Pottmann, Helmut
2010-07-26
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.
Hongchuan Yu; Zhang, Jian J.; Zheng Jiao
2014-01-01
We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solution...
Multimode geodesic branching components
Schulz, D.; Voges, E.
1983-01-01
Geodesic branching components are investigated for multimode guided wave optics. Geodesic structures with particular properties, e.g. focussing star couplers, are derived by a synthesis technique based on a theorem of Toraldo di Francia. Experimentally, the geodesic surfaces are printed on acrylic glass and are spin-coated with organic film waveguides.
Nonrelativistic Geodesic Motion
Mangiarotti, L
1999-01-01
We show that any second order dynamic equation on a configuration space $X\\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.
2016-01-01
We study geodesics on surfaces in the setting of classical differential geometry. We define the curvature of curves and surfaces in three-space and use the fundamental forms of a surface to measure lengths, angles, and areas. We follow Riemann and adopt a more abstract approach, and use tensor notation to discuss Gaussian curvature, Gauss's Theorema Egregium, geodesic curves, and the Gauss-Bonnet theorem. Properties of geodesics are proven by variational methods, showing the connection betwee...
Geodesics of simultaneity in Schwarzschild
Paiva, F M
2010-01-01
Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\\mu}\\dd x^\\mu=0$). These geodesics are studied in the exterior region of \\Sch's metric.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Spherical geodesic mesh generation
Energy Technology Data Exchange (ETDEWEB)
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Energy Technology Data Exchange (ETDEWEB)
Townsend, Paul K [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Wohlfarth, Mattias N R [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2004-12-07
For gravity coupled to N scalar fields, with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N + 1)-dimensional 'augmented' target space of Lorentzian signature (1, N), timelike if V > 0, null if V = 0 and spacelike if V < 0. Accelerating cosmologies correspond to timelike geodesics that lie within an 'acceleration subcone' of the 'lightcone'. Non-flat (k = {+-}1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N + 2, of signature (1, N + 1) for k = -1 and signature (2, N) for k = +1. This formalism is illustrated by cosmological solutions of models with an exponential potential, which are comprehensively analysed; the late-time behaviour for other potentials of current interest is deduced by comparison.
Townsend, P K; Townsend, Paul K.; Wohlfarth, Mattias N.R.
2004-01-01
For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `extended target space' of Lorentzian signature (1,N), timelike if V>0 and spacelike if V<0. Accelerating cosmologies correspond to timelike geodesics that lie within an `acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N+2, of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. We illustrate these results for various potentials of current interest, including exponential and inverse power potentials.
Aichholzer, Oswin; Korman Cozzetti, Matías; Pilz, Alexander; Vogtenhuber, Birgit
2014-01-01
The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset of at least four...
On Properties of Geodesic -Preinvex Functions
Directory of Open Access Journals (Sweden)
I. Ahmad
2009-01-01
Full Text Available The present paper deals with the properties of geodesic -preinvex functions and their relationships with -invex functions and strictly geodesic -preinvex functions. The geodesic -pre-pseudo-invex and geodesic -pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.
Deployable geodesic truss structure
Mikulas, Martin M., Jr. (Inventor); Rhodes, Marvin D. (Inventor); Simonton, J. Wayne (Inventor)
1987-01-01
A deployable geodesic truss structure which can be deployed from a stowed state to an erected state is described. The truss structure includes a series of bays, each bay having sets of battens connected by longitudinal cross members which give the bay its axial and torsional stiffness. The cross members are hinged at their mid point by a joint so that the cross members are foldable for deployment or collapsing. The bays are deployed and stabilized by actuator means connected between the mid point joints of the cross members. Hinged longerons may be provided to also connect the sets of battens and to collapse for stowing with the rest of the truss structure.
Horndeski black hole geodesics
Tretyakova, D A
2016-01-01
We examine geodesics for the scalar-tensor black holes in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits may not be present within some model parameters range. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations. We also present a new (although very similar to those previously known) solution, which contains the orbits we expect from a compact object, admits regular scalar field at the horizon and and can fit into the known stability criteria.
