implements one such strategy, depth template comparison, giving recognition rates between 80% and 90% is described.
Dynamic curvature sensing employing ionic-polymer–metal composite sensors
International Nuclear Information System (INIS)
Bahramzadeh, Yousef; Shahinpoor, Mohsen
2011-01-01
A dynamic curvature sensor is presented based on ionic-polymer–metal composite (IPMC) for curvature monitoring of deployable/inflatable dynamic space structures. Monitoring the curvature variation is of high importance in various engineering structures including shape monitoring of deployable/inflatable space structures in which the structural boundaries undergo a dynamic deployment process. The high sensitivity of IPMCs to the applied deformations as well as its flexibility make IPMCs a promising candidate for sensing of dynamic curvature changes. Herein, we explore the dynamic response of an IPMC sensor strip with respect to controlled curvature deformations subjected to different forms of input functions. Using a specially designed experimental setup, the voltage recovery effect, phase delay, and rate dependency of the output voltage signal of an IPMC curvature sensor are analyzed. Experimental results show that the IPMC sensor maintains the linearity, sensitivity, and repeatability required for curvature sensing. Besides, in order to describe the dynamic phenomena such as the rate dependency of the IPMC sensor, a chemo-electro-mechanical model based on the Poisson–Nernst–Planck (PNP) equation for the kinetics of ion diffusion is presented. By solving the governing partial differential equations the frequency response of the IPMC sensor is derived. The physical model is able to describe the dynamic properties of the IPMC sensor and the dependency of the signal on rate of excitations
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.
1979-11-01
The SLAC Electron Trajectory Program is described and instructions and examples for users are given. The program is specifically written to compute trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields. Starting options include Child's Law conditions on cathodes of various shapes. Either rectangular or cylindrically symmetric geometry may be used. Magntic fields may be specified using arbitrary configurations of coils, or the output of a magnet program such as Poisson or by an externally calculated array of the axial fields. The program is available in IBM FORTRAN but can be easily converted for use on other brands of hardware. The program is intended to be used with a plotter whose interface the user must provide
Energy Technology Data Exchange (ETDEWEB)
Herrmannsfeldt, W.B.
1979-11-01
The SLAC Electron Trajectory Program is described and instructions and examples for users are given. The program is specifically written to compute trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields. Starting options include Child's Law conditions on cathodes of various shapes. Either rectangular or cylindrically symmetric geometry may be used. Magntic fields may be specified using arbitrary configurations of coils, or the output of a magnet program such as Poisson or by an externally calculated array of the axial fields. The program is available in IBM FORTRAN but can be easily converted for use on other brands of hardware. The program is intended to be used with a plotter whose interface the user must provide.
DEFF Research Database (Denmark)
Dalgas, Karina Märcher
2015-01-01
pair-sending families in the Philippines, this dissertation examines the long-term trajectories of these young Filipinas. It shows how the au pairs’ local and transnational family relations develop over time and greatly influence their life trajectories. A focal point of the study is how au pairs...... that Filipina au pairs see their stay abroad as an avenue of personal development and social recognition, I examine how the au pairs re-position themselves within their families at home through migration, and how they navigate between the often conflicting expectations of participation in the sociality......Since 2000, thousands of young Filipino migrants have come to Denmark as au pairs. Officially, they are there to “broaden their cultural horizons” by living temporarily with a Danish host family, but they also conduct domestic labor in exchange for food and money, which allows them to send...
National Oceanic and Atmospheric Administration, Department of Commerce — Profile curvature was calculated from the bathymetry surface for each raster cell using the ArcGIS 3D Analyst "Curvature" Tool. Profile curvature describes the rate...
National Oceanic and Atmospheric Administration, Department of Commerce — Curvature was calculated from the bathymetry surface for each raster cell using the ArcGIS 3D Analyst "Curvature" Tool. Curvature describes the rate of change of...
Influence of Coanda surface curvature on performance of bladeless fan
Li, Guoqi; Hu, Yongjun; Jin, Yingzi; Setoguchi, Toshiaki; Kim, Heuy Dong
2014-10-01
The unique Coanda surface has a great influence on the performance of bladeless fan. However, there is few studies to explain the relationship between the performance and Coanda surface curvature at present. In order to gain a qualitative understanding of effect of the curvature on the performance of bladeless fan, numerical studies are performed in this paper. Firstly, three-dimensional numerical simulation is done by Fluent software. For the purpose to obtain detailed information of the flow field around the Coanda surface, two-dimensional numerical simulation is also conducted. Five types of Coanda surfaces with different curvature are designed, and the flow behaviour and the performance of them are analyzed and compared with those of the prototype. The analysis indicates that the curvature of Coanda surface is strongly related to blowing performance, It is found that there is an optimal curvature of Coanda surfaces among the studied models. Simulation result shows that there is a special low pressure region. With increasing curvature in Y direction, several low pressure regions gradually enlarged, then begin to merge slowly, and finally form a large area of low pressure. From the analyses of streamlines and velocity angle, it is found that the magnitude of the curvature affects the flow direction and reasonable curvature can induce fluid flow close to the wall. Thus, it leads to that the curvature of the streamlines is consistent with that of Coanda surface. Meanwhile, it also causes the fluid movement towards the most suitable direction. This study will provide useful information to performance improvements of bladeless fans.
International Nuclear Information System (INIS)
Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.
2006-12-01
The differential-geometric aspects of generalized de Rham-Hodge complexes naturally related with integrable multi-dimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic classes are studied. Special differential invariants of the Chern type are constructed, their importance for the integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson type nonlinear strongly integrable differential system is considered, its Cartan type connection mapping and related Chern type differential invariants are analyzed. (author)
A new circulation type classification based upon Lagrangian air trajectories
Directory of Open Access Journals (Sweden)
Alexandre M. Ramos
2014-10-01
Full Text Available A new classification method of the large-scale circulation characteristic for a specific target area (NW Iberian Peninsula is presented, based on the analysis of 90-h backward trajectories arriving in this area calculated with the 3-D Lagrangian particle dispersion model FLEXPART. A cluster analysis is applied to separate the backward trajectories in up to five representative air streams for each day. Specific measures are then used to characterise the distinct air streams (e.g., curvature of the trajectories, cyclonic or anticyclonic flow, moisture evolution, origin and length of the trajectories. The robustness of the presented method is demonstrated in comparison with the Eulerian Lamb weather type classification.A case study of the 2003 heatwave is discussed in terms of the new Lagrangian circulation and the Lamb weather type classifications. It is shown that the new classification method adds valuable information about the pertinent meteorological conditions, which are missing in an Eulerian approach. The new method is climatologically evaluated for the five-year time period from December 1999 to November 2004. The ability of the method to capture the inter-seasonal circulation variability in the target region is shown. Furthermore, the multi-dimensional character of the classification is shortly discussed, in particular with respect to inter-seasonal differences. Finally, the relationship between the new Lagrangian classification and the precipitation in the target area is studied.
Positive spatial curvature does not falsify the landscape
Horn, B.
2017-12-01
We present a simple cosmological model where the quantum tunneling of a scalar field rearranges the energetics of the matter sector, sending a stable static ancestor vacuum with positive spatial curvature into an inating solution with positive curvature. This serves as a proof of principle that an observation of positive spatial curvature does not falsify the hypothesis that our current observer patch originated from false vacuum tunneling in a string or field theoretic landscape. This poster submission is a summary of the work, and was presented at the 3rd annual ICPPA held in Moscow from October 2 to 5, 2017, by Prof. Rostislav Konoplich on behalf of the author.
Curvature perturbation and waterfall dynamics in hybrid inflation
International Nuclear Information System (INIS)
Abolhasani, Ali Akbar; Firouzjahi, Hassan; Sasaki, Misao
2011-01-01
We investigate the parameter spaces of hybrid inflation model with special attention paid to the dynamics of waterfall field and curvature perturbations induced from its quantum fluctuations. Depending on the inflaton field value at the time of phase transition and the sharpness of the phase transition inflation can have multiple extended stages. We find that for models with mild phase transition the induced curvature perturbation from the waterfall field is too large to satisfy the COBE normalization. We investigate the model parameter space where the curvature perturbations from the waterfall quantum fluctuations vary between the results of standard hybrid inflation and the results obtained here
Curvature perturbation and waterfall dynamics in hybrid inflation
Energy Technology Data Exchange (ETDEWEB)
Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjahi, Hassan [School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Sasaki, Misao, E-mail: abolhasani@mail.ipm.ir, E-mail: firouz@mail.ipm.ir, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2011-10-01
We investigate the parameter spaces of hybrid inflation model with special attention paid to the dynamics of waterfall field and curvature perturbations induced from its quantum fluctuations. Depending on the inflaton field value at the time of phase transition and the sharpness of the phase transition inflation can have multiple extended stages. We find that for models with mild phase transition the induced curvature perturbation from the waterfall field is too large to satisfy the COBE normalization. We investigate the model parameter space where the curvature perturbations from the waterfall quantum fluctuations vary between the results of standard hybrid inflation and the results obtained here.
Geometry-specific scaling of detonation parameters from front curvature
International Nuclear Information System (INIS)
Jackson, Scott I.; Short, Mark
2011-01-01
It has previously been asserted that classical detonation curvature theory predicts that the critical diameter and the diameter-effect curve of a cylindrical high-explosive charge should scale with twice the thickness of an analogous two-dimensional explosive slab. The varied agreement of experimental results with this expectation have led some to question the ability of curvature-based concepts to predict detonation propagation in non-ideal explosives. This study addresses such claims by showing that the expected scaling relationship (hereafter referred to d = 2w) is not consistent with curvature-based Detonation Shock Dynamics (DSD) theory.
Numerical studies of transverse curvature effects on transonic flow stability
Macaraeg, M. G.; Daudpota, Q. I.
1992-01-01
A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1-1.4) and aerodynamically relevant Reynolds numbers (5000-10,000 based on displacement thickness), the maximum growth rate is found to increase with curvature - the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.
Public and private space curvature in Robertson-Walker universes.
Rindler, W.
1981-05-01
The question is asked: what space curvature would a fundamental observer in an ideal Robertson-Walker universe obtain by direct local spatial measurements, i.e., without reference to the motion pattern of the other galaxies? The answer is that he obtains the curvatureK of his “private” space generated by all the geodesics orthogonal to his world line at the moment in question, and that ˜K is related to the usual curvatureK=k/R 2 of the “public” space of galaxies byK=K+H 2/c2, whereH is Hubble's parameter.
Lane changing trajectory planning and tracking control for intelligent vehicle on curved road.
Wang, Lukun; Zhao, Xiaoying; Su, Hao; Tang, Gongyou
2016-01-01
This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.
The Locus of the apices of projectile trajectories under constant drag
Hernández-Saldaña, H.
2017-01-01
We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained numerically and we find that the optimal launching angle is smaller than in the free drag case. This is a good example of problems with constant dissipation of energy that includes curvature, and it is proper for intermediate courses of mechanics.
Higher Curvature Gravity from Entanglement in Conformal Field Theories
Haehl, Felix M.; Hijano, Eliot; Parrikar, Onkar; Rabideau, Charles
2018-05-01
By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically anti-de Sitter (AdS) spacetime computes the entanglement entropies of ball-shaped regions in a conformal field theory using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around the AdS background. (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by the Wald entropy plus a particular correction term involving extrinsic curvatures. (iii) Conformal field theory relative entropy is dual to gravitational canonical energy (also in higher curvature theories of gravity). Especially for the second point, our novel derivation of this previously known statement does not involve the Euclidean replica trick.
On the projective curvature tensor of generalized Sasakian-space ...
African Journals Online (AJOL)
space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; ...
On a class of graphs with prescribed mean curvature
International Nuclear Information System (INIS)
Duong Minh Duc; Costa Salavessa, I.M. de
1989-11-01
We study a class of quasilinear elliptic equations on the unit ball of R n and apply these results to get the existence of graphs with prescribed mean curvature on n-hyperbolic spaces. (author). 18 refs
Higher-order curvature terms and extended inflation
International Nuclear Information System (INIS)
Wang Yun
1990-01-01
We consider higher-order curvature terms in context of the Brans-Dicke theory of gravity, and investigate the effects of these terms on extended inflationary theories. We find that the higher-order curvature terms tend to speed up inflation, although the original extended-inflation solutions are stable when these terms are small. Analytical solutions are found for two extreme cases: when the higher-order curvature terms are small, and when they dominate. A conformal transformation is employed in solving the latter case, and some of the subtleties in this technique are discussed. We note that percolation is less likely to occur when the higher-order curvature terms are present. An upper bound on α is expected if we are to avoid excessive and inadequate percolation of true-vacuum bubbles
Gauge and non-gauge curvature tensor copies
International Nuclear Information System (INIS)
Srivastava, P.P.
1982-10-01
A procedure for constructing curvature tensor copies is discussed using the anholonomic geometrical framework. The corresponding geometries are compared and the notion of gauge copy is elucidated. An explicit calculation is also made. (author)
Bacterial cell curvature through mechanical control of cell growth
DEFF Research Database (Denmark)
Cabeen, M.; Charbon, Godefroid; Vollmer, W.
2009-01-01
The cytoskeleton is a key regulator of cell morphogenesis. Crescentin, a bacterial intermediate filament-like protein, is required for the curved shape of Caulobacter crescentus and localizes to the inner cell curvature. Here, we show that crescentin forms a single filamentous structure...... that collapses into a helix when detached from the cell membrane, suggesting that it is normally maintained in a stretched configuration. Crescentin causes an elongation rate gradient around the circumference of the sidewall, creating a longitudinal cell length differential and hence curvature. Such curvature...... can be produced by physical force alone when cells are grown in circular microchambers. Production of crescentin in Escherichia coli is sufficient to generate cell curvature. Our data argue for a model in which physical strain borne by the crescentin structure anisotropically alters the kinetics...
Constant scalar curvature hypersurfaces in extended Schwarzschild space-time
International Nuclear Information System (INIS)
Pareja, M. J.; Frauendiener, J.
2006-01-01
We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat
Translating Solitons of Mean Curvature Flow of Noncompact Submanifolds
International Nuclear Information System (INIS)
Li Guanghan; Tian Daping; Wu Chuanxi
2011-01-01
We prove the existence and asymptotic behavior of rotationally symmetric solitons of mean curvature flow for noncompact submanifolds in Euclidean and Minkowski spaces, which generalizes part of the corresponding results for hypersurfaces of Jian.
Curvature and elasticity of substitution: what is the link?
Czech Academy of Sciences Publication Activity Database
Matveenko, Andrei; Matveenko, V.
2014-01-01
Roč. 10, č. 2 (2014), s. 7-20 ISSN 1800-5845 Grant - others:UK(CZ) GAUK 308214 Institutional support: PRVOUK-P23 Keywords : curvature * elasticity of substitution * production function Subject RIV: AH - Economics
Cosmic censorship, persistent curvature and asymptotic causal pathology
International Nuclear Information System (INIS)
Newman, R.P.A.C.
1984-01-01
The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)
No Large Scale Curvature Perturbations during Waterfall of Hybrid Inflation
Abolhasani, Ali Akbar; Firouzjahi, Hassan
2010-01-01
In this paper the possibility of generating large scale curvature perturbations induced from the entropic perturbations during the waterfall phase transition of standard hybrid inflation model is studied. We show that whether or not appreciable amounts of large scale curvature perturbations are produced during the waterfall phase transition depend crucially on the competition between the classical and the quantum mechanical back-reactions to terminate inflation. If one considers only the clas...
Existence of conformal metrics on spheres with prescribed Paneitz curvature
International Nuclear Information System (INIS)
Ben Ayed, Mohamed; El Mehdi, Khalil
2003-07-01
In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n ≥ 5. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given function defined on the sphere, under which we prove the existence of conformal metric with prescribed Paneitz curvature. (author)
Inflation in a shear-or curvature-dominated universe
International Nuclear Information System (INIS)
Steigman, G.; Turner, M.S.
1983-01-01
We show that new inflation occurs even if the universe is shear-or (negative) curvature-dominated when the phase transition begins. In such situations the size of a causally coherent region, after inflation, is only slightly smaller (by powers, but not by exponential factors) than the usual result. The creation and evolution of density perturbations is unaffected. This result is marked contrast to 'old' inflation, where shear- or curvature-domination could quench inflation. (orig.)
Curvature-driven acceleration: a utopia or a reality?
International Nuclear Information System (INIS)
Das, Sudipta; Banerjee, Narayan; Dadhich, Naresh
2006-01-01
The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature
Curvature-driven acceleration: a utopia or a reality?
Energy Technology Data Exchange (ETDEWEB)
Das, Sudipta [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Banerjee, Narayan [Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700 032 (India); Dadhich, Naresh [Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India)
2006-06-21
The present work shows that a combination of nonlinear contributions from the Ricci curvature in Einstein field equations can drive a late time acceleration of expansion of the universe. The transit from the decelerated to the accelerated phase of expansion takes place smoothly without having to resort to a study of asymptotic behaviour. This result emphasizes the need for thorough and critical examination of models with nonlinear contribution from the curvature.
Existence of conformal metrics on spheres with prescribed Paneitz curvature
Ben-Ayed, M
2003-01-01
In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n >= 5. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given function defined on the sphere, under which we prove the existence of conformal metric with prescribed Paneitz curvature.
Curvature effects in carbon nanomaterials: Exohedral versus endohedral supercapacitors
Huang, Jingsong; Bobby,; Sumpter, Bobby G.; Meunier, Vincent; Yushin, Gleb; Portet, Cristelle; Gogotsi, Yury
2010-01-01
Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior ...
Atomic fine structure in a space of constant curvature
International Nuclear Information System (INIS)
Bessis, N.; Bessis, G.; Shamseddine, R.
1982-01-01
As a contribution to a tentative formulation of atomic physics in a curved space, the determination of atomic fine structure energies in a space of constant curvature is investigated. Starting from the Dirac equation in a curved space-time, the analogue of the Pauli equation in a general coordinate system is derived. The theoretical curvature induced shifts and splittings of the fine structure energy levels are put in evidence and examined for the particular case of the hydrogenic n=2 levels. (author)
On $L_p$ Affine Surface Area and Curvature Measures
Zhao, Yiming
2015-01-01
The relationship between $L_p$ affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of $L_p$ affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Sch\\"utt & Werner's.
Curvature reduces bending strains in the quokka femur
Directory of Open Access Journals (Sweden)
Kyle McCabe
2017-03-01
Full Text Available This study explores how curvature in the quokka femur may help to reduce bending strain during locomotion. The quokka is a small wallaby, but the curvature of the femur and the muscles active during stance phase are similar to most quadrupedal mammals. Our hypothesis is that the action of hip extensor and ankle plantarflexor muscles during stance phase place cranial bending strains that act to reduce the caudal curvature of the femur. Knee extensors and biarticular muscles that span the femur longitudinally create caudal bending strains in the caudally curved (concave caudal side bone. These opposing strains can balance each other and result in less strain on the bone. We test this idea by comparing the performance of a normally curved finite element model of the quokka femur to a digitally straightened version of the same bone. The normally curved model is indeed less strained than the straightened version. To further examine the relationship between curvature and the strains in the femoral models, we also tested an extra-curved and a reverse-curved version with the same loads. There appears to be a linear relationship between the curvature and the strains experienced by the models. These results demonstrate that longitudinal curvature in bones may be a manipulable mechanism whereby bone can induce a strain gradient to oppose strains induced by habitual loading.