Geodesically Complete Universe
Bars, Itzhak
2011-01-01
This talk is about solving cosmological equations analytically without approximations, and discovering new phenomena that could not be noticed with approximate solutions. We found all the solutions of the Friedmann equations for a specific model, including all the zero-size-bounce solutions that do not violate the null energy condition, as well as all the finite-size-bounce solutions, and then discovered model independent phenomena. Among them is the notion of geodesic completeness for the geometry of the universe. From this we learned a few new general lessons for cosmology. Among them is that anisotropy provides a model independent attractor mechanism to some specific initial values for cosmological fields, and that there is a period of antigravity in the history of the universe. The results are obtained only at the classical gravity level. Effects of quantum gravity or string theory are unknown, they are not even formulated, so there are new theoretical challenges.
Directory of Open Access Journals (Sweden)
Mehmet KILIÇ
2016-09-01
Full Text Available The notion of geodesic, which may be regarded as an extension of the line segment in Euclidean geometry to the space we study in, has an important place in many branches of geometry, such as Riemannian geometry, Metric geometry, to name but a few. In this article, the concept of geodesic in a metric space will be introduced, then geodesics in the space (Rn, d1 will be characterized. Furthermore, some examples will be presented to demonstrate the effectiveness of the main result.
Geodesics and Geodesic Deviation for Impulsive Gravitational Waves
Steinbauer, R
1998-01-01
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac delta distribution. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this problem we proceed by first regularizing the delta singularity, then solving the regularized equation within classical smooth functions and, finally, obtaining a distributional, regularization-idependent limit as solution to the original problem. We also treat the Jacobi equation which, despite being linear in the deviation vector field, involves even more delicate singular expressions, like the ``square'' of the delta distribution. Again the same regularization procedure provides us with a perfectly well behaved smooth regularization and a regularization-independent distributi...
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of g...
Geodesic components for guided wave optics
Chang, W. L.; Voges, E.
1980-10-01
Geodesic elements for beam displacement, beam deflection, beam splitting, and imaging are derived for passive optical devices. The elements are suitable in particular for multimode devices, and a complex performance is achievable by the combined action of different geodesic structures on a common substrate. A general theorem of Toraldo di Francia (1957) on the geodesics of rotational surfaces is used to develop geodesic components for beam deflection and multiple beam splitting in a prescribed manner.
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li.
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of geodesic acoustic mode activity. Phenomenologically a radial propagation of zonal modes shows some characteristics of a classical analogon to second sound in quantum condensates.
On General Plane Fronted Waves. Geodesics
Candela, A M; Sánchez, M; Sanchez, Miguel
2003-01-01
A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = + 2 du dv + H(x,u) du^2$, with $(M_0, $ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity, causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of $H(x,u)$ with $x$ at infinity determines many properties of geodesics. Essentially, a subquadratic growth of $H$ ensures geodesic completeness and connectedness, while the critical situation appears when $H(x,u)$ behaves in some direction as $|x|^2$, as in the classical model of exact gravitational waves
Stability of Geodesically Complete Cosmologies
Creminelli, Paolo; Santoni, Luca; Trincherini, Enrico
2016-01-01
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} \\delta N~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Indian Academy of Sciences (India)
D B Lortan; S D Maharaj; N K Dadhich
2001-06-01
We investigate the propagation equations for the expansion, vorticity and shear for perfect ﬂuid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that ﬂuid ﬂow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic ﬂows: there exist no proper conformal Killing vectors ( ≠ 0) for perfect ﬂuids except for Robertson–Walker space-times. For a nonhomothetic vector ﬁeld the propagation of the quantity ln () along the integral curves of the symmetry vector is homogeneous.
MHD modeling on geodesic grids
Florinski, V; Balsara, D S; Meyer, C
2013-01-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional "Cartesian" frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a sim...
Stability of geodesically complete cosmologies
Energy Technology Data Exchange (ETDEWEB)
Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Pirtskhalava, David [Institute of Physics, École Polytechnique Fédérale de Lausanne,Lausanne, CH-1015 (Switzerland); Santoni, Luca; Trincherini, Enrico [Scuola Normale Superiore,Piazza dei Cavalieri 7, Pisa, 56126 (Italy); INFN - Sezione di Pisa,Largo B. Pontecorvo 3, Pisa, 56100 (Italy)
2016-11-22
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator {sup (3)} RδN is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Geodesic congruences in warped spacetimes
Ghosh, Suman; Kar, Sayan
2010-01-01
In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. We begin our investigations with the simplest case, namely geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes. Analytical expressions for the expansion scalar are obtained and the effect of including one or more thin branes (i.e. a background which is a slice of AdS spacetime) on its evolution, is pointed out. Subsequently, we move on to studying such congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using the analytical expressions for the velocity field components, we interpret the expansion, shear and rotation (ESR) along the flows. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in the ba...