Curvature recognition and force generation in phagocytosis
Directory of Open Access Journals (Sweden)
Prassler Jana
2010-12-01
Full Text Available Abstract Background The uptake of particles by actin-powered invagination of the plasma membrane is common to protozoa and to phagocytes involved in the immune response of higher organisms. The question addressed here is how a phagocyte may use geometric cues to optimize force generation for the uptake of a particle. We survey mechanisms that enable a phagocyte to remodel actin organization in response to particles of complex shape. Results Using particles that consist of two lobes separated by a neck, we found that Dictyostelium cells transmit signals concerning the curvature of a surface to the actin system underlying the plasma membrane. Force applied to a concave region can divide a particle in two, allowing engulfment of the portion first encountered. The phagosome membrane that is bent around the concave region is marked by a protein containing an inverse Bin-Amphiphysin-Rvs (I-BAR domain in combination with an Src homology (SH3 domain, similar to mammalian insulin receptor tyrosine kinase substrate p53. Regulatory proteins enable the phagocyte to switch activities within seconds in response to particle shape. Ras, an inducer of actin polymerization, is activated along the cup surface. Coronin, which limits the lifetime of actin structures, is reversibly recruited to the cup, reflecting a program of actin depolymerization. The various forms of myosin-I are candidate motor proteins for force generation in particle uptake, whereas myosin-II is engaged only in retracting a phagocytic cup after a switch to particle release. Thus, the constriction of a phagocytic cup differs from the contraction of a cleavage furrow in mitosis. Conclusions Phagocytes scan a particle surface for convex and concave regions. By modulating the spatiotemporal pattern of actin organization, they are capable of switching between different modes of interaction with a particle, either arresting at a concave region and applying force in an attempt to sever the particle
Moyal dynamics and trajectories
Braunss, G.
2010-01-01
We give first an approximation of the operator δh: f → δhf := h*planckf - f*planckh in terms of planck2n, n >= 0, where h\\equiv h(p,q), (p,q)\\in {\\mathbb R}^{2 n} , is a Hamilton function and *planck denotes the star product. The operator, which is the generator of time translations in a *planck-algebra, can be considered as a canonical extension of the Liouville operator Lh: f → Lhf := {h, f}Poisson. Using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the Hamilton-Jacobi method for classical dynamics to Moyal dynamics. The examples we have chosen are Hamiltonians with a one-dimensional quartic potential and two-dimensional radially symmetric nonrelativistic and relativistic Coulomb potentials, and the Hamiltonian for a Schwarzschild metric. We further state a conjecture concerning an extension of the Bohr-Sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories.
Repetitive Rockfall Trajectory Testing
Directory of Open Access Journals (Sweden)
Axel Volkwein
2018-03-01
Full Text Available Numerical simulations of rockfall trajectories are a standard procedure for evaluating rockfall hazards. For these simulations, corresponding software codes must be calibrated and evaluated based on field data. This study addresses methods of repeatable rockfall tests, and investigates whether it is possible to produce traceable and statistically analysable data. A testing series is described extensively covering how to conduct rockfall experiments and how certain elements of rockfall trajectories can be measured. The tests use acceleration and rotation sensors inside test blocks, a system to determine block positions over time, surveying measurements, and video recordings. All systems are evaluated regarding their usability in the field and for analyses. The highly detailed description of testing methods is the basis for sound understanding and reproducibility of the tests. This article serves as a reference for future publications and other rockfall field tests, both as a guide and as a basis for comparisons. First analyses deliver information on runout with a shadow angle ranging between 21 and 45 degrees for a slope consisting of homogeneous soft soil. A digital elevation model of the test site as well as point clouds of the used test blocks are part of this publication.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Primordial spectra from sudden turning trajectory
Noumi, Toshifumi; Yamaguchi, Masahide
2013-12-01
Effects of heavy fields on primordial spectra of curvature perturbations are discussed in inflationary models with a sudden turning trajectory. When heavy fields are excited after the sudden turn and oscillate around the bottom of the potential, the following two effects are generically induced: deformation of the inflationary background spacetime and conversion interactions between adiabatic and isocurvature perturbations, both of which can affect the primordial density perturbations. In this paper, we calculate primordial spectra in inflationary models with sudden turning potentials taking into account both of the two effects appropriately. We find that there are some non-trivial correlations between the two effects in the power spectrum and, as a consequence, the primordial scalar power spectrum has a peak around the scale exiting the horizon at the turn. Though both effects can induce parametric resonance amplifications, they are shown to be canceled out for the case with the canonical kinetic terms. The peak feature and the scale dependence of bispectra are also discussed.
Canonical transformations of Kepler trajectories
International Nuclear Information System (INIS)
Mostowski, Jan
2010-01-01
In this paper, canonical transformations generated by constants of motion in the case of the Kepler problem are discussed. It is shown that canonical transformations generated by angular momentum are rotations of the trajectory. Particular attention is paid to canonical transformations generated by the Runge-Lenz vector. It is shown that these transformations change the eccentricity of the orbit. A method of obtaining elliptic trajectories from the circular ones with the help of canonical trajectories is discussed.
Novel tilt-curvature coupling in lipid membranes
Terzi, M. Mert; Deserno, Markus
2017-08-01
On mesoscopic scales, lipid membranes are well described by continuum theories whose main ingredients are the curvature of a membrane's reference surface and the tilt of its lipid constituents. In particular, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] have shown how to systematically derive such a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress. Performing a dimensional reduction, they not only derive the basic form of the effective surface Hamiltonian but also express its emergent elastic couplings as trans-membrane moments of lower-level material parameters. In the present paper, we argue, though, that their derivation unfortunately missed a coupling term between curvature and tilt. This term arises because, as one moves along the membrane, the curvature-induced change of transverse distances contributes to the area strain—an effect that was believed to be small but nevertheless ends up contributing at the same (quadratic) order as all other terms in their Hamiltonian. We illustrate the consequences of this amendment by deriving the monolayer and bilayer Euler-Lagrange equations for the tilt, as well as the power spectra of shape, tilt, and director fluctuations. A particularly curious aspect of our new term is that its associated coupling constant is the second moment of the lipid monolayer's lateral stress profile—which within this framework is equal to the monolayer Gaussian curvature modulus, κ¯ m. On the one hand, this implies that many theoretical predictions now contain a parameter that is poorly known (because the Gauss-Bonnet theorem limits access to the integrated Gaussian curvature); on the other hand, the appearance of κ¯ m outside of its Gaussian curvature provenance opens opportunities for measuring it by more conventional means, for instance by monitoring a membrane's undulation spectrum at short scales.
Spinal curvature and characteristics of postural change in pregnant women.
Okanishi, Natsuko; Kito, Nobuhiro; Akiyama, Mitoshi; Yamamoto, Masako
2012-07-01
Pregnant women often report complaints due to physiological and postural changes. Postural changes during pregnancy may cause low back pain and pelvic girdle pain. This study aimed to compare the characteristics of postural changes in pregnant compared with non-pregnant women. Prospective case-control study. Pregnancy care center. Fifteen women at 17-34 weeks pregnancy comprised the study group, while 10 non-pregnant female volunteers comprised the control group. Standing posture was evaluated in the sagittal plane with static digital pictures. Two angles were measured by image analysis software: (1) between the trunk and pelvis; and (2) between the trunk and lower extremity. Spinal curvature was measured with Spinal Mouse® to calculate the means of sacral inclination, thoracic and lumbar curvature and inclination. The principal components were calculated until eigenvalues surpassed 1. Three distinct factors with eigenvalues of 1.00-2.49 were identified, consistent with lumbosacral spinal curvature and inclination, thoracic spine curvature, and inclination of the body. These factors accounted for 77.2% of the total variance in posture variables. Eleven pregnant women showed postural characteristics of lumbar kyphosis and sacral posterior inclination. Body inclination showed a variety of patterns compared with those in healthy women. Spinal curvature demonstrated a tendency for lumbar kyphosis in pregnant women. Pregnancy may cause changes in spinal curvature and posture, which may in turn lead to relevant symptoms. Our data provide a basis for investigating the effects of spinal curvature and postural changes on symptoms during pregnancy. © 2012 The Authors Acta Obstetricia et Gynecologica Scandinavica© 2012 Nordic Federation of Societies of Obstetrics and Gynecology.
Sequence periodicity in nucleosomal DNA and intrinsic curvature.
Nair, T Murlidharan
2010-05-17
Most eukaryotic DNA contained in the nucleus is packaged by wrapping DNA around histone octamers. Histones are ubiquitous and bind most regions of chromosomal DNA. In order to achieve smooth wrapping of the DNA around the histone octamer, the DNA duplex should be able to deform and should possess intrinsic curvature. The deformability of DNA is a result of the non-parallelness of base pair stacks. The stacking interaction between base pairs is sequence dependent. The higher the stacking energy the more rigid the DNA helix, thus it is natural to expect that sequences that are involved in wrapping around the histone octamer should be unstacked and possess intrinsic curvature. Intrinsic curvature has been shown to be dictated by the periodic recurrence of certain dinucleotides. Several genome-wide studies directed towards mapping of nucleosome positions have revealed periodicity associated with certain stretches of sequences. In the current study, these sequences have been analyzed with a view to understand their sequence-dependent structures. Higher order DNA structures and the distribution of molecular bend loci associated with 146 base nucleosome core DNA sequence from C. elegans and chicken have been analyzed using the theoretical model for DNA curvature. The curvature dispersion calculated by cyclically permuting the sequences revealed that the molecular bend loci were delocalized throughout the nucleosome core region and had varying degrees of intrinsic curvature. The higher order structures associated with nucleosomes of C.elegans and chicken calculated from the sequences revealed heterogeneity with respect to the deviation of the DNA axis. The results points to the possibility of context dependent curvature of varying degrees to be associated with nucleosomal DNA.
Trajectory Based Traffic Analysis
DEFF Research Database (Denmark)
Krogh, Benjamin Bjerre; Andersen, Ove; Lewis-Kelham, Edwin
2013-01-01
We present the INTRA system for interactive path-based traffic analysis. The analyses are developed in collaboration with traffic researchers and provide novel insights into conditions such as congestion, travel-time, choice of route, and traffic-flow. INTRA supports interactive point-and-click a......We present the INTRA system for interactive path-based traffic analysis. The analyses are developed in collaboration with traffic researchers and provide novel insights into conditions such as congestion, travel-time, choice of route, and traffic-flow. INTRA supports interactive point......-and-click analysis, due to a novel and efficient indexing structure. With the web-site daisy.aau.dk/its/spqdemo/we will demonstrate several analyses, using a very large real-world data set consisting of 1.9 billion GPS records (1.5 million trajectories) recorded from more than 13000 vehicles, and touching most...
Allen, Adriana; Hofmann, Pascale; Teh, Tse-Hui
2017-01-01
Water is an essential element in the future of cities. It shapes cities’ locations, form, ecology, prosperity and health. The changing nature of urbanisation, climate change, water scarcity, environmental values, globalisation and social justice mean that the models of provision of water services and infrastructure that have dominated for the past two centuries are increasingly infeasible. Conventional arrangements for understanding and managing water in cities are being subverted by a range of natural, technological, political, economic and social changes. The prognosis for water in cities remains unclear, and multiple visions and discourses are emerging to fill the space left by the certainty of nineteenth century urban water planning and engineering. This book documents a sample of those different trajectories, in terms of water transformations, option, services and politics. Water is a key element shaping urban form, economies and lifestyles, part of the ongoing transformation of cities. Cities are face...
The role of curvature in silica mesoporous crystals
Miyasaka, Keiichi; Bennett, Alfonso Garcia; Han, Lu; Han, Yu; Xiao, Changhong; Fujita, Nobuhisa; Castle, Toen; Sakamoto, Yasuhiro; Che, Shunai; Terasaki, Osamu
2012-01-01
Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems. © 2012 The Royal Society.
The role of curvature in silica mesoporous crystals
Miyasaka, Keiichi
2012-02-08
Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems. © 2012 The Royal Society.
Studying biomolecule localization by engineering bacterial cell wall curvature.
Directory of Open Access Journals (Sweden)
Lars D Renner
Full Text Available In this article we describe two techniques for exploring the relationship between bacterial cell shape and the intracellular organization of proteins. First, we created microchannels in a layer of agarose to reshape live bacterial cells and predictably control their mean cell wall curvature, and quantified the influence of curvature on the localization and distribution of proteins in vivo. Second, we used agarose microchambers to reshape bacteria whose cell wall had been chemically and enzymatically removed. By combining microstructures with different geometries and fluorescence microscopy, we determined the relationship between bacterial shape and the localization for two different membrane-associated proteins: i the cell-shape related protein MreB of Escherichia coli, which is positioned along the long axis of the rod-shaped cell; and ii the negative curvature-sensing cell division protein DivIVA of Bacillus subtilis, which is positioned primarily at cell division sites. Our studies of intracellular organization in live cells of E. coli and B. subtilis demonstrate that MreB is largely excluded from areas of high negative curvature, whereas DivIVA localizes preferentially to regions of high negative curvature. These studies highlight a unique approach for studying the relationship between cell shape and intracellular organization in intact, live bacteria.
The speed-curvature power law of movements: a reappraisal.
Zago, Myrka; Matic, Adam; Flash, Tamar; Gomez-Marin, Alex; Lacquaniti, Francesco
2018-01-01
Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.
Kick-Off Point (KOP and End of Buildup (EOB Data Analysis in Trajectory Design
Directory of Open Access Journals (Sweden)
Novrianti Novrianti
2017-06-01
Full Text Available Well X is a development well which is directionally drilled. Directional drilling is choosen because the coordinate target of Well X is above the buffer zone. The directional track plan needs accurate survey calculation in order to make the righ track for directional drilling. There are many survey calculation in directional drilling such as tangential, underbalance, average angle, radius of curvature, and mercury method. Minimum curvature method is used in this directional track plan calculation. This method is used because it gives less error than other method. Kick-Off Point (KOP and End of Buildup (EOB analysis is done at 200 ft, 400 ft, and 600 ft depth to determine the trajectory design and optimal inclination. The hole problem is also determined in this trajectory track design. Optimal trajectory design determined at 200 ft depth because the inclination below 35º and also already reach the target quite well at 1632.28 ft TVD and 408.16 AHD. The optimal inclination at 200 ft KOP depth because the maximum inclination is 18.87º which is below 35º. Hole problem will occur if the trajectory designed at 600 ft. The problems are stuck pipe and the casing or tubing will not able to bend.
Segmenting Trajectories by Movement States
Buchin, M.; Kruckenberg, H.; Kölzsch, A.; Timpf, S.; Laube, P.
2013-01-01
Dividing movement trajectories according to different movement states of animals has become a challenge in movement ecology, as well as in algorithm development. In this study, we revisit and extend a framework for trajectory segmentation based on spatio-temporal criteria for this purpose. We adapt
Geometric Algorithms for Trajectory Analysis
Staals, Frank
2015-01-01
Technology such as the Global Positing System (GPS) has made tracking moving entities easy and cheap. As a result there is a large amount of trajectory data available, and an increasing demand on tools and techniques to analyze such data. We consider several analysis tasks for trajectory data,
Lunar Cube Transfer Trajectory Options
Folta, David; Dichmann, Donald James; Clark, Pamela E.; Haapala, Amanda; Howell, Kathleen
2015-01-01
Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can b e considered which have a wide range of transfer duration, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO) geostationary transfer orbits (GTO) and higher energy direct lunar transfer and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.
Waterfall field in hybrid inflation and curvature perturbation
International Nuclear Information System (INIS)
Gong, Jinn-Ouk; Sasaki, Misao
2011-01-01
We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the δN formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation
Waterfall field in hybrid inflation and curvature perturbation
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA Leiden (Netherlands); Sasaki, Misao, E-mail: jgong@lorentz.leidenuniv.nl, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2011-03-01
We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the δN formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation.
Evolution of curvature perturbation in generalized gravity theories
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
On the scalar curvature of self-dual manifolds
International Nuclear Information System (INIS)
Kim, J.
1992-08-01
We generalize LeBrun's explicit ''hyperbolic ansatz'' construction of self-dual metrics on connected sums of conformally flat manifolds and CP 2 's through a systematic use of the theory of hyperbolic geometry and Kleinian groups. (This construction produces, for example, all self-dual manifolds with semi-free S 1 -action and with either nonnegative scalar curvature or positive-definite intersection form.) We then point out a simple criterion for determining the sign of the scalar curvature of these conformal metrics. Exploiting this, we then show that the sign of the scalar curvature can change on connected components of the moduli space of self-dual metrics, thereby answering a question raised by King and Kotschick. (author). Refs
CURVATURE-DRIVEN MOLECULAR FLOW ON MEMBRANE SURFACE.
Mikucki, Michael; Zhou, Y C
2017-01-01
This work presents a mathematical model for the localization of multiple species of diffusion molecules on membrane surfaces. Morphological change of bilayer membrane in vivo is generally modulated by proteins. Most of these modulations are associated with the localization of related proteins in the crowded lipid environments. We start with the energetic description of the distributions of molecules on curved membrane surface, and define the spontaneous curvature of bilayer membrane as a function of the molecule concentrations on membrane surfaces. A drift-diffusion equation governs the gradient flow of the surface molecule concentrations. We recast the energetic formulation and the related governing equations by using an Eulerian phase field description to define membrane morphology. Computational simulations with the proposed mathematical model and related numerical techniques predict (i) the molecular localization on static membrane surfaces at locations with preferred mean curvatures, and (ii) the generation of preferred mean curvature which in turn drives the molecular localization.
Vibration Analysis of Circular Arch Element Using Curvature
Directory of Open Access Journals (Sweden)
H. Saffari
2008-01-01
Full Text Available In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.
Linearized curvatures for auxiliary fields in the de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Vasiliev, M A
1988-09-19
New consistent linearized curvatures in the de Sitter space are constructed. The sequence of actions, describing bosonic and fermionic gauge auxiliary fields, is found based on these curvatures. The proposed actions are parametrized by two integer parameters, n greater than or equal to 0 and m greater than or equal to 0. The simplest case n=m=0 corresponds in the flat limit to the auxiliary fields of 'new minimal' supergravity. The hamiltonian formulation is developed for the auxiliary fields suggested; hamiltonians and first- and second-class constraints are constructed. Using these results, it is shown that the systems of fields proposed possess no dynamical degrees of freedom in de Sitter and flat spaces. In addition the hamiltonian formalism is analysed for some free dynamical systems based on linearized higher-spin curvatures introduced previously.
Local divergence and curvature divergence in first order optics
Mafusire, Cosmas; Krüger, Tjaart P. J.
2018-06-01
The far-field divergence of a light beam propagating through a first order optical system is presented as a square root of the sum of the squares of the local divergence and the curvature divergence. The local divergence is defined as the ratio of the beam parameter product to the beam width whilst the curvature divergence is a ratio of the space-angular moment also to the beam width. It is established that the beam’s focusing parameter can be defined as a ratio of the local divergence to the curvature divergence. The relationships between the two divergences and other second moment-based beam parameters are presented. Their various mathematical properties are presented such as their evolution through first order systems. The efficacy of the model in the analysis of high power continuous wave laser-based welding systems is briefly discussed.