Constrained Geodesic Centers of a Simple Polygon
Oh, Eunjin; Son, Wanbin; Ahn, Hee-Kap
2016-01-01
For any two points in a simple polygon P, the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regions. In this paper, we show how to compute the geodesic centers constrained to a set of line segment...
Quantum frictionless trajectories versus geodesics
Barbado, Luis C; Garay, Luis J
2015-01-01
Moving particles outside a star will generally experience quantum friction caused by Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring back-scattering). They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
A Note on Geodesically Bounded -Trees
Directory of Open Access Journals (Sweden)
Kirk WA
2010-01-01
Full Text Available It is proved that a complete geodesically bounded -tree is the closed convex hull of the set of its extreme points. It is also noted that if is a closed convex geodesically bounded subset of a complete -tree and if a nonexpansive mapping satisfies then has a fixed point. The latter result fails if is only continuous.
On Non-commutative Geodesic Motion
Ulhoa, S C; Santos, A F
2013-01-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
On non-commutative geodesic motion
Ulhoa, S. C.; Amorim, R. G. G.; Santos, A. F.
2014-07-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
2017-05-01
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Quantum frictionless trajectories versus geodesics
Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.
2015-10-01
Moving particles outside a star will generally experience quantum friction caused by the Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring backscattering). Along these trajectories, observers perceive just stellar emission, without further contribution from the Unruh effect. They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that it could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
Null Geodesics in Brane World Scenarios
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Feng; ZHANG Yuan-Zhong
2004-01-01
We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z2 symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate thc Z2 symmetry.
Line graphs and $2$-geodesic transitivity
Devillers, Alice; Jin, Wei; Li, Cai Heng; Praeger, Cheryl E.
2012-01-01
For a graph $\\Gamma$, a positive integer $s$ and a subgroup $G\\leq \\Aut(\\Gamma)$, we prove that $G$ is transitive on the set of $s$-arcs of $\\Gamma$ if and only if $\\Gamma$ has girth at least $2(s-1)$ and $G$ is transitive on the set of $(s-1)$-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic $2$-geodesic transitive graphs are the complete multipartite graph $K_{3[2]}$ and the icosahedron. Secondly we classify 2-geodesic transitive graphs ...
Multichannel image regularization using anisotropic geodesic filtering
Energy Technology Data Exchange (ETDEWEB)
Grazzini, Jacopo A [Los Alamos National Laboratory
2010-01-01
This paper extends a recent image-dependent regularization approach introduced in aiming at edge-preserving smoothing. For that purpose, geodesic distances equipped with a Riemannian metric need to be estimated in local neighbourhoods. By deriving an appropriate metric from the gradient structure tensor, the associated geodesic paths are constrained to follow salient features in images. Following, we design a generalized anisotropic geodesic filter; incorporating not only a measure of the edge strength, like in the original method, but also further directional information about the image structures. The proposed filter is particularly efficient at smoothing heterogeneous areas while preserving relevant structures in multichannel images.
Separable geodesic action slicing in stationary spacetimes
Bini, Donato; Jantzen, Robert T
2014-01-01
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlev\\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.
Ramified optimal transportation in geodesic metric spaces
Xia, Qinglan
2009-01-01
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimen...
Dissertation: Geodesics of Random Riemannian Metrics
LaGatta, Tom
2011-01-01
We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on $\\mathbb R^d$. We are motivated in our study by the random geometry of first-passage percolation (FPP), a lattice model which was developed to model fluid flow through porous media. By adapting techniques from standard FPP, we prove a shape theorem for our model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one. In differential geometry, geodesics are curves which locally minimize length. They need not do so globally: consider great circles on a sphere. For lattice models of FPP, there are many open questions related to minimizing geodesics; similarly, it is interesting from a geometric perspective when geodesics are globally minimizing. In the present study, we show that for any fixed st...