Model-independent Constraints on Cosmic Curvature and Opacity
Energy Technology Data Exchange (ETDEWEB)
Wang, Guo-Jian; Li, Zheng-Xiang; Xia, Jun-Qing; Zhu, Zong-Hong [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Wei, Jun-Jie, E-mail: gjwang@mail.bnu.edu.cn, E-mail: zxli918@bnu.edu.cn, E-mail: xiajq@bnu.edu.cn, E-mail: zhuzh@bnu.edu.cn, E-mail: jjwei@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)
2017-09-20
In this paper, we propose to estimate the spatial curvature of the universe and the cosmic opacity in a model-independent way with expansion rate measurements, H ( z ), and type Ia supernova (SNe Ia). On the one hand, using a nonparametric smoothing method Gaussian process, we reconstruct a function H ( z ) from opacity-free expansion rate measurements. Then, we integrate the H ( z ) to obtain distance modulus μ {sub H}, which is dependent on the cosmic curvature. On the other hand, distances of SNe Ia can be determined by their photometric observations and thus are opacity-dependent. In our analysis, by confronting distance moduli μ {sub H} with those obtained from SNe Ia, we achieve estimations for both the spatial curvature and the cosmic opacity without any assumptions for the cosmological model. Here, it should be noted that light curve fitting parameters, accounting for the distance estimation of SNe Ia, are determined in a global fit together with the cosmic opacity and spatial curvature to get rid of the dependence of these parameters on cosmology. In addition, we also investigate whether the inclusion of different priors for the present expansion rate ( H {sub 0}: global estimation, 67.74 ± 0.46 km s{sup −1} Mpc{sup −1}, and local measurement, 73.24 ± 1.74 km s{sup −1} Mpc{sup −1}) exert influence on the reconstructed H ( z ) and the following estimations of the spatial curvature and cosmic opacity. Results show that, in general, a spatially flat and transparent universe is preferred by the observations. Moreover, it is suggested that priors for H {sub 0} matter a lot. Finally, we find that there is a strong degeneracy between the curvature and the opacity.
Some curvature properties of quarter symmetric metric connections
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-08-01
A linear connection Γ ji h with torsion tensor T j h P i -T i h P j , where T j h is an arbitrary (1,1) tensor field and P i is a 1-form, has been called a quarter-symmetric connection by Golab. Some properties of such connections have been studied by Rastogi, Mishra and Pandey, and Yano and Imai. In this paper based on the curvature tensor of quarter-symmetric metric connection we define a tensor analogous to conformal curvature tensor and study some properties of such a tensor. (author)
Vertex Normals and Face Curvatures of Triangle Meshes
Sun, Xiang
2016-08-12
This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ŉormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.
Berry Curvature in Magnon-Phonon Hybrid Systems.
Takahashi, Ryuji; Nagaosa, Naoto
2016-11-18
We study theoretically the Berry curvature of the magnon induced by the hybridization with the acoustic phonons via the spin-orbit and dipolar interactions. We first discuss the magnon-phonon hybridization via the dipolar interaction, and show that the dispersions have gapless points in momentum space, some of which form a loop. Next, when both spin-orbit and dipolar interactions are considered, we show anisotropic texture of the Berry curvature and its divergence with and without gap closing. Realistic evaluation of the consequent anomalous velocity is given for yttrium iron garnet.
Directory of Open Access Journals (Sweden)
Lie Guo
2014-01-01
Full Text Available To enhance the active safety and realize the autonomy of intelligent vehicle on highway curved road, a lane changing trajectory is planned and tracked for lane changing maneuver on curved road. The kinematics model of the intelligent vehicle with nonholonomic constraint feature and the tracking error model are established firstly. The longitudinal and lateral coupling and the difference of curvature radius between the outside and inside lane are taken into account, which is helpful to enhance the authenticity of desired lane changing trajectory on curved road. Then the trajectory tracking controller of closed-loop control structure is derived using integral backstepping method to construct a new virtual variable. The Lyapunov theory is applied to analyze the stability of the proposed tracking controller. Simulation results demonstrate that this controller can guarantee the convergences of both the relative position tracking errors and the position tracking synchronization.
International Nuclear Information System (INIS)
Akbar, M.M.; D'Eath, P.D.
2003-01-01
The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact (S 3 ) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii (a,b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii (a,b), we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a 'cusp catastrophe' structure with a non-self-intersecting 'catastrophe manifold' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between a and b holds. The action of this solution is proportional to -a 3 for large a (∼b) and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a 'bolt' is investigated in a forthcoming paper
Generic trajectory representation and trajectory following for wheeled robots
DEFF Research Database (Denmark)
Kjærgaard, Morten; Andersen, Nils Axel; Ravn, Ole
2014-01-01
will drive. Safe: Avoid fatal collisions. Based on a survey of existing methods and algorithms the article presents a generic way to represent constraints for different types of robots, a generic way to represent trajectories using Bëzier curves, a method to convert the trajectory so it can be driven...... in a smooth motion, a method to create a safe velocity profile for the robot, and a path following controller....
Low Thrust Trajectory Design for GSFC Missions
National Aeronautics and Space Administration — The Evolutionary Mission Trajectory Generator (EMTG) is a global trajectory optimization tool. EMTG is intended for use in designing interplanetary missions which...
Black hole production in particle collisions and higher curvature gravity
International Nuclear Information System (INIS)
Rychkov, Vyacheslav S.
2004-01-01
The problem of black hole production in trans-Planckian particle collisions is revisited, in the context of large extra dimensions scenarios of TeV-scale gravity. The validity of the standard description of this process (two colliding Aichelburg-Sexl shock waves in classical Einstein gravity) is questioned. It is observed that the classical spacetime has large curvature along the transverse collision plane, as signaled by the curvature invariant (R μνλσ ) 2 . Thus quantum gravity effects, and in particular higher curvature corrections to the Einstein gravity, cannot be ignored. To give a specific example of what may happen, the collision is reanalyzed in the Einstein-Lanczos-Lovelock gravity theory, which modifies the Einstein-Hilbert Lagrangian by adding a particular 'Gauss-Bonnet' combination of curvature squared terms. The analysis uses a series of approximations, which reduce the field equations to a tractable second order nonlinear PDE of the Monge-Ampere type. It is found that the resulting spacetime is significantly different from the pure Einstein case in the future of the transverse collision plane. These considerations cast serious doubts on the geometric cross section estimate, which is based on the classical Einstein gravity description of the black hole production process
On conformal Paneitz curvature equations in higher dimensional spheres
International Nuclear Information System (INIS)
El Mehdi, Khalil
2004-11-01
We study the problem of prescribing the Paneitz curvature on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results. (author)
Continuous-Curvature Path Generation Using Fermat's Spiral
Directory of Open Access Journals (Sweden)
Anastasios M. Lekkas
2013-10-01
Full Text Available This paper proposes a novel methodology, based on Fermat's spiral (FS, for constructing curvature-continuous parametric paths in a plane. FS has a zero curvature at its origin, a property that allows it to be connected with a straight line smoothly, that is, without the curvature discontinuity which occurs at the transition point between a line and a circular arc when constructing Dubins paths. Furthermore, contrary to the computationally expensive clothoids, FS is described by very simple parametric equations that are trivial to compute. On the downside, computing the length of an FS arc involves a Gaussian hypergeometric function. However, this function is absolutely convergent and it is also shown that it poses no restrictions to the domain within which the length can be calculated. In addition, we present an alternative parametrization of FS which eliminates the parametric speed singularity at the origin, hence making the spiral suitable for path-tracking applications. A detailed description of how to construct curvature-continuous paths with FS is given.
Eigenvalue estimates for submanifolds with bounded f-mean curvature
Indian Academy of Sciences (India)
GUANGYUE HUANG
1College of Mathematics and Information Science, Henan Normal University,. Xinxiang 453007 ... submanifolds in a hyperbolic space with the norm of their mean curvature vector bounded above by a constant. ..... [2] Batista M, Cavalcante M P and Pyo J, Some isoperimetric inequalities and eigenvalue estimates in ...
Multiple spinal curvatures in a captive African dwarf crocodile ...
African Journals Online (AJOL)
A 4 year old African dwarf crocodile that had been domiciled at the Zoological Gardens, University of Ibadan for 2 years was presented with a history of anorexia of two weeks' duration and reluctance to move for about a week prior to presentation. Physical examination revealed body curvatures and radiography was ...
Intracellular magnetophoresis of amyloplasts and induction of root curvature
Kuznetsov, O. A.; Hasenstein, K. H.
1996-01-01
High-gradient magnetic fields (HGMFs) were used to induce intracellular magnetophoresis of amyloplasts. The HGMFs were generated by placing a small ferromagnetic wedge into a uniform magnetic field or at the gap edge between two permanent magnets. In the vicinity of the tip of the wedge the dynamic factor of the magnetic field, delta(H2/2), was about 10(9) Oe2.cm-1, which subjected the amyloplasts to a force comparable to that of gravity. When roots of 2-d-old seedlings of flax (Linum usitatissimum L.) were positioned vertically and exposed to an HGMF, curvature away from the wedge was transient and lasted approximately 1 h. Average curvature obtained after placing magnets, wedge and seedlings on a 1-rpm clinostat for 2 h was 33 +/- 5 degrees. Roots of horizontally placed control seedlings without rotation curved about 47 +/- 4 degrees. The time course of curvature and changes in growth rate were similar for gravicurvature and for root curvature induced by HGMFs. Microscopy showed displacement of amyloplasts in vitro and in vivo. Studies with Arabidopsis thaliana (L.) Heynh. showed that the wild type responded to HGMFs but the starchless mutant TC7 did not. The data indicate that a magnetic force can be used to study the gravisensing and response system of roots.
Zero mean curvature surfaces of mixed type in Minkowski space
International Nuclear Information System (INIS)
Klyachin, V A
2003-01-01
We investigate zero mean curvature surfaces in the Minkowski space R 3 1 such that their first fundamental quadratic form changes signature. Part of such a surface is space-like and part is time-like. We obtain complete information about the structure of the set of points where the surface changes type and prove the related existence and uniqueness theorems
On the Curvature and Heat Flow on Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Ohta Shin-ichi
2014-01-01
Full Text Available We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.
The Paneitz curvature problem on lower dimensional spheres
Ben-Ayed, M
2003-01-01
In this paper we prescribe a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n is an element of left brace 5, 6 right brace. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.
Forelimb bone curvature in terrestrial and arboreal mammals
Directory of Open Access Journals (Sweden)
Keith Henderson
2017-04-01
Full Text Available It has recently been proposed that the caudal curvature (concave caudal side observed in the radioulna of terrestrial quadrupeds is an adaptation to the habitual action of the triceps muscle which causes cranial bending strains (compression on cranial side. The caudal curvature is proposed to be adaptive because longitudinal loading induces caudal bending strains (increased compression on the caudal side, and these opposing bending strains counteract each other leaving the radioulna less strained. If this is true for terrestrial quadrupeds, where triceps is required for habitual elbow extension, then we might expect that in arboreal species, where brachialis is habitually required to maintain elbow flexion, the radioulna should instead be cranially curved. This study measures sagittal curvature of the ulna in a range of terrestrial and arboreal primates and marsupials, and finds that their ulnae are curved in opposite directions in these two locomotor categories. This study also examines sagittal curvature in the humerus in the same species, and finds differences that can be attributed to similar adaptations: the bone is curved to counter the habitual muscle action required by the animal’s lifestyle, the difference being mainly in the distal part of the humerus, where arboreal animals tend have a cranial concavity, thought to be in response the carpal and digital muscles that pull cranially on the distal humerus.
Axial Length/Corneal Radius of Curvature Ratio and Refractive ...
African Journals Online (AJOL)
2017-12-05
Dec 5, 2017 ... variously described as determined by the ocular biometric variables. There have been many studies on the relationship between refractive error and ocular axial length (AL), anterior chamber depth, corneal radius of curvature (CR), keratometric readings as well as other ocular biometric variables such as ...
GEOMETRY OF COMPLETE HYPERSURFACES EVOLVED BY MEAN CURVATURE FLOW
Institute of Scientific and Technical Information of China (English)
盛为民
2003-01-01
Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.
Cosmological models with positive scalar spatial curvature and Λ>0
Ponce de Leon, J.
1987-12-01
Some exact spherically symmetric solutions of the Einstein field equations with Λ>0 and positive three-curvature are given. They have reasonable physical properties and represent universes which do not undergo inflation but have a non-de Sitter behaviour for large times. This paper extends some previous results in the literature. Permanent address: Apartado 2816, Caracas 1010-A, Venezuela.
Critical dimension of strings with an extrinsic curvature
International Nuclear Information System (INIS)
Matsuki, T.; Viswanathan, K.S.
1988-01-01
The conformal anomaly is calculated by using the path-integral method to determine the critical dimension for a string theory with an extrinsic curvature by appropriately defining the first-order form of this Lagrangian. The critical dimension, defined by the vanishing of the Liouville kinetic term, is found to be D = 26, the same as for the ordinary bosonic string theory
Distributional curvature of time-dependent cosmic strings
Wilson, J P
1997-01-01
Colombeau's theory of generalised functions is used to calculate the contributions, at the rotation axis, to the distributional curvature for a time-dependent radiating cosmic string, and hence the mass per unit length of the string source. This mass per unit length is compared with the mass at null infinity, giving evidence for a global energy conservation law.
Automatic quantification of local and global articular cartilage surface curvature
DEFF Research Database (Denmark)
Folkesson, Jenny; Dam, Erik B; Olsen, Ole F
2008-01-01
The objective of this study was to quantitatively assess the surface curvature of the articular cartilage from low-field magnetic resonance imaging (MRI) data, and to investigate its role in populations with varying radiographic signs of osteoarthritis (OA), cross-sectionally and longitudinally...
Directable weathering of concave rock using curvature estimation.
Jones, Michael D; Farley, McKay; Butler, Joseph; Beardall, Matthew
2010-01-01
We address the problem of directable weathering of exposed concave rock for use in computer-generated animation or games. Previous weathering models that admit concave surfaces are computationally inefficient and difficult to control. In nature, the spheroidal and cavernous weathering rates depend on the surface curvature. Spheroidal weathering is fastest in areas with large positive mean curvature and cavernous weathering is fastest in areas with large negative mean curvature. We simulate both processes using an approximation of mean curvature on a voxel grid. Both weathering rates are also influenced by rock durability. The user controls rock durability by editing a durability graph before and during weathering simulation. Simulations of rockfall and colluvium deposition further improve realism. The profile of the final weathered rock matches the shape of the durability graph up to the effects of weathering and colluvium deposition. We demonstrate the top-down directability and visual plausibility of the resulting model through a series of screenshots and rendered images. The results include the weathering of a cube into a sphere and of a sheltered inside corner into a cavern as predicted by the underlying geomorphological models.
Generalized Curvature-Matter Couplings in Modified Gravity
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Tiberiu Harko
2014-07-01
Full Text Available In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.
Curvature-induced symmetry breaking in nonlinear Schrodinger models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth
2000-01-01
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...
Other Earths: Search for Life and the Constant Curvature
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Khoshyaran M. M.
2015-07-01
Full Text Available The objective of this paper is to propose a search methodology for finding other exactly similar earth like planets (or sister earths. The theory is based on space consisting of Riemann curves or highways. A mathematical model based on constant curvature, a moving frame bundle, and gravitational dynamics is introduced.
Supported lipid bilayers with controlled curvature via colloidal lithography
DEFF Research Database (Denmark)
Sundh, Maria; Manandhar, Michal; Svedhem, Sofia
2011-01-01
Supported lipid bilayers (SLBs) at surfaces provide a route to quantitatively study molecular interactions with and at lipid membranes via different surface-based analytical techniques. Here, a method to fabricate SLBs with controlled curvatures, in the nanometer regime over large areas, is prese...
Papapetrou's naked singularity is a strong curvature singularity
International Nuclear Information System (INIS)
Hollier, G.P.
1986-01-01
Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)
Remarks on the boundary curve of a constant mean curvature topological disc
DEFF Research Database (Denmark)
Brander, David; Lopéz, Rafael
2017-01-01
We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the bo......We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature...
Galileo's Trajectory with Mild Resistance
Groetsch, C. W.
2012-01-01
An aspect of Galileo's classical trajectory that persists in a simple resistance model is noted. The resistive model provides a case study for the classroom analysis of limiting behaviour of an implicitly defined function. (Contains 1 note.)
Flight test trajectory control analysis
Walker, R.; Gupta, N.
1983-01-01
Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver.
Long Range Aircraft Trajectory Prediction
Magister, Tone
2009-01-01
The subject of the paper is the improvement of the aircraft future trajectory prediction accuracy for long-range airborne separation assurance. The strategic planning of safe aircraft flights and effective conflict avoidance tactics demand timely and accurate conflict detection based upon future four–dimensional airborne traffic situation prediction which is as accurate as each aircraft flight trajectory prediction. The improved kinematics model of aircraft relative flight considering flight ...
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
Effect of nano-scale curvature on the intrinsic blood coagulation system
Kushida, Takashi; Saha, Krishnendu; Subramani, Chandramouleeswaran; Nandwana, Vikas; Rotello, Vincent M.
2014-01-01
The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation ‘silent’ surface, while nanoparticles with lower surface curvature shows denaturation and concomitant coagulation. PMID:25341004
Extrinsic Isoperimetric Analysis on Submanifolds with Curvatures bounded from below
DEFF Research Database (Denmark)
Markvorsen, Steen; Palmer, Vicente
2010-01-01
and on the radial part of the intrinsic unit normals at the boundaries of the extrinsic spheres, respectively. In the same vein we also establish lower bounds on the mean exit time for Brownian motions in the extrinsic balls, i.e. lower bounds for the time it takes (on average) for Brownian particles to diffuse......We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field...... within the extrinsic ball from a given starting point before they hit the boundary of the extrinsic ball. In those cases, where we may extend our analysis to hold all the way to infinity, we apply a capacity comparison technique to obtain a sufficient condition for the submanifolds to be parabolic, i...
Curvature effects on carbon nanomaterials: Exohedral versus endhohedral supercapacitors
Energy Technology Data Exchange (ETDEWEB)
Huang, J; Sumpter, B. G.; Meunier, V.; Yushin, G.; Portet, C.; Gogotsi, Y.
2011-01-31
Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior of nanoporous carbon materials. This finding is in good agreement with the trend of recent experimental data. Our analysis suggests that electrical energy storage can be improved by exploiting the highly curved surfaces of carbon nanotube arrays with diameters on the order of 1 nm.
Non-linear realizations and higher curvature supergravity
Energy Technology Data Exchange (ETDEWEB)
Farakos, F. [Dipartimento di Fisica e Astronomia ' ' Galileo Galilei' ' , Universita di Padova (Italy); INFN, Sezione di Padova (Italy); Ferrara, S. [Department of Theoretical Physics, Geneva (Switzerland); INFN - Laboratori Nazionali di Frascati, Frascati (Italy); Department of Physics and Astronomy, Mani L. Bhaumik Institute for Theoretical Physics, U.C.L.A., Los Angeles, CA (United States); Kehagias, A. [Physics Division, National Technical University of Athens (Greece); Luest, D. [Arnold Sommerfeld Center for Theoretical Physics, Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)
2017-12-15
We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss-Bonnet multiplet and discuss the emergence of a new scalar degree of freedom. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Curvature effects in carbon nanomaterials: Exohedral versus endohedral supercapacitors
Energy Technology Data Exchange (ETDEWEB)
Huang, Jingsong [ORNL; Sumpter, Bobby G [ORNL; Meunier, Vincent [ORNL; Gogotsi, Yury G. [Drexel University; Yushin, Gleb [Georgia Institute of Technology; Portet, Cristelle [Drexel University
2010-01-01
Capacitive energy storage mechanisms in nanoporous carbon supercapacitors hinge on endohedral interactions in carbon materials with macro-, meso-, and micropores that have negative surface curvature. In this article, we show that because of the positive curvature found in zero-dimensional carbon onions or one-dimensional carbon nanotube arrays, exohedral interactions cause the normalized capacitance to increase with decreasing particle size or tube diameter, in sharp contrast to the behavior of nanoporous carbon materials. This finding is in good agreement with the trend of recent experimental data. Our analysis suggests that electrical energy storage can be improved by exploiting the highly curved surfaces of carbon nanotube arrays with diameters on the order of 1 nm.
On M-theory fourfold vacua with higher curvature terms
International Nuclear Information System (INIS)
Grimm, Thomas W.; Pugh, Tom G.; Weißenbacher, Matthias
2015-01-01
We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kähler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions
Substrate Curvature Regulates Cell Migration -A Computational Study
He, Xiuxiu; Jiang, Yi
Cell migration in host microenvironment is essential to cancer etiology, progression and metastasis. Cellular processes of adhesion, cytoskeletal polymerization, contraction, and matrix remodeling act in concert to regulate cell migration, while local extracellular matrix architecture modulate these processes. In this work we study how stromal microenvironment with native and cell-derived curvature at micron-meter scale regulate cell motility pattern. We developed a 3D model of single cell migration on a curved substrate. Mathematical analysis of cell morphological adaption to the cell-substrate interface shows that cell migration on convex surfaces deforms more than on concave surfaces. Both analytical and simulation results show that curved surfaces regulate the cell motile force for cell's protruding front through force balance with focal adhesion and cell contraction. We also found that cell migration on concave substrates is more persistent. These results offer a novel biomechanical explanation to substrate curvature regulation of cell migration. NIH 1U01CA143069.
Glauber theory and the quantum coherence of curvature inhomogeneities
Giovannini, Massimo
2017-01-12
The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose-Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.
Generating ekpyrotic curvature perturbations before the big bang
International Nuclear Information System (INIS)
Lehners, Jean-Luc; Turok, Neil; McFadden, Paul; Steinhardt, Paul J.
2007-01-01
We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, which can be entirely described using 4D effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modeled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtained and that the spectral tilt n s tends to range from slightly blue to red, with 0.97 s <1.02 for the simplest models, a range compatible with current observations but shifted by a few percent towards the blue compared to the prediction of the simplest, large-field inflationary models
Imprint of spatial curvature on inflation power spectrum
International Nuclear Information System (INIS)
Masso, Eduard; Zsembinszki, Gabriel; Mohanty, Subhendra; Nautiyal, Akhilesh
2008-01-01
If the Universe had a large curvature before inflation there is a deviation from the scale invariant perturbations of the inflaton at the beginning of inflation. This may have some effect on the cosmic microwave background anisotropy at large angular scales. We calculate the density perturbations for both open and closed universe cases using the Bunch-Davies vacuum condition on the initial state. We use our power spectrum to calculate the temperature anisotropy spectrum and compare the results with the Wilkinson microwave anisotropy map five year data. We find that our power spectrum gives a lower quadrupole anisotropy when Ω-1>0, but matches the temperature anisotropy calculated from the standard Ratra-Peebles power spectrum at large l. The determination of spatial curvature from temperature anisotropy data is not much affected by the different power spectra which arise from the choice of different boundary conditions for the inflaton perturbation.
Thermodynamic curvature of soft-sphere fluids and solids
Brańka, A. C.; Pieprzyk, S.; Heyes, D. M.
2018-02-01
The influence of the strength of repulsion between particles on the thermodynamic curvature scalar R for the fluid and solid states is investigated for particles interacting with the inverse power (r-n) potential, where r is the pair separation and 1 /n is the softness. Exact results are obtained for R in certain limiting cases, and the R behavior determined for the systems in the fluid and solid phases. It is found that in such systems the thermodynamic curvature can be positive for very soft particles, negative for steeply repulsive (or large n ) particles across almost the entire density range, and can change sign between negative and positive at a certain density. The relationship between R and the form of the interaction potential is more complex than previously suggested, and it may be that R is an indicator of the relative importance of energy and entropy contributions to the thermodynamic properties of the system.
Directory of Open Access Journals (Sweden)
E. W. Grafarend
1997-06-01
Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.
Reheating via a generalized nonminimal coupling of curvature to matter
International Nuclear Information System (INIS)
Bertolami, Orfeu; Frazao, Pedro; Paramos, Jorge
2011-01-01
In this work, one shows that a generalized nonminimal coupling between geometry and matter is compatible with Starobinsky inflation and leads to a successful process of preheating, a reheating scenario based on the production of massive particles via parametric resonance. The model naturally extends the usual preheating mechanism, which resorts to an ad hoc scalar curvature-dependent mass term for a scalar field χ, and also encompasses a previously studied preheating channel based upon a nonstandard kinetic term.
Investigating undergraduate students’ ideas about the curvature of the Universe
Directory of Open Access Journals (Sweden)
Kim Coble
2018-06-01
Full Text Available [This paper is part of the Focused Collection on Astronomy Education Research.] As part of a larger project studying undergraduate students’ understanding of cosmology, we explored students’ ideas about the curvature of the Universe. We investigated preinstruction ideas held by introductory astronomy (ASTRO 101 students at three participating universities and postinstruction ideas at one. Through thematic analysis of responses to questions on three survey forms and preinstruction interviews, we found that prior to instruction a significant fraction of students said the Universe is round. Students’ reasoning for this included that the Universe contains round objects, therefore it must also be round, or an incorrect idea that the big bang theory describes an explosion from a central point. We also found that a majority of students think that astronomers use the term curvature to describe properties, such as dimensions, angles, or size, of the Universe or objects in the Universe, or that astronomers use the term curvature to describe the bending of space due to gravity. Students are skeptical that the curvature of the Universe can be measured, to a greater or lesser degree depending on question framing. Postinstruction responses to a multiple-choice exam question and interviews at one university indicate that students are more likely to correctly respond that the Universe as a whole is not curved postinstruction, though the idea that the Universe is round still persists for some students. While we see no evidence that priming with an elliptical or rectangular map of the cosmic microwave background on a postinstruction exam affects responses, students do cite visualizations such as diagrams among the reasons for their responses in preinstruction surveys.
Torsion and curvature in higher dimensional supergravity theories
International Nuclear Information System (INIS)
Smith, A.W.; Pontificia Univ. Catolica do Rio de Janeiro
1983-01-01
This work is an extension of Dragon's theorems to higher dimensional space-time. It is shown that the first set of Bianchi identities allow us to express the curvature components in terms of torsion components and its covariant derivatives. It is also shown that the second set of Bianchi identities does not give any new information which is not already contained in the first one. (Author) [pt
Global and local curvature in density functional theory.
Zhao, Qing; Ioannidis, Efthymios I; Kulik, Heather J
2016-08-07
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Reflectionlessness, kurtosis and top curvature of potential barriers
International Nuclear Information System (INIS)
Ahmed, Zafar
2006-01-01
Apart from the rectangular barrier, other barriers having a single maximum generally display reflectivity, R(E), as a smoothly decreasing function of energy. We conjecture that symmetric potential barriers with a single maximum entail zeros or sharp minima in R(E) provided they have either their coefficient of kurtosis lying in the range (1.8, 3.0), or their top curvature as zero, or both
Curvature of super Diff(S1)/S1
International Nuclear Information System (INIS)
Oh, P.; Ramond, P.
1987-01-01
Motivated by the work of Bowick and Rajeev, we calculate the curvature of the infinite-dimensional flag manifolds Diff(S 1 )/S 1 and Super Diff(S 1 )/S 1 using standard finite-dimensional coset space techniques. We regularize the infinite by ζ-function regularization and recover the conformal and superconformal anomalies respectively for a specific choice of the torsion. (orig.)
ON THE CURVATURE OF DUST LANES IN GALACTIC BARS
International Nuclear Information System (INIS)
Comeron, Sebastien; MartInez-Valpuesta, Inma; Knapen, Johan H.; Beckman, John E.
2009-01-01
We test the theoretical prediction that the straightest dust lanes in bars are found in strongly barred galaxies, or more specifically, that the degree of curvature of the dust lanes is inversely proportional to the strength of the bar. The test uses archival images of barred galaxies for which a reliable nonaxisymmetric torque parameter (Q b ) and the radius at which Q b has been measured (r(Q b )) have been published in the literature. Our results confirm the theoretical prediction but show a large spread that cannot be accounted for by measurement errors. We simulate 238 galaxies with different bar and bulge parameters in order to investigate the origin of the spread in the dust lane curvature versus Q b relation. From these simulations, we conclude that the spread is greatly reduced when describing the bar strength as a linear combination of the bar parameters Q b and the quotient of the major and minor axes of the bar, a/b. Thus, we conclude that the dust lane curvature is predominantly determined by the parameters of the bar.
Curvature profiles as initial conditions for primordial black hole formation
International Nuclear Information System (INIS)
Polnarev, Alexander G; Musco, Ilia
2007-01-01
This work is part of an ongoing research programme to study possible primordial black hole (PBH) formation during the radiation-dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann-Robertson-Walker model, which are required for PBH formation. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity fields, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We present general analytic solutions for the density and velocity profiles. These solutions enable us to consider in a self-consistent way the formation of PBHs in a wide variety of cosmological situations with the cosmological fluid being treated as an arbitrary mixture of different components with different equations of state. We obtain the analytical solutions for the density and velocity profiles as functions of the initial time. We then use two different parametrizations for the curvature profile and follow numerically the evolution of initial configurations
Generic Properties of Curvature Sensing through Vision and Touch
Directory of Open Access Journals (Sweden)
Birgitta Dresp-Langley
2013-01-01
Full Text Available Generic properties of curvature representations formed on the basis of vision and touch were examined as a function of mathematical properties of curved objects. Virtual representations of the curves were shown on a computer screen for visual scaling by sighted observers (experiment 1. Their physical counterparts were placed in the two hands of blindfolded and congenitally blind observers for tactile scaling. The psychophysical data show that curvature representations in congenitally blind individuals, who never had any visual experience, and in sighted observers, who rely on vision most of the time, are statistically linked to the same mathematical properties of the curves. The perceived magnitude of object curvature, sensed through either vision or touch, is related by a mathematical power law, with similar exponents for the two sensory modalities, to the aspect ratio of the curves, a scale invariant geometric property. This finding supports biologically motivated models of sensory integration suggesting a universal power law for the adaptive brain control and balance of motor responses to environmental stimuli from any sensory modality.
Finger vein extraction using gradient normalization and principal curvature
Choi, Joon Hwan; Song, Wonseok; Kim, Taejeong; Lee, Seung-Rae; Kim, Hee Chan
2009-02-01
Finger vein authentication is a personal identification technology using finger vein images acquired by infrared imaging. It is one of the newest technologies in biometrics. Its main advantage over other biometrics is the low risk of forgery or theft, due to the fact that finger veins are not normally visible to others. Extracting finger vein patterns from infrared images is the most difficult part in finger vein authentication. Uneven illumination, varying tissues and bones, and changes in the physical conditions and the blood flow make the thickness and brightness of the same vein different in each acquisition. Accordingly, extracting finger veins at their accurate positions regardless of their thickness and brightness is necessary for accurate personal identification. For this purpose, we propose a new finger vein extraction method which is composed of gradient normalization, principal curvature calculation, and binarization. As local brightness variation has little effect on the curvature and as gradient normalization makes the curvature fairly uniform at vein pixels, our method effectively extracts finger vein patterns regardless of the vein thickness or brightness. In our experiment, the proposed method showed notable improvement as compared with the existing methods.
Berry Curvature and Nonlocal Transport Characteristics of Antidot Graphene
Directory of Open Access Journals (Sweden)
Jie Pan
2017-09-01
Full Text Available Antidot graphene denotes a monolayer of graphene structured by a periodic array of holes. Its energy dispersion is known to display a gap at the Dirac point. However, since the degeneracy between the A and B sites is preserved, antidot graphene cannot be described by the 2D massive Dirac equation, which is suitable for systems with an inherent A/B asymmetry. From inversion and time-reversal-symmetry considerations, antidot graphene should therefore have zero Berry curvature. In this work, we derive the effective Hamiltonian of antidot graphene from its tight-binding wave functions. The resulting Hamiltonian is a 4×4 matrix with a nonzero intervalley scattering term, which is responsible for the gap at the Dirac point. Furthermore, nonzero Berry curvature is obtained from the effective Hamiltonian, owing to the double degeneracy of the eigenfunctions. The topological manifestation is shown to be robust against randomness perturbations. Since the Berry curvature is expected to induce a transverse conductance, we have experimentally verified this feature through nonlocal transport measurements, by fabricating three antidot graphene samples with a triangular array of holes, a fixed periodicity of 150 nm, and hole diameters of 100, 80, and 60 nm. All three samples display topological nonlocal conductance, with excellent agreement with the theory predictions.
Curvature-driven instabilities in the Elmo Bumpy Torus (EBT)
International Nuclear Information System (INIS)
Abe, H.; Spong, D.A.; Antonsen, T.M. Jr.; Tsang, K.T.; Nguyen, K.T.
1982-01-01
Curvature-driven instabilities are analyzed for an EBT configuration which consists of plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic (MHD) theory. Stability criteria are obtained for five possible modes: the conventional hot electron interchange, a high-frequency hot electron interchange (at frequencies greater than the ion-cyclotron frequency), a compressional instability, a background plasma interchange, and an interacting pressure-driven interchange. A wide parameter regime for stable operation is found, which, however, severely deteriorates for a band of intermediate mode numbers. Finite Larmor radius effects can eliminate this deterioration; moreover, all short-wavelength curvature-driven modes are stabilized if the hot electron Larmor radius rho/sub h/ satisfies (kappa/sub perpendicular/rho/sub h/) 2 > 2Δ/[Rβ/sub h/(1 + P'/sub parallel//P'/sub perpendicular/)], where kappa/sub perpendicular/ is the transverse wavenumber, Δ is the ring half-width, R is the mid-plane radius of curvature, β/sub h/ is the hot electron beta value, and P' is the pressure gradient. Resonant wave-particle instabilities predicted by a new low frequency variational principle show that a variety of remnant instabilities may still persist
Factors affecting root curvature of mandibular first molar
International Nuclear Information System (INIS)
Choi, Hang Moon; Yi, Won Jin; Heo, Min Suk; Kim, Jung Hwa; Choi, Soon Chul; Park, Tae Won
2006-01-01
To find the cause of root curvature by use of panoramic and lateral cephalometric radiograph. Twenty six 1st graders whose mandibular 1st molars just emerged into the mouth were selected. Panoramic and lateral cephalometric radiograph were taken at grade 1 and 6, longitudinally. In cephalometric radio graph, mandibular plane angle, ramus-occlusal place angle, gonial angle, and gonion-gnathion distance(Go-Gn distance) were measured. In panoramic radiograph, elongated root length and root angle were measured by means of digital subtraction radiography. Occlusal plane-tooth axis angle was measured, too. Pearson correlations were used to evaluate the relationships between root curvature and elongated length and longitudinal variations of all variables. Multiple regression equation using related variables was computed. The pearson correlation coefficient between curved angle and longitudinal variations of occlusal plane-tooth axis angle and ramus-occlusal plane angle was 0.350 and 0.401, respectively (p 1 +0.745X 2 (Y: root angle, X 1 : variation of occlusal plane-tooth axis angle, X 2 : variation of ramus-occlusal plane angle). It was suspected that the reasons of root curvature were change of tooth axis caused by contact with 2nd deciduous tooth and amount of mesial and superior movement related to change of occlusal plane
Favaro, Alberto; Lad, Akash; Formenti, Davide; Zani, Davide Danilo; De Momi, Elena
2017-03-01
In a translational neuroscience/neurosurgery perspective, sheep are considered good candidates to study because of the similarity between their brain and the human one. Automatic planning systems for safe keyhole neurosurgery maximize the probe/catheter distance from vessels and risky structures. This work consists in the development of a trajectories planner for straight catheters placement intended to be used for investigating the drug diffusivity mechanisms in sheep brain. Automatic brain segmentation of gray matter, white matter and cerebrospinal fluid is achieved using an online available sheep atlas. Ventricles, midbrain and cerebellum segmentation have been also carried out. The veterinary surgeon is asked to select a target point within the white matter to be reached by the probe and to define an entry area on the brain cortex. To mitigate the risk of hemorrhage during the insertion process, which can prevent the success of the insertion procedure, the trajectory planner performs a curvature analysis of the brain cortex and wipes out from the poll of possible entry points the sulci, as part of brain cortex where superficial blood vessels are naturally located. A limited set of trajectories is then computed and presented to the surgeon, satisfying an optimality criteria based on a cost function which considers the distance from critical brain areas and the whole trajectory length. The planner proved to be effective in defining rectilinear trajectories accounting for the safety constraints determined by the brain morphology. It also demonstrated a short computational time and good capability in segmenting gyri and sulci surfaces.
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Wisneski, Kimberly J; Johnson, Michelle J
2007-03-23
Robotic therapy is at the forefront of stroke rehabilitation. The Activities of Daily Living Exercise Robot (ADLER) was developed to improve carryover of gains after training by combining the benefits of Activities of Daily Living (ADL) training (motivation and functional task practice with real objects), with the benefits of robot mediated therapy (repeatability and reliability). In combining these two therapy techniques, we seek to develop a new model for trajectory generation that will support functional movements to real objects during robot training. We studied natural movements to real objects and report on how initial reaching movements are affected by real objects and how these movements deviate from the straight line paths predicted by the minimum jerk model, typically used to generate trajectories in robot training environments. We highlight key issues that to be considered in modelling natural trajectories. Movement data was collected as eight normal subjects completed ADLs such as drinking and eating. Three conditions were considered: object absent, imagined, and present. This data was compared to predicted trajectories generated from implementing the minimum jerk model. The deviations in both the plane of the table (XY) and the sagittal plane of torso (XZ) were examined for both reaches to a cup and to a spoon. Velocity profiles and curvature were also quantified for all trajectories. We hypothesized that movements performed with functional task constraints and objects would deviate from the minimum jerk trajectory model more than those performed under imaginary or object absent conditions. Trajectory deviations from the predicted minimum jerk model for these reaches were shown to depend on three variables: object presence, object orientation, and plane of movement. When subjects completed the cup reach their movements were more curved than for the spoon reach. The object present condition for the cup reach showed more curvature than in the object
Directory of Open Access Journals (Sweden)
Wisneski Kimberly J
2007-03-01
Full Text Available Abstract Background Robotic therapy is at the forefront of stroke rehabilitation. The Activities of Daily Living Exercise Robot (ADLER was developed to improve carryover of gains after training by combining the benefits of Activities of Daily Living (ADL training (motivation and functional task practice with real objects, with the benefits of robot mediated therapy (repeatability and reliability. In combining these two therapy techniques, we seek to develop a new model for trajectory generation that will support functional movements to real objects during robot training. We studied natural movements to real objects and report on how initial reaching movements are affected by real objects and how these movements deviate from the straight line paths predicted by the minimum jerk model, typically used to generate trajectories in robot training environments. We highlight key issues that to be considered in modelling natural trajectories. Methods Movement data was collected as eight normal subjects completed ADLs such as drinking and eating. Three conditions were considered: object absent, imagined, and present. This data was compared to predicted trajectories generated from implementing the minimum jerk model. The deviations in both the plane of the table (XY and the saggital plane of torso (XZ were examined for both reaches to a cup and to a spoon. Velocity profiles and curvature were also quantified for all trajectories. Results We hypothesized that movements performed with functional task constraints and objects would deviate from the minimum jerk trajectory model more than those performed under imaginary or object absent conditions. Trajectory deviations from the predicted minimum jerk model for these reaches were shown to depend on three variables: object presence, object orientation, and plane of movement. When subjects completed the cup reach their movements were more curved than for the spoon reach. The object present condition for the cup
Classical models for Regge trajectories
International Nuclear Information System (INIS)
Biedenharn, L.C.; Van Dam, H.; Marmo, G.; Morandi, G.; Mukunda, N.; Samuel, J.; Sudarshan, E.C.G.