On superintegrable systems closed to geodesic motion
Tsiganov, A V
1997-01-01
In this work we consider superintegrable systems in the classical $r$-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational potentials from geodesic motion on $R^{2n}$.
On geodesic deviation in Schwarzschild spacetime
Philipp, Dennis; Laemmerzahl, Claus; Deshpande, Kaustubh
2015-01-01
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for...
Geodesics in the static Mallett spacetime
Olum, Ken D
2010-01-01
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Characterization of Null Geodesics on Kerr Spacetimes
Paganini, Claudio F; Oancea, Marius A
2016-01-01
We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore we show that from the point of view of any timelike observer outside of a black hole, trapping can be understood as a smooth set of spacelike directions on the observers' celestial sphere.
Photon Geodesics in FRW Cosmologies
Bikwa, Ojeh; Shevchuk, Andrew
2011-01-01
The Hubble radius is a particular manifestation of the Universe's gravitational horizon, R_h(t_0)=c/H_0, the distance beyond which physical processes remain unobservable to us at the present epoch. Based on recent observations of the cosmic microwave background (CMB) with WMAP, and ground-based and HST searches for Type Ia supernovae, we now know that R_h(t_0)~13.5 Glyr. This coincides with the maximum distance (ct_0~13.7 Glyr) light could have traveled since the big bang. However, the physical meaning of R_h is still not universally understood or accepted, though the minimalist view holds that it is merely the proper distance at which the rate of cosmic recession reaches the speed of light c. Even so, it is sometimes argued that we can see light from sources beyond R_h, the claim being that R_h lies at a redshift of only ~2, whereas the CMB was produced at a much greater redshift (~1100). In this paper, we build on recent developments with the gravitational radius by actually calculating null geodesics for a...
Institute of Scientific and Technical Information of China (English)
XIANG; Kainan
2001-01-01
［1］ Cruzeiro, A. B., Malliavin, P., Renormalized differential geometry on path spaces: Structural equation, curvature, J. Funct. Anal., 1996, 139: 119-181.［2］ Stroock, D. W., Some thoughts about Riemannian structures on path spaces, preprint, 1996.［3］ Driver, B., A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal., 1992, 109: 272-376.［4］ Enchev, O., Stroock, D. W., Towards a Riemannian geometry on the path space over a Riemannian manifold, J. Funct. Anal., 1995, 134: 392-416.［5］ Hsu, E., Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal., 1995, 134: 417-450.［6］ Lyons, T. J., Qian, Z. M., A class of vector fields on path space, J.Funct. Anal., 1997, 145: 205-223.［7］ Li, X. D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal., to be published.［8］ Driver, B., Towards calculus and geometry on path spaces, in Proc. Symp. Pure and Appl. Math. 57 (ed. Cranston, M., Pinsky, M.), Cornell: AMS, 1993, 1995.
Craniofacial Reconstruction Evaluation by Geodesic Network
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, various precise iteration equalities and inequalities of Morse indices for the closed geodesics are established. As applications of these formulae, multiplicity results of closed geodesics on some Riemannian manifolds are proved.
Orbifold Riemann surfaces and geodesic algebras
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L O [Steklov Mathematical Institute, Moscow (Russian Federation)], E-mail: chekhov@mi.ras.ru
2009-07-31
We study the Teichmueller theory of Riemann surfaces with orbifold points of order 2 using the fat graph technique. The previously developed technique of quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebras of geodesic functions is applicable to the surfaces with orbifold points. We describe classical and quantum braid group relations for particular sets of geodesic functions corresponding to A{sub n} and D{sub n} algebras and describe their central elements for the Poisson and quantum algebras.
'Proper acceleration' of a null geodesic in curved spacetime
Tian Gui Hua; Liang Can Bin
2002-01-01
Given a null geodesic in Minkowski spacetime, there exists a one-parameter family of observers in 'hyperbolic' motion which approaches the null geodesic as the parameter x sub 0 approaches zero. It is well known that the proper acceleration of the observers in the family approaches infinity as their world line approaches the null geodesic. The main purpose of this paper is to generalize this result to future-complete null geodesics in curved spacetimes.