1987-01-01
Two classical models for particles with internal structure and which describe Regge trajectories are developed. The remarkable geometric and other properties of the two internal spaces are highlighted. It is shown that the conditions of positive time-like four-velocity and energy momentum for the classical system imply strong and physically reasonable conditions on the Regge mass-spin relationship
Classical Trajectories and Quantum Spectra
Mielnik, Bogdan; Reyes, Marco A.
1996-01-01
A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.
Visiting Vehicle Ground Trajectory Tool
Hamm, Dustin
2013-01-01
The International Space Station (ISS) Visiting Vehicle Group needed a targeting tool for vehicles that rendezvous with the ISS. The Visiting Vehicle Ground Trajectory targeting tool provides the ability to perform both realtime and planning operations for the Visiting Vehicle Group. This tool provides a highly reconfigurable base, which allows the Visiting Vehicle Group to perform their work. The application is composed of a telemetry processing function, a relative motion function, a targeting function, a vector view, and 2D/3D world map type graphics. The software tool provides the ability to plan a rendezvous trajectory for vehicles that visit the ISS. It models these relative trajectories using planned and realtime data from the vehicle. The tool monitors ongoing rendezvous trajectory relative motion, and ensures visiting vehicles stay within agreed corridors. The software provides the ability to update or re-plan a rendezvous to support contingency operations. Adding new parameters and incorporating them into the system was previously not available on-the-fly. If an unanticipated capability wasn't discovered until the vehicle was flying, there was no way to update things.
Controlling X-ray beam trajectory with a flexible hollow glass fibre
Energy Technology Data Exchange (ETDEWEB)
Tanaka, Yoshihito, E-mail: yotanaka@riken.jp [RIKEN, 1-1-1 Kouto, Sayo-cho, Hyogo 679-5148 (Japan); Kwansei Gakuin University, Gakuen, Sanda, Hyogo 669-1337 (Japan); Nakatani, Takashi; Onitsuka, Rena [Kwansei Gakuin University, Gakuen, Sanda, Hyogo 669-1337 (Japan); Sawada, Kei [RIKEN, 1-1-1 Kouto, Sayo-cho, Hyogo 679-5148 (Japan); Takahashi, Isao [Kwansei Gakuin University, Gakuen, Sanda, Hyogo 669-1337 (Japan)
2014-01-01
X-ray beam trajectory control has been performed by using a 1.5 m-long flexible hollow glass fibre. A two-dimensional scan of a synchrotron radiation beam was demonstrated for X-ray absorption mapping. A metre-length flexible hollow glass fibre with 20 µm-bore and 1.5 mm-cladding diameters for transporting a synchrotron X-ray beam and controlling the trajectory has been examined. The large cladding diameter maintains a moderate curvature to satisfy the shallow glancing angle of total reflection. The observed transmission efficiency was more than 20% at 12.4 keV. As a demonstration, a wide-area scan of a synchrotron radiation beam was performed to identify the elements for a fixed metal film through its absorption spectra.
Holonomy Attractor Connecting Spaces of Different Curvature Responsible for ``Anomalies''
Binder, Bernd
2009-03-01
In this lecture paper we derive Magic Angle Precession (MAP) from first geometric principles. MAP can arise in situations, where precession is multiply related to spin, linearly by time or distance (dynamic phase, rolling, Gauss law) and transcendentally by the holonomy loop path (geometric phase). With linear spin-precession coupling, gyroscopes can be spun up and down to very high frequencies via low frequency holonomy control induced by external accelerations, which provides for extreme coupling strengths or "anomalies" that can be tested by the powerball or gyrotwister device. Geometrically, a gyroscopic manifold with spherical metric is tangentially aligned to a precession wave channel with conic or hyperbolic metric (like the relativistic Thomas precession). Transporting triangular spin/precession vector relations across the tangential boundary of contact with SO(3) Lorentz symmetry, we get extreme vector currents near the attractor fixed points in precession phase space, where spin currents remain intact while crossing the contact boundaries between regions of different curvature signature (-1, 0, +1). The problem can be geometrically solved by considering a curvature invariant triangular condition, which holds on surfaces with different curvature that are in contact and locally parallel. In this case two out of three angles are identical, whereas the third angle is different due to holonomy. If we require that the side length ratio corresponding to these angles are invariant we get a geodesic chaotic attractor, which is a cosine map cos(x)˜Mx in parameter space providing for fixed points, limit cycle bifurcations, and singularities. The situation could be quite natural and common in the context of vector currents in curved spacetime and gauge theories. MAP could even be part of the electromagnetic interaction, where the electric charge is the geometric U(1) precession spin current and gauge potential with magnetic effects given by extra rotations under the
An Improved Method to Measure the Cosmic Curvature
Energy Technology Data Exchange (ETDEWEB)
Wei, Jun-Jie; Wu, Xue-Feng, E-mail: jjwei@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)
2017-04-01
In this paper, we propose an improved model-independent method to constrain the cosmic curvature by combining the most recent Hubble parameter H ( z ) and supernovae Ia (SNe Ia) data. Based on the H ( z ) data, we first use the model-independent smoothing technique, Gaussian processes, to construct a distance modulus μ {sub H} ( z ), which is susceptible to the cosmic curvature parameter Ω{sub k}. In contrary to previous studies, the light-curve-fitting parameters, which account for the distance estimation of SN (μ {sub SN}( z )), are set free to investigate whether Ω {sub k} has a dependence on them. By comparing μ {sub H} ( z ) to μ {sub SN}(z), we put limits on Ω {sub k}. Our results confirm that Ω {sub k} is independent of the SN light-curve parameters. Moreover, we show that the measured Ω {sub k} is in good agreement with zero cosmic curvature, implying that there is no significant deviation from a flat universe at the current observational data level. We also test the influence of different H(z) samples and different Hubble constant H {sub 0} values, finding that different H(z) samples do not have a significant impact on the constraints. However, different H {sub 0} priors can affect the constraints of Ω {sub k} to some degree. The prior of H {sub 0} = 73.24 ± 1.74 km s{sup −1} Mpc{sup −1} gives a value of Ω {sub k}, a little bit above the 1 σ confidence level away from 0, but H{sub 0} = 69.6 ± 0.7 km s{sup −1} Mpc{sup −1} gives it below 1 σ .
A Japanese Stretching Intervention Can Modify Lumbar Lordosis Curvature.
Kadono, Norio; Tsuchiya, Kazushi; Uematsu, Azusa; Kamoshita, Hiroshi; Kiryu, Kazunori; Hortobágyi, Tibor; Suzuki, Shuji
2017-08-01
Eighteen healthy male adults were assigned to either an intervention or control group. Isogai dynamic therapy (IDT) is one of Japanese stretching interventions and has been practiced for over 70 years. However, its scientific quantitative evidence remains unestablished. The objective of this study was to determine whether IDT could modify lumbar curvature in healthy young adults compared with stretching exercises used currently in clinical practice. None of previous studies have provided data that conventional stretching interventions could modify spinal curvatures. However, this study provides the first evidence that a specific form of a Japanese stretching intervention can acutely modify the spinal curvatures. We compared the effects of IDT, a Japanese stretching intervention (n=9 males), with a conventional stretching routine (n=9 males) used widely in clinics to modify pelvic tilt and lumbar lordosis (LL) angle. We measured thoracic kyphosis (TK) and LL angles 3 times during erect standing using the Spinal Mouse before and after each intervention. IDT consisted of: (1) hip joint correction, (2) pelvic tilt correction, (3) lumbar alignment correction, and (4) squat exercise stretch. The control group performed hamstring stretches while (1) standing and (2) sitting. IDT increased LL angle to 25.1 degrees (±5.9) from 21.2 degrees (±6.9) (P=0.047) without changing TK angle (pretest: 36.8 degrees [±6.9]; posttest: 36.1 degrees [±6.5]) (P=0.572). The control group showed no changes in TK (P=0.819) and LL angles (P=0.744). IDT can thus be effective for increasing LL angle, hence anterior pelvic tilt. Such modifications could ameliorate low back pain and improve mobility in old adults with an unfavorable pelvic position.
Curvature fluctuations as progenitors of large scale holes
International Nuclear Information System (INIS)
Vittorio, N.; Santangelo, P.; Occhionero, F.
1984-01-01
The authors extend previous work to study the formation and evolution of deep holes, under the assumption that they arise from curvature or energy perturbations in the Hubble flow. Their algorithm, which makes use of the spherically symmetric and pressureless Tolman-Bondi solution, can embed a perturbation in any cosmological background. After recalling previous results on the central depth of the hole and its radial dimension, they give here specific examples of density and peculiar velocity profiles, which may have a bearing on whether galaxy formation is a dissipative or dissipationless process. (orig.)
Curvature effect on tearing modes in presence of neoclassical friction
Energy Technology Data Exchange (ETDEWEB)
Maget, Patrick; Mellet, Nicolas; Meshcheriakov, Dmytro; Garbet, Xavier [CEA, IRFM, F-13108 Saint Paul-lez-Durance (France); Lütjens, Hinrich [Centre de Physique Théorique, Ecole Polytechnique, CNRS (France)
2013-11-15
Neoclassical physics (here associated to the poloidal variation of the magnetic field strength along field lines in a tokamak) is well known for driving self-generated plasma current and nonlinear magnetic islands associated to it in high performance, ITER relevant plasma discharges. It is demonstrated that the neoclassical friction between a magnetic perturbation and plasma flow already impacts magnetic islands in the linear regime, by inducing a weakening of curvature stabilization for tearing modes. This conclusion holds in particular for regimes where convection is influencing the pressure dynamics, as shown using a simple analytical model and confirmed in full Magneto-Hydro-Dynamics simulations.
The natural selection of metabolism explains curvature in allometric scaling
Witting, Lars
2016-01-01
I simulate the evolution of metabolism and mass to explain the curvature in the metabolic allometry for placental and marsupial mammals. I assume that the release of inter-specific competition by the extinction of dinosaurs 65 million years ago made it possible for each clade to diversity into a multitude of species across a wide range of niches. The natural selection of metabolism and mass was then fitted to explain the maximum observed body masses over time, as well as the current inter-spe...
The evolution of space curves by curvature and torsion
International Nuclear Information System (INIS)
Richardson, G; King, J R
2002-01-01
We apply Lie group based similarity methods to the study of a new, and widely relevant, class of objects, namely motions of a space curve. In particular, we consider the motion of a curve evolving with a curvature κ and torsion τ dependent velocity law. We systematically derive the Lie point symmetries of all such laws of motion and use these to catalogue all their possible similarity reductions. This calculation reveals special classes of law with high degrees of symmetry (and a correspondingly large number of similarity reductions). Of particular note is one class which is invariant under general linear transformations in space. This has potential applications in pattern and signal recognition
Rigid particle revisited: Extrinsic curvature yields the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, Alexei, E-mail: alexei.deriglazov@ufjf.edu.br [Depto. de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian St., Yerevan 0025 (Armenia); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation)
2014-03-01
We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation. -- Highlights: •New way of canonical quantization of relativistic rigid particle is proposed. •Quantization made in terms of so(3.2) angular momentum algebra. •Quantization yields massive Dirac equation.
Field equations for gravity quadratic in the curvature
International Nuclear Information System (INIS)
Rose, B.
1992-01-01
Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs
2008 ULTRASONIC BENCHMARK STUDIES OF INTERFACE CURVATURE--A SUMMARY
International Nuclear Information System (INIS)
Schmerr, L. W.; Huang, R.; Raillon, R.; Mahaut, S.; Leymarie, N.; Lonne, S.; Song, S.-J.; Kim, H.-J.; Spies, M.; Lupien, V.
2009-01-01
In the 2008 QNDE ultrasonic benchmark session researchers from five different institutions around the world examined the influence that the curvature of a cylindrical fluid-solid interface has on the measured NDE immersion pulse-echo response of a flat-bottom hole (FBH) reflector. This was a repeat of a study conducted in the 2007 benchmark to try to determine the sources of differences seen in 2007 between model-based predictions and experiments. Here, we will summarize the results obtained in 2008 and analyze the model-based results and the experiments.
Trajectories of delinquency and parenting styles
Hoeve, M.; van Blokland, A.; Dubas, J.S.; Loeber, R; Gerris, J.R.M.; van der Laan, P.H.
2008-01-01
We investigated trajectories of adolescent delinquent development using data from the Pittsburgh Youth Study and examined the extent to which these different trajectories are differentially predicted by childhood parenting styles. Based on self-reported and official delinquency seriousness, covering
Trajectories of Delinquency and Parenting Styles
Hoeve, M.; Blokland, A.A.J.; Dubas, J.S.; Loeber, R.; Gerris, J.R.M.; Laan, P.H. van der
2008-01-01
We investigated trajectories of adolescent delinquent development using data from the Pittsburgh Youth Study and examined the extent to which these different trajectories are differentially predicted by childhood parenting styles. Based on self-reported and official delinquency seriousness, covering
User Oriented Trajectory Search for Trip Recommendation
Ding, Ruogu
2012-01-01
Trajectory sharing and searching have received significant attention in recent years. In this thesis, we propose and investigate the methods to find and recommend the best trajectory to the traveler, and mainly focus on a novel technique named User
Efficient Trajectory Options Allocation for the Collaborative Trajectory Options Program
Rodionova, Olga; Arneson, Heather; Sridhar, Banavar; Evans, Antony
2017-01-01
The Collaborative Trajectory Options Program (CTOP) is a Traffic Management Initiative (TMI) intended to control the air traffic flow rates at multiple specified Flow Constrained Areas (FCAs), where demand exceeds capacity. CTOP allows flight operators to submit the desired Trajectory Options Set (TOS) for each affected flight with associated Relative Trajectory Cost (RTC) for each option. CTOP then creates a feasible schedule that complies with capacity constraints by assigning affected flights with routes and departure delays in such a way as to minimize the total cost while maintaining equity across flight operators. The current version of CTOP implements a Ration-by-Schedule (RBS) scheme, which assigns the best available options to flights based on a First-Scheduled-First-Served heuristic. In the present study, an alternative flight scheduling approach is developed based on linear optimization. Results suggest that such an approach can significantly reduce flight delays, in the deterministic case, while maintaining equity as defined using a Max-Min fairness scheme.
Directory of Open Access Journals (Sweden)
Yin Song
2014-12-01
Full Text Available Though the importance of curvature continuity on compressor blade performances has been realized, there are two major questions that need to be solved, i.e., the respective effects of curvature continuity at the leading-edge blend point and the main surface, and the contradiction between the traditional theory and experimental observations in the effect of those novel leading-edge shapes with smaller curvature discontinuity and sharper nose. In this paper, an optimization method to design continuous-curvature blade profiles which deviate little from datum blades is proposed, and numerical and theoretical analysis is carried out to investigate the continuous-curvature effect on blade performances. The results show that the curvature continuity at the leading-edge blend point helps to eliminate the separation bubble, thus improving the blade performance. The main-surface curvature continuity is also beneficial, although its effects are much smaller than those of the blend-point curvature continuity. Furthermore, it is observed that there exist two factors controlling the leading-edge spike, i.e., the curvature discontinuity at the blend point which dominates at small incidences, and the nose curvature which dominates at large incidences. To the authors’ knowledge, such mechanisms have not been reported before, and they can help to solve the sharp-leading-edge paradox.
Aircraft 4D trajectories planning under uncertainties
Chaimatanan , Supatcha; Delahaye , Daniel; Mongeau , Marcel
2015-01-01
International audience; To sustain the rapidly increasing air traffic demand, the future air traffic management system will rely on a concept, called Trajectory-Based Operations (TBO), that will require aircraft to follow an assigned 4D trajectory (time-constrained trajectory) with high precision. TBO involves separating aircraft via strategic (long-term) trajectory deconfliction rather than the currently-practicing tactical (short-term) conflict resolution. In this context, this paper presen...
Effect of Plate Curvature on Blast Response of Structural Steel Plates
Veeredhi, Lakshmi Shireen Banu; Ramana Rao, N. V.; Veeredhi, Vasudeva Rao
2018-04-01
In the present work an attempt is made, through simulation studies, to determine the effect of plate curvature on the blast response of a door structure made of ASTM A515 grade 50 steel plates. A door structure with dimensions of 5.142 m × 2.56 m × 10 mm having six different radii of curvatures is analyzed which is subjected to blast load. The radii of curvature investigated are infinity (flat plate), 16.63, 10.81, 8.26, 6.61 and 5.56 m. In the present study, a stand-off distance of 11 m is considered for all the cases. Results showed that the door structure with smallest radius of curvature experienced least plastic deformation and yielding when compared to a door with larger radius of curvature with same projected area. From the present Investigation, it is observed that, as the radius of curvature of the plate increases, the deformation mode gradually shifts from indentation mode to flexural mode. The plates with infinity and 16.63 m radius of curvature have undergone flexural mode of deformation and plates with 6.61 and 5.56 m radius of curvature undergo indentation mode of deformation. Whereas, mixed mode of deformation that consists of both flexural and indentation mode of deformations are seen in the plates with radius of curvature 10.81 and 8.26 m. As the radius of curvature of the plate decreases the ability of the plate to mitigate the effect the blast loads increased. It is observed that the plate with smaller radius of curvature deflects most of the blast energy and results in least indentation mode of deformation. The most significant observation made in the present investigation is that the strain energy absorbed by the steel plate gets reduced to 1/3 rd when the radius of curvature is approximately equal to the stand-off distance which could be the critical radius of curvature.
Towards Efficient Search for Activity Trajectories
DEFF Research Database (Denmark)
Zheng, Kai; Shang, Shuo; Yuan, Jing
2013-01-01
, recent proliferation in location-based web applications (e.g., Foursquare, Facebook) has given rise to large amounts of trajectories associated with activity information, called activity trajectory. In this paper, we study the problem of efficient similarity search on activity trajectory database. Given...
Methods for control over learning individual trajectory
Mitsel, A. A.; Cherniaeva, N. V.
2015-09-01
The article discusses models, methods and algorithms of determining student's optimal individual educational trajectory. A new method of controlling the learning trajectory has been developed as a dynamic model of learning trajectory control, which uses score assessment to construct a sequence of studied subjects.
Memory for curvature of objects: haptic touch vs. vision.
Ittyerah, Miriam; Marks, Lawrence E
2007-11-01
The present study examined the role of vision and haptics in memory for stimulus objects that vary along the dimension of curvature. Experiment 1 measured haptic-haptic (T-T) and haptic-visual (T-V) discrimination of curvature in a short-term memory paradigm, using 30-second retention intervals containing five different interpolated tasks. Results showed poorest performance when the interpolated tasks required spatial processing or movement, thereby suggesting that haptic information about shape is encoded in a spatial-motor representation. Experiment 2 compared visual-visual (V-V) and visual-haptic (V-T) short-term memory, again using 30-second delay intervals. The results of the ANOVA failed to show a significant effect of intervening activity. Intra-modal visual performance and cross-modal performance were similar. Comparing the four modality conditions (inter-modal V-T, T-V; intra-modal V-V, T-T, by combining the data of Experiments 1 and 2), in a global analysis, showed a reliable interaction between intervening activity and experiment (modality). Although there appears to be a general tendency for spatial and movement activities to exert the most deleterious effects overall, the patterns are not identical when the initial stimulus is encoded haptically (Experiment 1) and visually (Experiment 2).