A Conformal Extension Theorem based on Null Conformal Geodesics
Lübbe, Christian
2008-01-01
In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and Luebbe.
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of...
Geodesic curvature driven surface microdomain formation.
Adkins, Melissa R; Zhou, Y C
2017-09-15
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Geodesic curvature driven surface microdomain formation
Adkins, Melissa R.; Zhou, Y. C.
2017-09-01
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Geodesic Acoustic Propagation and Ballooning Mode Formalism
Li, M. B.; Diamond, P. H.; Young, G. G.; Arakawa, M.
2005-10-01
Relevance of ballooning formalism (BMF) in nonlinear interaction of toroidal electromagnetic drift waves in the presence of zonal flows and Geodesic Acoustic Oscillation (GAO) is critically examined from a physical argument of radial propagation of wave packets. To achieve the quasi-translational invariance of poloidal harmonics which is necessary for the BMF, the geodesic curvature induced transfer [1] of fluctuation energy in radial direction should occur faster than the time scale of physical interest. Of course, this does not happen necessarily in drift-Alfven (DALF) turbulence simulations [2]. This observation casts considerable doubts on the applicability of various codes based on the BMF concept to nonlinear electromagnetic problems. [1] B. Scott, Phys. Letters A 320 (2003) 53. [2] B. Scott, New J. Phys 7 (2005) 92.
Free of centrifugal acceleration spacetime - Geodesics
Culetu, Hristu
2013-01-01
A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $\\rho = -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. We found that the Tolman-Komar gravitational energy is finite everywhere. The timelike and null geodesics of the spacetime are examined.
On the Geodesic Nature of Wegner's Flow
Itto, Yuichi; Abe, Sumiyoshi
2008-01-01
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Studying null and time-like geodesics in the classroom
Müller, Thomas; 10.1088/0143-0807/32/3/011
2011-01-01
In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have some explicit examples available which show the different behaviour of geodesics. In this paper we present the GeodesicViewer, an interactive tool for studying the behaviour of geodesics in many different space-times. The geodesics can be represented in several ways, depending on the space-time in question. The use of a local reference frame and 'Cartesian-like' coordinates helps the students to develop some intuition in various situations. We present the various features of the GeodesicViewer in the form of readily formulated exercises for the students.
Symmetries of geodesic motion in Gödel-type spacetimes
Energy Technology Data Exchange (ETDEWEB)
Camci, U., E-mail: ucamci@akdeniz.edu.tr [Department of Physics, Akdeniz University, 07058 Antalya (Turkey)
2014-07-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Gödel-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for t-dot , r-dot ,φ-dot and ż of each classes I-IV which depends essentially on two independent parameters m and w, we explicitly integrated the geodesic equations of motion for the corresponding Gödel-type spacetimes.
Geodesics and Newton's Law in Brane Backgrounds
Mück, W; Volovich, I V
2000-01-01
In brane world models our universe is considered as a brane imbedded into ahigher dimensional space. We discuss the behaviour of geodesics in theRandall-Sundrum background and point out that free massive particles cannotmove along the brane only. The brane is repulsive, and matter will be expelledfrom the brane into the extra dimension. This is rather undesirable, and hencewe study an alternative model with a non-compact extra dimension, but with anattractive brane embedded into the higher dimensional space. We study thelinearized gravity equations and show that Newton's gravitational law is validon the brane also in the alternative background.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
Focal properties of geodesic waveguide lenses
Verber, C. M.; Vahey, D. W.; Wood, V. E.
1976-01-01
The focal properties of uncorrected geodesic lenses in ion-exchanged glass waveguides are reported. A 13.8-mm-focal-length lens resolved beams with an angular separation of 27.6 mrad, while a 28-mm-focal-length lens resolved beams with an angular separation of only 3.3 mrad. Intensity profiles of the focal region of the former lens revealed a 40-micron spot size when the input aperture was 5 mm, and a spot size of 7.7 microns when the aperture was reduced to 1 mm. This value is close to the diffraction-limited spot size of 5.7 microns.