Characterizing Suspension Plasma Spray Coating Formation Dynamics through Curvature Measurements
Chidambaram Seshadri, Ramachandran; Dwivedi, Gopal; Viswanathan, Vaishak; Sampath, Sanjay
2016-12-01
Suspension plasma spraying (SPS) enables the production of variety of microstructures with unique mechanical and thermal properties. In SPS, a liquid carrier (ethanol/water) is used to transport the sub-micrometric feedstock into the plasma jet. Considering complex deposition dynamics of SPS technique, there is a need to better understand the relationships among spray conditions, ensuing particle behavior, deposition stress evolution and resultant properties. In this study, submicron yttria-stabilized zirconia particles suspended in ethanol were sprayed using a cascaded arc plasma torch. The stresses generated during the deposition of the layers (termed evolving stress) were monitored via the change in curvature of the substrate measured using an in situ measurement apparatus. Depending on the deposition conditions, coating microstructures ranged from feathery porous to dense/cracked deposits. The evolving stresses and modulus were correlated with the observed microstructures and visualized via process maps. Post-deposition bi-layer curvature measurement via low temperature thermal cycling was carried out to quantify the thermo-elastic response of different coatings. Lastly, preliminary data on furnace cycle durability of different coating microstructures were evaluated. This integrated study involving in situ diagnostics and ex situ characterization along with process maps provides a framework to describe coating formation mechanisms, process parametrics and microstructure description.
Constant curvature algebras and higher spin action generating functions
International Nuclear Information System (INIS)
Hallowell, K.; Waldron, A.
2005-01-01
The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R)-bar R 2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for the actions and gauge invariances of massive, partially massless and massless (for both Bose and Fermi statistics) higher spins on constant curvature backgrounds. These are formulated in terms of a minimal set of covariant, unconstrained, fields rather than towers of auxiliary fields. Partially massless gauge transformations are shown to arise as degeneracies of the flat, massless gauge transformation in one dimension higher. Moreover, our results and calculus offer a considerable simplification over existing techniques for handling higher spins. In particular, we show how theories of arbitrary spin in dimension d can be rewritten in terms of a single scalar field in dimension 2d where the d additional dimensions correspond to coordinate differentials. We also develop an analogous framework for spinor-tensor fields in terms of the corresponding superalgebra
Limited capacity for contour curvature in iconic memory.
Sakai, Koji
2006-06-01
We measured the difference threshold for contour curvature in iconic memory by using the cued discrimination method. The study stimulus consisting of 2 to 6 curved contours was briefly presented in the fovea, followed by two lines as cues. Subjects discriminated the curvature of two cued curves. The cue delays were 0 msec. and 300 msec. in Exps. 1 and 2, respectively, and 50 msec. before the study offset in Exp. 3. Analysis of data from Exps. 1 and 2 showed that the Weber fraction rose monotonically with the increase in set size. Clear set-size effects indicate that iconic memory has a limited capacity. Moreover, clear set-size effect in Exp. 3 indicates that perception itself has a limited capacity. Larger set-size effects in Exp. 1 than in Exp. 3 suggest that iconic memory after perceptual process has limited capacity. These properties of iconic memory at threshold level are contradictory to the traditional view that iconic memory has a high capacity both at suprathreshold and categorical levels.
Nonlinear quantum gravity on the constant mean curvature foliation
International Nuclear Information System (INIS)
Wang, Charles H-T
2005-01-01
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analysed as nonlinear quantum minisuperspaces in the context of the proposed theory
Conversion of radius of curvature to power (and vice versa)
Wickenhagen, Sven; Endo, Kazumasa; Fuchs, Ulrike; Youngworth, Richard N.; Kiontke, Sven R.
2015-09-01
Manufacturing optical components relies on good measurements and specifications. One of the most precise measurements routinely required is the form accuracy. In practice, form deviation from the ideal surface is effectively low frequency errors, where the form error most often accounts for no more than a few undulations across a surface. These types of errors are measured in a variety of ways including interferometry and tactile methods like profilometry, with the latter often being employed for aspheres and general surface shapes such as freeforms. This paper provides a basis for a correct description of power and radius of curvature tolerances, including best practices and calculating the power value with respect to the radius deviation (and vice versa) of the surface form. A consistent definition of the sagitta is presented, along with different cases in manufacturing that are of interest to fabricators and designers. The results make clear how the definitions and results should be documented, for all measurement setups. Relationships between power and radius of curvature are shown that allow specifying the preferred metric based on final accuracy and measurement method. Results shown include all necessary equations for conversion to give optical designers and manufacturers a consistent and robust basis for decision-making. The paper also gives guidance on preferred methods for different scenarios for surface types, accuracy required, and metrology methods employed.
DEFF Research Database (Denmark)
Axén, Iben; Leboeuf-Yde, Charlotte
2013-01-01
Low back pain is not a self-limiting problem, but rather a recurrent and sometimes persistent disorder. To understand the course over time, detailed investigation, preferably using repeated measurements over extended periods of time, is needed. New knowledge concerning short-term trajectories...... indicates that the low back pain 'episode' is short lived, at least in the primary care setting, with most patients improving. Nevertheless, in the long term, low back pain often runs a persistent course with around two-thirds of patients estimated to be in pain after 12 months. Some individuals never have...... low back pain, but most have it on and off or persistently. Thus, the low back pain 'condition' is usually a lifelong experience. However, subgroups of patients with different back pain trajectories have been identified and linked to clinical parameters. Further investigation is warranted...
Ion trajectories quadrupole mass filters
International Nuclear Information System (INIS)
Ursu, D.; Lupsa, N.; Muntean, F.
1994-01-01
The present paper aims at bringing some contributions to the understanding of ion motion in quadrupole mass filters. The theoretical treatment of quadrupole mass filter is intended to be a concise derivation of the important physical relationships using Mathieu functions. A simple iterative method of numerical computation has been used to simulate ion trajectories in an ideal quadrupole field. Finally, some examples of calculation are presented with the aid of computer graphics. (Author) 14 Figs., 1 Tab., 20 Refs
Interference, reduced action, and trajectories
Floyd, Edward R.
2006-01-01
Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichroma...
Identification of digitized particle trajectories
Grote, H; Lassalle, J C; Zanella, P
1973-01-01
High-energy Physics Laboratories make increasing use of particle detectors which directly produce digital measurements of trajectories at very high rates. Data collected in vast amounts during experiments are then analysed by computer programs whose first task is the recognition of tracks and reconstruction of the interesting events. This paper discusses the applicability of various Pattern Recognition approaches. Examples are given of the problems and the practical achievements in this field.
Observational constraints on dark energy and cosmic curvature
International Nuclear Information System (INIS)
Wang Yun; Mukherjee, Pia
2007-01-01
Current observational bounds on dark energy depend on our assumptions about the curvature of the universe. We present a simple and efficient method for incorporating constraints from cosmic microwave background (CMB) anisotropy data and use it to derive constraints on cosmic curvature and dark energy density as a free function of cosmic time using current CMB, Type Ia supernova (SN Ia), and baryon acoustic oscillation data. We show that there are two CMB shift parameters, R≡√(Ω m H 0 2 )r(z CMB ) (the scaled distance to recombination) and l a ≡πr(z CMB )/r s (z CMB ) (the angular scale of the sound horizon at recombination), with measured values that are nearly uncorrelated with each other. Allowing nonzero cosmic curvature, the three-year WMAP (Wilkinson Microwave Anisotropy Probe) data give R=1.71±0.03, l a =302.5±1.2, and Ω b h 2 =0.02173±0.00082, independent of the dark energy model. The corresponding bounds for a flat universe are R=1.70±0.03, l a =302.2±1.2, and Ω b h 2 =0.022±0.00082. We give the covariance matrix of (R,l a ,Ω b h 2 ) from the three-year WMAP data. We find that (R,l a ,Ω b h 2 ) provide an efficient and intuitive summary of CMB data as far as dark energy constraints are concerned. Assuming the Hubble Space Telescope (HST) prior of H 0 =72±8 (km/s) Mpc -1 , using 182 SNe Ia (from the HST/GOODS program, the first year Supernova Legacy Survey, and nearby SN Ia surveys), (R,l a ,Ω b h 2 ) from WMAP three-year data, and SDSS (Sloan Digital Sky Survey) measurement of the baryon acoustic oscillation scale, we find that dark energy density is consistent with a constant in cosmic time, with marginal deviations from a cosmological constant that may reflect current systematic uncertainties or true evolution in dark energy. A flat universe is allowed by current data: Ω k =-0.006 -0.012-0.025 +0.013+0.025 for assuming that the dark energy equation of state w X (z) is constant, and Ω k =-0.002 -0.018-0.032 +0.018+0.041 for w X (z
Effect of nano-scale curvature on the intrinsic blood coagulation system
Kushida, Takashi; Saha, Krishnendu; Subramani, Chandramouleeswaran; Nandwana, Vikas; Rotello, Vincent M.
2014-11-01
The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation `silent' surface, while nanoparticles with lower surface curvature show denaturation and concomitant coagulation.The intrinsic coagulation activity of silica nanoparticles strongly depends on their surface curvature. Nanoparticles with higher surface curvature do not denature blood coagulation factor XII on its surface, providing a coagulation `silent' surface, while nanoparticles with lower surface curvature show denaturation and concomitant coagulation. Electronic supplementary information (ESI) available: Physical properties and scanning electron micrographs (SEM) of silica NPs, intrinsic coagulation activity after 3 h. See DOI: 10.1039/c4nr04128c
Quantifying the Relationship Between Curvature and Electric Potential in Lipid Bilayers
DEFF Research Database (Denmark)
Bruhn, Dennis Skjøth; Lomholt, Michael Andersen; Khandelia, Himanshu
2016-01-01
Cellular membranes mediate vital cellular processes by being subject to curvature and transmembrane electrical potentials. Here we build upon the existing theory for flexoelectricity in liquid crystals to quantify the coupling between lipid bilayer curvature and membrane potentials. Using molecular...... dynamics simulations, we show that head group dipole moments, the lateral pressure profile across the bilayer and spontaneous curvature all systematically change with increasing membrane potentials. In particu- lar, there is a linear dependence between the bending moment (the product of bending rigidity...
Wasnik, Vaibhav; Wingreen, Ned; Mukhopadhyay, Ranjan
2012-02-01
Recent experiments suggest that in the bacterium, B. subtilis, the cue for the localization of small sporulation protein, SpoVM, that plays a central role in spore coat formation, is curvature of the bacterial plasma membrane. This curvature-dependent localization is puzzling given the orders of magnitude difference in lengthscale of an individual protein and radius of curvature of the membrane. Here we develop a minimal model to study the relationship between curvature-dependent membrane absorption of SpoVM and clustering of membrane-associated SpoVM and compare our results with experiments.
Measurement of curvature and twist of a deformed object using digital holography
International Nuclear Information System (INIS)
Chen Wen; Quan Chenggen; Cho Jui Tay
2008-01-01
Measurement of curvature and twist is an important aspect in the study of object deformation. In recent years, several methods have been proposed to determine curvature and twist of a deformed object using digital shearography. Here we propose a novel method to determine the curvature and twist of a deformed object using digital holography and a complex phasor. A sine/cosine transformation method and two-dimensional short time Fourier transform are proposed subsequently to process the wrapped phase maps. It is shown that high-quality phase maps corresponding to curvature and twist can be obtained. An experiment is conducted to demonstrate the validity of the proposed method
Directory of Open Access Journals (Sweden)
Carlo Ciulla
2015-11-01
Full Text Available This research presents signal-image post-processing techniques called Intensity-Curvature Measurement Approaches with application to the diagnosis of human brain tumors detected through Magnetic Resonance Imaging (MRI. Post-processing of the MRI of the human brain encompasses the following model functions: (i bivariate cubic polynomial, (ii bivariate cubic Lagrange polynomial, (iii monovariate sinc, and (iv bivariate linear. The following Intensity-Curvature Measurement Approaches were used: (i classic-curvature, (ii signal resilient to interpolation, (iii intensity-curvature measure and (iv intensity-curvature functional. The results revealed that the classic-curvature, the signal resilient to interpolation and the intensity-curvature functional are able to add additional information useful to the diagnosis carried out with MRI. The contribution to the MRI diagnosis of our study are: (i the enhanced gray level scale of the tumor mass and the well-behaved representation of the tumor provided through the signal resilient to interpolation, and (ii the visually perceptible third dimension perpendicular to the image plane provided through the classic-curvature and the intensity-curvature functional.
A major QTL controls susceptibility to spinal curvature in the curveback guppy
Directory of Open Access Journals (Sweden)
Dreyer Christine
2011-01-01
Full Text Available Abstract Background Understanding the genetic basis of heritable spinal curvature would benefit medicine and aquaculture. Heritable spinal curvature among otherwise healthy children (i.e. Idiopathic Scoliosis and Scheuermann kyphosis accounts for more than 80% of all spinal curvatures and imposes a substantial healthcare cost through bracing, hospitalizations, surgery, and chronic back pain. In aquaculture, the prevalence of heritable spinal curvature can reach as high as 80% of a stock, and thus imposes a substantial cost through production losses. The genetic basis of heritable spinal curvature is unknown and so the objective of this work is to identify quantitative trait loci (QTL affecting heritable spinal curvature in the curveback guppy. Prior work with curveback has demonstrated phenotypic parallels to human idiopathic-type scoliosis, suggesting shared biological pathways for the deformity. Results A major effect QTL that acts in a recessive manner and accounts for curve susceptibility was detected in an initial mapping cross on LG 14. In a second cross, we confirmed this susceptibility locus and fine mapped it to a 5 cM region that explains 82.6% of the total phenotypic variance. Conclusions We identify a major QTL that controls susceptibility to curvature. This locus contains over 100 genes, including MTNR1B, a candidate gene for human idiopathic scoliosis. The identification of genes associated with heritable spinal curvature in the curveback guppy has the potential to elucidate the biological basis of spinal curvature among humans and economically important teleosts.
Directory of Open Access Journals (Sweden)
Xiang Shen
2017-03-01
Full Text Available This article presents computational algorithms for the design, analysis, and optimization of airfoil aerodynamic performance. The prescribed surface curvature distribution blade design (CIRCLE method is applied to a symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 to remove their surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analysis is used to investigate the effects of curvature distribution on aerodynamic performance of the original and modified airfoils. An inviscid–viscid interaction scheme is introduced to predict the positions of laminar separation bubbles. The results are compared with experimental data obtained from tests on the original airfoil geometry. The computed aerodynamic advantages of the modified airfoils are analyzed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 results in a larger laminar separation bubble at lower angles of attack and lower Reynolds numbers. It also affects the inherent performance of the airfoil at higher Reynolds numbers. It is shown that at relatively high angles of attack, a continuous slope-of-curvature distribution reduces the skin friction by suppressing both laminar and turbulent separation, and by delaying laminar-turbulent transition. It is concluded that the surface curvature distribution has significant effects on the boundary layer behavior and consequently an improved curvature distribution will lead to higher aerodynamic efficiency.
Spectral combination of spherical gravitational curvature boundary-value problems
PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel
2018-04-01
Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error
Short, Daniel J.
be applied to characterize the refractive effects. To help with the time-lapse image refraction analysis process, a second order ray trace scheme has been developed. The ray trace is based on existing lens system tracing procedures, but is adapted for use with the atmospheric refractivity profile. The standard practice of ray tracing uses linear approximations through each element to obtain a ray path, however, the method described in this dissertation uses a quadratic correction term in order to more accurately and efficiently simulate the curvature of rays as they propagate through a gradient refractive index medium such as the atmosphere. Although a variety of finite element solutions have been implemented to describe ray trajectories in nonlinear refractive mediums, the new ray tracer described here is much easier to implement and provides quick, intuitive results. The method is tested against exact analytical ray height solutions for known profiles and was found to give nearly identical results. The ray trace was then applied to real atmospheric data and was found to give plausible results. The tay trace gives a visual aid in understanding the physical path the light takes in traversing the potential field. This will be beneficial in linking optical data to weather model data in an effort to develop a forecasting model for refraction. By selecting the correct boundary and initial conditions, we are able to model rays through the profile. Understanding the system will ultimately help in later analysis. A primary objective of this dissertation is to expand on the work mentioned above on image dislocation and consider the effects of towering (stretching) and stooping (compression) in the imagery. These effects can be explained as a type of lensing by the atmosphere due to nonlinear gradients. To achieve towering and stooping, a curved vertical index profile is required. Where a positive lensing action by the medium causes some ray focusing, back projection from at
Surface Curvature in Island Groups and Discontinuous Cratonic Structures
McDowell, M. S.
2002-05-01
The Canadian Archipelago includes eight major islands and a host of smaller ones. They are separated by water bodies, of varying widths attributable to glacial activity and ocean currents. Land form varies from relatively rugged mountains (~2000 m) in eastern, glacial, islands, to low lying western, similar to the continental topography adjacent. The Arctic region is thought to have been low average elevation before the Pleistocene. To a picture puzzler, it all looks like it fit together. Experimentally cutting apart the islands from large scale maps shows that the rough edges match fairly well. However, when those independent pieces are sutured together, without restraint, as in free air, the fit is far better. Far more importantly, they consistently form a noticeably concave surface. This tendency is not at all apparent in flat surface or computer screen manipulation; the pieces need to be "hand joined" or on a molded surface to allow the assembly to freely form as it will. Fitting together the coastlines above 60 \\deg north, from 120 \\deg west to 45 \\deg east, and comparing the resulting contracted area to the original, obtains an 8 percent area reduction. The curvature "humps" a trial planar section of 15 cms by 1.6 cm, a substantial difference in the radius of curvature. If you rashly suggest applying that formula globally, the resulting sphere would have a surface area of 4.7 x108,(down from 5 x108), and therefore radius of 6117 km, down from 6400, which is a rather preposterous conclusion. As nobody would believe it, I tested the idea elsewhere. The Huronian succession of six named cratons is adjacent on the south. I cut this map apart, too, and fit it together, once again getting a curvature, this time more pronounced. I am trying it with the Indonesian Archipelago, although this area has volcanic complications, and with Precambrian Basins in western Australia and Nimibia, Africa. Indications are - an essentially similar pattern of fit, but non uniform
Converting entropy to curvature perturbations after a cosmic bounce
Energy Technology Data Exchange (ETDEWEB)
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno; Wilson-Ewing, Edward [Max Planck Institute for Gravitational Physics, Albert Einstein Institute,14476 Potsdam-Golm (Germany)
2016-10-04
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Observational constraints on the primordial curvature power spectrum
Emami, Razieh; Smoot, George F.
2018-01-01
CMB temperature fluctuation observations provide a precise measurement of the primordial power spectrum on large scales, corresponding to wavenumbers 10‑3 Mpc‑1 lesssim k lesssim 0.1 Mpc‑1, [1-7, 11]. Luminous red galaxies and galaxy clusters probe the matter power spectrum on overlapping scales (0.02 Mpc‑1 lesssim k lesssim 0.7 Mpc‑1 [10, 12-20]), while the Lyman-alpha forest reaches slightly smaller scales (0.3 Mpc‑1 lesssim k lesssim 3 Mpc‑1 [22]). These observations indicate that the primordial power spectrum is nearly scale-invariant with an amplitude close to 2 × 10‑9, [5, 23-28]. These observations strongly support Inflation and motivate us to obtain observations and constraints reaching to smaller scales on the primordial curvature power spectrum and by implication on Inflation. We are able to obtain limits to much higher values of k lesssim 105 Mpc‑1 and with less sensitivity even higher k lesssim 1019‑ 1023 Mpc‑1 using limits from CMB spectral distortions and other limits on ultracompact minihalo objects (UCMHs) and Primordial Black Holes (PBHs). PBHs are one of the known candidates for the Dark Matter (DM). Due to their very early formation, they could give us valuable information about the primordial curvature perturbations. These are complementary to other cosmological bounds on the amplitude of the primordial fluctuations. In this paper, we revisit and collect all the published constraints on both PBHs and UCMHs. We show that unless one uses the CMB spectral distortion, PBHs give us a very relaxed bounds on the primordial curvature perturbations. UCMHs, on the other hand, are very informative over a reasonable k range (3 lesssim k lesssim 106 Mpc‑1) and lead to significant upper-bounds on the curvature spectrum. We review the conditions under which the tighter constraints on the UCMHs could imply extremely strong bounds on the fraction of DM that could be PBHs in reasonable models. Failure to satisfy these conditions would
Reachability by paths of bounded curvature in a convex polygon
Ahn, Heekap; Cheong, Otfried; Matoušek, Jiřǐ; Vigneron, Antoine E.
2012-01-01
Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.
Constraints on amplitudes of curvature perturbations from primordial black holes
International Nuclear Information System (INIS)
Bugaev, Edgar; Klimai, Peter
2009-01-01
We calculate the primordial black hole (PBH) mass spectrum produced from a collapse of the primordial density fluctuations in the early Universe using, as an input, several theoretical models giving the curvature perturbation power spectra P R (k) with large (∼10 -2 -10 -1 ) values at some scale of comoving wave numbers k. In the calculation we take into account the explicit dependence of gravitational (Bardeen) potential on time. Using the PBH mass spectra, we further calculate the neutrino and photon energy spectra in extragalactic space from evaporation of light PBHs, and the energy density fraction contained in PBHs today (for heavier PBHs). We obtain the constraints on the model parameters using available experimental data (including data on neutrino and photon cosmic backgrounds). We briefly discuss the possibility that the observed 511 keV line from the Galactic center is produced by annihilation of positrons evaporated by PBHs.
Generalized curvature and the equations of D=11 supergravity
Energy Technology Data Exchange (ETDEWEB)
Bandos, Igor A. [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Institute for Theoretical Physics, NSC ' Kharkov Institute of Physics and Technology' , UA-61108 Kharkov (Ukraine); Azcarraga, Jose A. de [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain)]. E-mail: j.a.de.azcarraga@ific.uv.es; Picon, Moises [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-2535 (United States); Varela, Oscar [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Michigan Center for Theoretical Physics, Randall Laboratory, Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120 (United States)
2005-05-26
It is known that, for zero fermionic sector, {psi}{sub {mu}}{sup {alpha}}(x)=0, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression, Rab{alpha}{gamma}{gamma}b{gamma}{beta}=0, which is a condition on the curvature R{alpha}{beta} of the generalized connection w. In this Letter we show that the equation Rbc{alpha}{gamma}{gamma}abc{gamma}{beta}=4i((D-bar {psi}){sub bc}{gamma}{sup [abc{sub {beta}({psi}{sub d}{gamma}{sup d}]){sub {alpha}}), where D-bar is the covariant derivative for the generalized connection w, collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing, {psi}{sub {mu}}{sup {alpha}}(x)<>0.
Curvature-driven morphing of non-Euclidean shells
Pezzulla, Matteo; Stoop, Norbert; Jiang, Xin; Holmes, D. P.
2017-05-01
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.
Higher-curvature corrections to holographic entanglement with momentum dissipation
Energy Technology Data Exchange (ETDEWEB)
Tanhayi, M.R. [Islamic Azad University Central Tehran Branch (IAUCTB), Department of Physics, Faculty of Basic Science, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Vazirian, R. [Islamic Azad University Central Tehran Branch (IAUCTB), Department of Physics, Faculty of Basic Science, Tehran (Iran, Islamic Republic of)
2018-02-15
We study the effects of Gauss-Bonnet corrections on some nonlocal probes (entanglement entropy, n-partite information and Wilson loop) in the holographic model with momentum relaxation. Higher-curvature terms as well as scalar fields make in fact nontrivial corrections to the coefficient of the universal term in entanglement entropy. We use holographic methods to study such corrections. Moreover, holographic calculation indicates that mutual and tripartite information undergo a transition beyond which they identically change their values. We find that the behavior of the transition curves depends on the sign of the Gauss-Bonnet coupling λ. The transition for λ > 0 takes place in larger separation of subsystems than that of λ < 0. Finally, we examine the behavior of modified part of the force between external point-like objects as a function of Gauss-Bonnet coupling and its sign. (orig.)
The string model with the extrinsic curvature term
International Nuclear Information System (INIS)
Itoi, C.; Kubota, Hiroshi
1988-01-01
The string model with the extrinsic curvature is studied which is a gauge invariant field theory with higher order derivatives. We present an equivalent action without any higher order derivatives which keeps the gauge invariance. We point out the difficulty caused by the second class constraints in Dirac's canonical method. Following a new method for dynamical systems with second class constraints, we construct a equivalent model which has no second class constraints but has a new gauge invariance. This gauge invariance guarantees the equivalence between the original model and new one. We show that the model can be quantized in this formalism. In a simple model, we show the nilpotence of the BRST charge under certain conditions, and discuss the unitarity of the theory. (author)
Inflation in non-minimal matter-curvature coupling theories
Energy Technology Data Exchange (ETDEWEB)
Gomes, C.; Bertolami, O. [Departamento de Física e Astronomia and Centro de Física do Porto, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre s/n, 4169-007 Porto (Portugal); Rosa, J.G., E-mail: claudio.gomes@fc.up.pt, E-mail: joao.rosa@ua.pt, E-mail: orfeu.bertolami@fc.up.pt [Departamento de Física da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro (Portugal)
2017-06-01
We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions for some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.
Design of footbridge with double curvature made of UHPC
Kněž, P.; Tej, P.; Čítek, D.; Kolísko, J.
2017-09-01
This paper presents design of footbridge with double curvature made of UHPC. The structure is designed as a single-span bridge. The span of the bridge is 10.00 m, and the width of the deck is 1.50 m. The thickness of shell structure is 0.03 m for walls and 0.045 m for deck. The main structure of the bridge is one arch shell structure with sidewalls made of UHPC with dispersed steel fibers with conventional reinforcement only at anchoring areas. The structure was designed on the basis of the numerical model. Model was subsequently clarified on the basis of the first test elements. Paper presents detailed course on design of the bridge and presentation will contain also installation in landscape and results of static and dynamic loading tests.
Development of an Integrated Intelligent Multi -Objective Framework for UAV Trajectory Generation
Wilburn, Jennifer Nicole
This thesis explores a variety of path planning and trajectory generation schemes intended for small, fixed-wing Unmanned Aerial Vehicles. Throughout this analysis, discrete and pose-based methods are investigated. Pose-based methods are the focus of this research due to their increased flexibility and typically lower computational overhead. Path planning in 3 dimensions is also performed. The 3D Dubins methodology presented is an extension of a previously suggested approach and addresses both the mathematical formulation of the methodology, as well as an assessment of numerical issues encountered and the solutions implemented for these. The main contribution of this thesis is a 3-dimensional clothoid trajectory generation algorithm, which produces flyable paths of continuous curvature to ensure a more followable commanded path. This methodology is an extension of the 3D Dubins method and the 2D clothoid method, which have been implemented herein. To ensure flyability of trajectories produced by 3D pose-based trajectory generation methodologies, a set of criteria are specified to limit the possible solutions to only those flyable by the aircraft. Additionally, several assumptions are made concerning the motion of the aircraft in order to simplify the path generation problem. The 2D and 3D clothoid and Dubins trajectory planners are demonstrated through a trajectory tracking performance comparison between first the 2D Dubins and 2D clothoid methods using a position proportional-integral-derivative controller, then the 3D Dubins and 3D clothoid methods using both a position proportional-integral-derivative controller and an outer-loop non-linear dynamic inversion controller, within the WVU UAV Simulation Environment. These comparisons are demonstrated for both nominal and off-nominal conditions, and show that for both 2D and 3D implementations, the clothoid path planners yields paths with better trajectory tracking performance as compared to the Dubins path planners
Non-Gaussianities and curvature perturbations from hybrid inflation
Clesse, Sébastien; Garbrecht, Björn; Zhu, Yi
2014-03-01
For the original hybrid inflation as well as the supersymmetric F-term and D-term hybrid models, we calculate the level of non-Gaussianities and the power spectrum of curvature perturbations generated during the waterfall, taking into account the contribution of entropic modes. We focus on the regime of mild waterfall, in which inflation continues for more than about 60 e-folds N during the waterfall. We find that the associated fNL parameter goes typically from fNL≃-1/Nexit in the regime with N ≫60, where Nexit is the number of e-folds between the time of Hubble exit of a pivot scale and the end of inflation, down to fNL˜-0.3 when N ≳60, i.e., much smaller in magnitude than the current bound from Planck. Considering only the adiabatic perturbations, the power spectrum is red, with a spectral index ns=1-4/Nexit in the case N ≫60, whereas in the case N≳60, it increases up to unity. Including the contribution of entropic modes does not change observable predictions in the first case, and the spectral index is too low for this regime to be viable. In the second case, entropic modes are a relevant source for the power spectrum of curvature perturbations, of which the amplitude increases by several orders of magnitude. When spectral index values are consistent with observational constraints, the primordial spectrum amplitude is much larger than the observed value and can even lead to black hole formation. We conclude that, due to the important contribution of entropic modes, the parameter space leading to a mild waterfall phase is excluded by cosmic microwave background observations for all the considered models.
Nonlinear damping of drift waves by strong flow curvature
International Nuclear Information System (INIS)
Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.
1993-01-01
A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method
Inferring Lévy walks from curved trajectories: A rescaling method
Tromer, R. M.; Barbosa, M. B.; Bartumeus, F.; Catalan, J.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.
2015-08-01
An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).
Optimal trajectories of aircraft and spacecraft
Miele, A.
1990-01-01
Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful
Ray trajectories for Alcubierre spacetime
International Nuclear Information System (INIS)
Anderson, Tom H; Mackay, Tom G; Lakhtakia, Akhlesh
2011-01-01
The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are continuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a micro- or nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a focusing lens, most notably at high speeds
Stochastic and fractal analysis of fracture trajectories
Bessendorf, Michael H.
1987-01-01
Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.
DEFF Research Database (Denmark)
van der Horst, Sander; van de Wiel, Jelmer E.; Ferreira, Carlos Simao
2016-01-01
Blades on a Vertical Axis Wind Turbine (VAWT) experience curved streamlines, caused by the rotation of the turbine. This phenomenon is known as flow curvature and has effects on the aerodynamic loading of the blades. Several authors have proposed methods to account for flow curvature, resulting...
Gigli, Nicola
2018-01-01
The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Protein shape and crowding drive domain formation and curvature in biological membranes
Frese, R.N.; Pamies, Josep C.; Olsen, John D.; Bahatyrova, S.; van der Weij-de Wit, Chantal D.; Aartsma, Thijs J.; Otto, Cornelis; Hunter, C. Neil; Frenkel, Daan; van Grondelle, Rienk
2007-01-01
Folding, curvature, and domain formation are characteristics of many biological membranes. Yet the mechanisms that drive both curvature and the formation of specialized domains enriched in particular protein complexes are unknown. For this reason, studies in membranes whose shape and organization
Measurements of the Curvature of Protrusions/Retrusions on Migrating Recrystallization Boundaries
DEFF Research Database (Denmark)
Zhang, Yubin; Godfrey, A.; Juul Jensen, Dorte
2009-01-01
Two methods to quantify protrusions/retrusions and to estimate local boundary curvature from sample plane sections are proposed. The methods are used to evaluate the driving force due to curvature of the protrusions/retrusions for partially recrystallized pure nickel cold rolled to 96% reduction...
The zero curvature formulation of the KP and the sKP equations
International Nuclear Information System (INIS)
Barcelos Neto, J.; Das, A.; Panda, S.; Roy, S.
1992-01-01
The Kadomtsev-Petviashvili equation is derived from the zero curvature condition associated with the gauge group SL(2,R) in 2+1 dimensions. A fermionic extension of the KP equation is also obtained using the zero curvature condition of the super group OS p (2/1), which reduces upon appropriate restriction to the Kupershmidt equation. (author). 17 refs
DEFF Research Database (Denmark)
Folkesson, Jenny; Dam, Erik B; Olsen, Ole F
2007-01-01
for intersubject comparisons. Digital phantoms were created to establish the accuracy of the curvature estimation methods. RESULTS: A comparison of the two curvature estimation methods to ground truth yielded absolute pairwise differences of 1.1%, and 4.8%, respectively. The interscan reproducibility for the two...
Single Lipid Molecule Dynamics on Supported Lipid Bilayers with Membrane Curvature
Directory of Open Access Journals (Sweden)
Philip P. Cheney
2017-03-01
Full Text Available The plasma membrane is a highly compartmentalized, dynamic material and this organization is essential for a wide variety of cellular processes. Nanoscale domains allow proteins to organize for cell signaling, endo- and exocytosis, and other essential processes. Even in the absence of proteins, lipids have the ability to organize into domains as a result of a variety of chemical and physical interactions. One feature of membranes that affects lipid domain formation is membrane curvature. To directly test the role of curvature in lipid sorting, we measured the accumulation of two similar lipids, 1,2-Dihexadecanoyl-sn-glycero-3-phosphoethanolamine (DHPE and hexadecanoic acid (HDA, using a supported lipid bilayer that was assembled over a nanopatterned surface to obtain regions of membrane curvature. Both lipids studied contain 16 carbon, saturated tails and a head group tag for fluorescence microscopy measurements. The accumulation of lipids at curvatures ranging from 28 nm to 55 nm radii was measured and fluorescein labeled DHPE accumulated more than fluorescein labeled HDA at regions of membrane curvature. We then tested whether single biotinylated DHPE molecules sense curvature using single particle tracking methods. Similar to groups of fluorescein labeled DHPE accumulating at curvature, the dynamics of single molecules of biotinylated DHPE was also affected by membrane curvature and highly confined motion was observed.
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
Energy Technology Data Exchange (ETDEWEB)
Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)
2013-12-15
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.
Constant scalar curvature hypersurfaces in (3 + 1) -dimensional GHMC Minkowski spacetimes
Smith, Graham
2018-06-01
We prove that every (3 + 1) -dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In other words, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is a smooth submersion.
Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces
International Nuclear Information System (INIS)
Fu, Yu
2013-01-01
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces
Distinguished trajectories in time dependent vector fields
Madrid, J. A. Jimenez; Mancho, Ana M.
2008-01-01
We introduce a new definition of distinguished trajectory that generalizes the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with hyperbolic and nonhyperbolic types of stability. The definition is implemented numerically and the procedure consists of determining a path of limit coordinates. It has been successfully applied to known examples of distinguished trajectories. In the context of high...
Trajectories of Delinquency and Parenting Styles
Hoeve, Machteld; Blokland, Arjan; Dubas, Judith Semon; Loeber, Rolf; Gerris, Jan R. M.; van der Laan, Peter H.
2007-01-01
We investigated trajectories of adolescent delinquent development using data from the Pittsburgh Youth Study and examined the extent to which these different trajectories are differentially predicted by childhood parenting styles. Based on self-reported and official delinquency seriousness, covering ages 10?19, we identified five distinct delinquency trajectories differing in both level and change in seriousness over time: a nondelinquent, minor persisting, moderate desisting, serious persist...
Decentralized flight trajectory planning of multiple aircraft
Yokoyama, Nobuhiro; 横山 信宏
2008-01-01
Conventional decentralized algorithms for optimal trajectory planning tend to require prohibitive computational time as the number of aircraft increases. To overcome this drawback, this paper proposes a novel decentralized trajectory planning algorithm adopting a constraints decoupling approach for parallel optimization. The constraints decoupling approach is formulated as the path constraints of the real-time trajectory optimization problem based on nonlinear programming. Due to the parallel...
Amphipathic motifs in BAR domains are essential for membrane curvature sensing
DEFF Research Database (Denmark)
Bhatia, Vikram K; Madsen, Kenneth L; Bolinger, Pierre-Yves
2009-01-01
BAR (Bin/Amphiphysin/Rvs) domains and amphipathic alpha-helices (AHs) are believed to be sensors of membrane curvature thus facilitating the assembly of protein complexes on curved membranes. Here, we used quantitative fluorescence microscopy to compare the binding of both motifs on single...... nanosized liposomes of different diameters and therefore membrane curvature. Characterization of members of the three BAR domain families showed surprisingly that the crescent-shaped BAR dimer with its positively charged concave face is not able to sense membrane curvature. Mutagenesis on BAR domains showed...... that membrane curvature sensing critically depends on the N-terminal AH and furthermore that BAR domains sense membrane curvature through hydrophobic insertion in lipid packing defects and not through electrostatics. Consequently, amphipathic motifs, such as AHs, that are often associated with BAR domains...
Moore, Joan G.; Moore, John
1992-01-01
The flow in the NASA Low-Speed Impeller is affected by both curvature and rotation. The flow curves due to the following: (1) geometric curvature, e.g. the curvature of the hub and shroud profiles in the meridional plane and the curvature of the backswept impeller blades; and (2) secondary flow vortices, e.g. the tip leakage vortex. Changes in the turbulence and effective turbulent viscosity in the impeller are investigated. The effects of these changes on three-dimensional flow development are discussed. Two predictions of the flow in the impeller, one with, and one without modification to the turbulent viscosity due to rotation and curvature, are compared. Some experimental and theoretical background for the modified mixing length model of turbulent viscosity will also be presented.
Trajectory similarity join in spatial networks
Shang, Shuo
2017-09-07
The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider the case of trajectory similarity join (TS-Join), where the objects are trajectories of vehicles moving in road networks. Thus, given two sets of trajectories and a threshold θ, the TS-Join returns all pairs of trajectories from the two sets with similarity above θ. This join targets applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide a purposeful definition of similarity. To enable efficient TS-Join processing on large sets of trajectories, we develop search space pruning techniques and take into account the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer algorithm. For each trajectory, the algorithm first finds similar trajectories. Then it merges the results to achieve a final result. The algorithm exploits an upper bound on the spatiotemporal similarity and a heuristic scheduling strategy for search space pruning. The algorithm\\'s per-trajectory searches are independent of each other and can be performed in parallel, and the merging has constant cost. An empirical study with real data offers insight in the performance of the algorithm and demonstrates that is capable of outperforming a well-designed baseline algorithm by an order of magnitude.
Privacy-Preserving Trajectory Collection
DEFF Research Database (Denmark)
Gidofalvi, Gyozo; Xuegang, Huang; Pedersen, Torben Bach
2008-01-01
In order to provide context--aware Location--Based Services, real location data of mobile users must be collected and analyzed by spatio--temporal data mining methods. However, the data mining methods need precise location data, while the mobile users want to protect their location privacy....... To remedy this situation, this paper first formally defines novel location privacy requirements. Then, it briefly presents a system for privacy--preserving trajectory collection that meets these requirements. The system is composed of an untrusted server and clients communicating in a P2P network. Location...... data is anonymized in the system using data cloaking and data swapping techniques. Finally, the paper empirically demonstrates that the proposed system is effective and feasible....
Mobility, Education and Life Trajectories
DEFF Research Database (Denmark)
Olwig, Karen Fog; Valentin, Karen
2015-01-01
Travel for educational purposes, once the privilege of the upper class, has become a global mass phenomenon in recent years. This special issue examines, within different cultural and historical contexts, the close relationship between migration, education and social mobility. Adopting...... the perspective that education includes a broad range of formative experiences, the articles explore different educational trajectories and the local, regional and transnational relations in which they are embedded. Three key issues emerge from the analyses: firstly, the central role of temporality in terms...... of both the overall historical conditions and the specific biographical circumstances shaping educational opportunities; secondly, the complex agendas informing individuals’ migration and the adjustment of these agendas in the light of the vagaries of migrant life; and thirdly, the importance of migrants...
Entanglement evolution for quantum trajectories
International Nuclear Information System (INIS)
Vogelsberger, S; Spehner, D
2011-01-01
Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or 'realization') corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the 'Fifth International Workshop DICE2010' by the first author and have been the subject of a prior publication.
Technical description of the RIVM trajectory model
Energy Technology Data Exchange (ETDEWEB)
De Waal, E.S.; Van Pul, W.A.J.
1995-12-01
The RIVM trajectory model, described in this report, enables calculation of a backward or forward trajectory. These trajectories are used to `follow` previous released air pollution in a backward mode or to `find` the origin of air pollution in a forward mode. The trajectories are used in the smog forecasting and in the TREND model for the distribution of materials in Europe. Presently 6-hourly ECMWF wind fields at 1000 and 850 hPa, with 3 deg x 3 deg latitude-longitude resolution are used. Wind fields with a different resolution in latitude-longitude can also be used after simple adjustments. An iterative method, described elsewhere, is applied to calculate the trajectories. Within limits, the user is free to choose the time step (1, 2 or 6-hour), transport height, length, starting or arrival date and starting or arrival position of the trajectory. The differences between the trajectories calculated with time steps of 1, 2 and 6 h were small. For the 96-hour trajectories at 1000 and 850 hPa the deviations were generally within 1 deg latitude and longitude, i.e. 100-200 km. The trajectory calculated with the 6-hour time step could be used without a great loss in accuracy compared to the calculations with the 1-hour time step. A typical error in the trajectory path at 1000 and 850 hPa was 500 km, which is about 30% of a typical travel distance. However, close to quickly changing weather systems, such as cyclones, the error can be as large as the travel distance and makes the calculations unreliable. The error in the forecasted trajectory was found to be larger than the above error estimation due to larger uncertainties in the forecasted compared to the analyzed wind fields. A manual on how to run the model is also given. 5 figs., 3 tabs., 5 refs., 6 appendices
Parallel trajectory similarity joins in spatial networks
Shang, Shuo
2018-04-04
The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider two cases of trajectory similarity joins (TS-Joins), including a threshold-based join (Tb-TS-Join) and a top-k TS-Join (k-TS-Join), where the objects are trajectories of vehicles moving in road networks. Given two sets of trajectories and a threshold θ, the Tb-TS-Join returns all pairs of trajectories from the two sets with similarity above θ. In contrast, the k-TS-Join does not take a threshold as a parameter, and it returns the top-k most similar trajectory pairs from the two sets. The TS-Joins target diverse applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide purposeful definitions of similarity. To enable efficient processing of the TS-Joins on large sets of trajectories, we develop search space pruning techniques and enable use of the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer search framework that lays the foundation for the algorithms for the Tb-TS-Join and the k-TS-Join that rely on different pruning techniques to achieve efficiency. For each trajectory, the algorithms first find similar trajectories. Then they merge the results to obtain the final result. The algorithms for the two joins exploit different upper and lower bounds on the spatiotemporal trajectory similarity and different heuristic scheduling strategies for search space pruning. Their per-trajectory searches are independent of each other and can be performed in parallel, and the mergings have constant cost. An empirical study with real data offers insight in the performance of the algorithms and demonstrates that they are capable of outperforming well-designed baseline algorithms by an order of magnitude.
Parallel trajectory similarity joins in spatial networks
Shang, Shuo; Chen, Lisi; Wei, Zhewei; Jensen, Christian S.; Zheng, Kai; Kalnis, Panos
2018-01-01
The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider two cases of trajectory similarity joins (TS-Joins), including a threshold-based join (Tb-TS-Join) and a top-k TS-Join (k-TS-Join), where the objects are trajectories of vehicles moving in road networks. Given two sets of trajectories and a threshold θ, the Tb-TS-Join returns all pairs of trajectories from the two sets with similarity above θ. In contrast, the k-TS-Join does not take a threshold as a parameter, and it returns the top-k most similar trajectory pairs from the two sets. The TS-Joins target diverse applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide purposeful definitions of similarity. To enable efficient processing of the TS-Joins on large sets of trajectories, we develop search space pruning techniques and enable use of the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer search framework that lays the foundation for the algorithms for the Tb-TS-Join and the k-TS-Join that rely on different pruning techniques to achieve efficiency. For each trajectory, the algorithms first find similar trajectories. Then they merge the results to obtain the final result. The algorithms for the two joins exploit different upper and lower bounds on the spatiotemporal trajectory similarity and different heuristic scheduling strategies for search space pruning. Their per-trajectory searches are independent of each other and can be performed in parallel, and the mergings have constant cost. An empirical study with real data offers insight in the performance of the algorithms and demonstrates that they are capable of outperforming well-designed baseline algorithms by an order of magnitude.
The hybrid inflation waterfall and the primordial curvature perturbation
International Nuclear Information System (INIS)
Lyth, David H.
2012-01-01
Without demanding a specific form for the inflaton potential, we obtain an estimate of the contribution to the curvature perturbation generated during the linear era of the hybrid inflation waterfall. The spectrum of this contribution peaks at some wavenumber k = k * , and goes like k 3 for k * , making it typically negligible on cosmological scales. The scale k * can be outside the horizon at the end of inflation, in which case ζ = −(g 2 −(g 2 )) with g gaussian. Taking this into account, the cosmological bound on the abundance of black holes is likely to be satisfied if the curvaton mass m much bigger than the Hubble parameter H, but is likely to be violated if m∼< H. Coming to the contribution to ζ from the rest of the waterfall, we are led to consider the use of the 'end-of-inflation' formula, giving the contribution to ζ generated during a sufficiently sharp transition from nearly-exponential inflation to non-inflation, and we state for the first time the criterion for the transition to be sufficiently sharp. Our formulas are applied to supersymmetric GUT inflation and to supernatural/running-mass inflation
Entropy bound and causality violation in higher curvature gravity
International Nuclear Information System (INIS)
Neupane, Ishwaree P; Dadhich, Naresh
2009-01-01
In any quantum theory of gravity we do expect corrections to Einstein gravity to occur. Yet, at a fundamental level, it is not apparent what the most relevant corrections are. We argue that the generic curvature square corrections present in the lower dimensional actions of various compactified string theories provide a natural passage between the classical and quantum realms of gravity. The Gauss-Bonnet and (Riemann) 2 gravities, in particular, provide concrete examples in which inconsistency of a theory, such as a violation of microcausality, and a classical limit on black hole entropy are correlated. In such theories the ratio of the shear viscosity to the entropy density, η/s, can be smaller than for a boundary conformal field theory with Einstein gravity dual. This result is interesting from the viewpoint that nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme densities and temperatures may violate the conjectured KSS bound η/s ≥ 1/4π, albeit marginally so.
Warps, grids and curvature in triple vector bundles
Flari, Magdalini K.; Mackenzie, Kirill
2018-06-01
A triple vector bundle is a cube of vector bundle structures which commute in the (strict) categorical sense. A grid in a triple vector bundle is a collection of sections of each bundle structure with certain linearity properties. A grid provides two routes around each face of the triple vector bundle, and six routes from the base manifold to the total manifold; the warps measure the lack of commutativity of these routes. In this paper we first prove that the sum of the warps in a triple vector bundle is zero. The proof we give is intrinsic and, we believe, clearer than the proof using decompositions given earlier by one of us. We apply this result to the triple tangent bundle T^3M of a manifold and deduce (as earlier) the Jacobi identity. We further apply the result to the triple vector bundle T^2A for a vector bundle A using a connection in A to define a grid in T^2A . In this case the curvature emerges from the warp theorem.
Membrane curvature stress and antibacterial activity of lactoferricin derivatives.
Zweytick, Dagmar; Tumer, Sabine; Blondelle, Sylvie E; Lohner, Karl
2008-05-02
We have studied correlation of non-lamellar phase formation and antimicrobial activity of two cationic amphipathic peptides, termed VS1-13 and VS1-24 derived from a fragment (LF11) of human lactoferricin on Escherichia coli total lipid extracts. Compared to LF11, VS1-13 exhibits minor, but VS1-24 significantly higher antimicrobial activity. X-ray experiments demonstrated that only VS1-24 decreased the onset of cubic phase formation of dispersions of E. coli lipid extracts, significantly, down to physiological relevant temperatures. Cubic structures were identified to belong to the space groups Pn3m and Im3m. Formation of latter is enhanced in the presence of VS1-24. Additionally, the presence of this peptide caused membrane thinning in the fluid phase, which may promote cubic phase formation. VS1-24 containing a larger hydrophobic volume at the N-terminus than its less active counterpart VS1-13 seems to increase curvature stress in the bilayer and alter the behaviour of the membrane significantly enhancing disruption.
Cosmology of a holographic induced gravity model with curvature effects
International Nuclear Information System (INIS)
Bouhmadi-Lopez, Mariam; Errahmani, Ahmed; Ouali, Taoufiq
2011-01-01
We present a holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalizes the normal Dvali-Gabadadze-Porrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and a holographic dark energy with the Hubble scale as the infrared cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal Dvali-Gabadadze-Porrati branch (without Gauss-Bonnet modifications) nor in a standard four-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.
Scalar brane backgrounds in higher order curvature gravity
International Nuclear Information System (INIS)
Charmousis, Christos; Davis, Stephen C.; Dufaux, Jean-Francois
2003-01-01
We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularly emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Generically, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element. (author)
The geometry of plane waves in spaces of constant curvature
International Nuclear Information System (INIS)
Tran, H.V.
1988-01-01
We examined the geometry of possible plane wave fronts in spaces of constant curvature for three cases in which the cosmological constant is positive, zero, or negative. The cosmological constant and a second-order invariant determined by a congruence of null rays were used in the investigation. We embedded the spaces under investigation in a flat five-dimensional space, and studied the null hyperplanes passing through the origin of the flat five-dimensional space. The embedded spaces are represented by quadrics in the five-dimensional space. The plane wave fronts are represented by the intersection of the quadric with null hyperplanes passing through the origin of the five-dimensional space. We concluded that in Minkowski spaces (zero cosmological constant), the plane-fronted waves will intersect if and only if the second-order invariant mentioned above is non-zero. For deSitter spaces (positive cosmological constant), plane-fronted waves will always intersect. For anti-deSitter spaces (negative cosmological constant), plane-fronted waves may but need not intersect
Dual curvature acoustically damped concentrating collector. Final technical report
Energy Technology Data Exchange (ETDEWEB)
Smith, G.A.; Rausch, R.A.
1980-05-01
A development program was conducted to investigate the design and performance parameters of a novel, dual curvature, concentrating solar collector. The reflector of the solar collector is achieved with a stretched-film reflective surface that approximates a hyperbolic paraboloid and is capable of line-focusing at concentration ratios ranging from 10 to 20X. A prototype collector was designed based on analytical and experimental component trade-off activities as well as economic analyses of solar thermal heating and cooling systems incorporating this type of collector. A prototype collector incorporating six 0.66 x 1.22 m (2 x 4 ft) was fabricated and subjected to a limited thermal efficiency test program. A peak efficiency of 36% at 121/sup 0/C (250/sup 0/F) was achieved based upon the gross aperture area. Commercialization activities were conducted, including estimated production costs of $134.44/m/sup 2/ ($12.49/ft/sup 2/) for the collector assembly (including a local suntracker and controls) and $24.33/m/sup 2/ ($2.26/ft/sup 2/) for the reflector subassembly.
Phase separation in artificial vesicles driven by light and curvature
Rinaldin, Melissa; Pomp, Wim; Schmidt, Thomas; Giomi, Luca; Kraft, Daniela; Physics of Life Processes Team; Soft; Bio Mechanics Collaboration; Self-Assembly in Soft Matter Systems Collaboration
The role of phase-demixing in living cells, leading to the lipid-raft hypothesis, has been extensively studied. Lipid domains of higher lipid chain order are proposed to regulate protein spatial organization. Giant Unilamellar Vesicles provide an artificial model to study phase separation. So far temperature was used to initiate the process. Here we introduce a new methodology based on the induction of phase separation by light. To this aim, the composition of the lipid membrane is varied by photo-oxidation of lipids. The control of the process gained by using light allowed us to observe vesicle shape fluctuations during phase-demixing. The presence of fluctuations near the critical mixing point resembles features of a critical process. We quantitatively analyze these fluctuations using a 2d elastic model, from which we can estimate the material parameters such as bending rigidity and surface tension, demonstrating the non-equilibrium critical behaviour. Finally, I will describe recent attempts toward tuning the membrane composition by controlling the vesicle curvature.
The hybrid inflation waterfall and the primordial curvature perturbation
Lyth, David H.
2012-05-01
Without demanding a specific form for the inflaton potential, we obtain an estimate of the contribution to the curvature perturbation generated during the linear era of the hybrid inflation waterfall. The spectrum of this contribution peaks at some wavenumber k = k*, and goes like k3 for k Lt k*, making it typically negligible on cosmological scales. The scale k* can be outside the horizon at the end of inflation, in which case ζ = -(g2-langg2rang) with g gaussian. Taking this into account, the cosmological bound on the abundance of black holes is likely to be satisfied if the curvaton mass m much bigger than the Hubble parameter H, but is likely to be violated if mlsimH. Coming to the contribution to ζ from the rest of the waterfall, we are led to consider the use of the `end-of-inflation' formula, giving the contribution to ζ generated during a sufficiently sharp transition from nearly-exponential inflation to non-inflation, and we state for the first time the criterion for the transition to be sufficiently sharp. Our formulas are applied to supersymmetric GUT inflation and to supernatural/running-mass inflation. A preliminary version of this paper appeared as arXiv:1107.1681.
The hybrid inflation waterfall and the primordial curvature perturbation
Energy Technology Data Exchange (ETDEWEB)
Lyth, David H., E-mail: d.lyth@lancaster.ac.uk [Consortium for Fundamental Physics, Cosmology and Astroparticle Group, Department of Physics, Lancaster University, Lancaster LA1 4YB (United Kingdom)
2012-05-01
Without demanding a specific form for the inflaton potential, we obtain an estimate of the contribution to the curvature perturbation generated during the linear era of the hybrid inflation waterfall. The spectrum of this contribution peaks at some wavenumber k = k{sub *}, and goes like k{sup 3} for k << k{sub *}, making it typically negligible on cosmological scales. The scale k{sub *} can be outside the horizon at the end of inflation, in which case ζ = −(g{sup 2}−(g{sup 2})) with g gaussian. Taking this into account, the cosmological bound on the abundance of black holes is likely to be satisfied if the curvaton mass m much bigger than the Hubble parameter H, but is likely to be violated if m∼
Linear response to long wavelength fluctuations using curvature simulations
Energy Technology Data Exchange (ETDEWEB)
Baldauf, Tobias; Zaldarriaga, Matias [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ (United States); Seljak, Uroš [Physics Department, Astronomy Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA (United States); Senatore, Leonardo, E-mail: baldauf@ias.edu, E-mail: useljak@berkeley.edu, E-mail: senatore@stanford.edu, E-mail: matiasz@ias.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA (United States)
2016-09-01
We study the local response to long wavelength fluctuations in cosmological N -body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naïve derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.
Microscopic Model of Automobile Lane-changing Virtual Desire Trajectory by Spline Curves
Directory of Open Access Journals (Sweden)
Yulong Pei
2010-05-01
Full Text Available With the development of microscopic traffic simulation models, they have increasingly become an important tool for transport system analysis and management, which assist the traffic engineer to investigate and evaluate the performance of transport network systems. Lane-changing model is a vital component in any traffic simulation model, which could improve road capacity and reduce vehicles delay so as to reduce the likelihood of congestion occurrence. Therefore, this paper addresses the virtual desire trajectory, a vital part to investigate the behaviour divided into four phases. Based on the boundary conditions, β-spline curves and the corresponding reverse algorithm are introduced firstly. Thus, the relation between the velocity and length of lane-changing is constructed, restricted by the curvature, steering velocity and driving behaviour. Then the virtual desire trajectory curves are presented by Matlab and the error analysis results prove that this proposed description model has higher precision in automobile lane-changing process reconstruction, compared with the surveyed result. KEY WORDS: traffic simulation, lane-changing model, virtual desire trajectory, β-spline curves, driving behaviour
Trajectories of Intimate Partner Violence Victimization
Directory of Open Access Journals (Sweden)
Kevin M. Swartout
2012-08-01
Full Text Available Introduction: The purposes of this study were to assess the extent to which latent trajectories of female intimate partner violence (IPV victimization exist; and, if so, use negative childhood experiences to predict trajectory membership.Methods: We collected data from 1,575 women at 5 time-points regarding experiences during adolescence and their 4 years of college. We used latent class growth analysis to fit a series of personcentered, longitudinal models ranging from 1 to 5 trajectories. Once the best-fitting model was selected, we used negative childhood experience variables—sexual abuse, physical abuse, and witnessing domestic violence—to predict most-likely trajectory membership via multinomial logistic regression.Results: A 5-trajectory model best fit the data both statistically and in terms of interpretability. The trajectories across time were interpreted as low or no IPV, low to moderate IPV, moderate to low IPV, high to moderate IPV, and high and increasing IPV, respectively. Negative childhood experiences differentiated trajectory membership, somewhat, with childhood sexual abuse as a consistent predictor of membership in elevated IPV trajectories.Conclusion: Our analyses show how IPV risk changes over time and in different ways. These differential patterns of IPV suggest the need for prevention strategies tailored for women that consider victimization experiences in childhood and early adulthood. [West J Emerg Med. 2012;13(3:272–277.
From the trajectory to the density memory
International Nuclear Information System (INIS)
Cakir, Rasit; Krokhin, Arkadii; Grigolini, Paolo
2007-01-01
In this paper we discuss the connection between trajectory and density memory. The first form of memory is a property of a stochastic trajectory, whose stationary correlation function shows that the fluctuation at a given time depends on the earlier fluctuations. The density memory is a property of a collection of trajectories, whose density time evolution is described by a time convoluted equation showing that the density time evolution depends on its past history. We show that the trajectory memory does not necessarily yields density memory, and that density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory. We focus our attention on a time-convoluted diffusion equation, when the memory kernel is an inverse power law with (i) negative and (ii) positive tail. In case (i) there exist both renewal trajectories and trajectories with memory, compatible with this equation. Case (ii), which has eluded so far a convincing interpretation in terms of trajectories, is shown to be compatible only with trajectory memory
User oriented trajectory search for trip recommendation
Shang, Shuo; Ding, Ruogu; Yuan, Bo; Xie, Kexin; Zheng, Kai; Kalnis, Panos
2012-01-01
trajectory search by locations (spatial domain only), we consider both spatial and textual domains in the new UOTS query. Given a trajectory data set, the query input contains a set of intended places given by the traveler and a set of textual attributes