Light geodesics near an evaporating black hole
Energy Technology Data Exchange (ETDEWEB)
Guerreiro, Thiago, E-mail: thiago.barbosa@unige.ch; Monteiro, Fernando, E-mail: fernando.monteiro@unige.ch
2015-10-16
Quantum effects imply that an infalling observer cannot cross the event horizon of an evaporating black hole, even in her proper time. The Penrose diagram of an evaporating black hole is different from the one usually reported in the literature. We show that before the observer can cross the horizon the black hole disappears. Possible observational consequences are discussed. - Highlights: • We calculate the in-falling light geodesics in an evaporating black hole. • For our calculation we use a non-static metric called Vaydia metric. • We show that in-falling light cannot cross the event horizon. • In this case there is no information paradox.
Geodesic least squares regression on information manifolds
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2014-12-05
We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply this to scaling laws in magnetic confinement fusion.
Black Hole Decay as Geodesic Motion
Sen-Gupta, K; Gupta, Kumar S.; Sen, Siddhartha
2003-01-01
We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The decay rate is shown to be correctly described by geodesic motion in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. We also show that the near-horizon conformal symmetry predicts a precise correction term to the usual expression for the decay rate of black holes. The results obtained here are a consequence of the holographic nature of the system.
Geodesics in the (anti-)de Sitter spacetime
Tho, Nguyen Phuc Ky
2016-01-01
A class of exact solutions of the geodesic equations in (anti-)de Sitter spacetimes is presented. The geodesics for test particles in $AdS_4$ and $dS_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. The world lines of test particles are not dependent on their energy as noted. Spontaneous symmetry breaking of $AdS_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in the vacuum. Interestingly, the energy of a pair and the time its particles moving along their geodesics can be related by a relation similar to Heisenberg uncertainty one pertaining quantum vacuum fluctuations. The sinusoidal geodesics of $AdS_4$ spacetime can describe the world lines of the virtual particles and antiparticles. The hyperbolic sine geodesics of $dS_4$ spacetime can explain why galaxies move apart with positive accelerations.
A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies
Nilsson, Ulf S.; Uggla, Claes; Wainwright, John
2000-10-01
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of space-time anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.
A Perspicuous Description of the Schwarzschild Black Hole Geodesics
Arik, Metin
2016-01-01
Schwarzschild black hole is the simplest black hole that is studied most in detail. Its behavior is best understood by looking at the geodesics of the particles under the influence of its gravitational field. In this paper, the focus of attention is giving a perspicuous description of the Schwarzschild geodesics by using analogue potential approach. Specifically we discuss geodesics of light and of a massive particle in the case that their angular momentum is non zero in the Schwarzschild spacetime. This discussion is done by defining analogue potentials out of geodesic equations and defining relevant dimensionless conserved quantities. Then, we designate how geodesics change in response to the change of these quantities. Our results indicate the relation between the particles' motion near black hole horizon and their angular momentum. Furthermore, we make a comparison between Newtonian Physics (NP) and General Relativity (GR) in the language of the analogue potential approach.
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Geralico, Andrea; Jantzen, Robert T.
2011-04-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Jantzen, Robert T
2014-01-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Focusing of geodesic congruences in an accelerated expanding Universe
Albareti, F D; de la Cruz-Dombriz, A
2012-01-01
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from...
Integrable vs Nonintegrable Geodesic Soliton Behavior
Fringer, O B
1999-01-01
We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler-Poincare equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program for ideal fluids, but where the kinetic energy metric is different from the L2 norm of the velocity. These pde possess a finite-dimensional invariant manifold of particle-like (measure-valued) solutions we call ``pulsons.'' We solve the particle dynamics of the two-pulson interaction analytically as a canonical Hamiltonian system for geodesic motion with two degrees of freedom and a conserved momentum. The result of this two-pulson interaction for rear-end collisions is elastic scattering with a phase shift, as occurs with solitons. In contrast, head-on antisymmetric collisons of pulsons tend to form singularities.
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of FEGC to the radial flow. The reason for the reduction of damping rate is that when the effect of FEGC counts, the new resonant velocity becomes much larger than ions thermal velocity with equilibrium distribution obeying Maxwellian distribution, compared with unmodified Landau resonant velocity. Especially, FEGC changes the characters of the frequency and damping rate of low-frequency GAM as functions of safety factor $q$ .
An Algorithm for Constructing Principal Geodesics in Phylogenetic Treespace.
Nye, Tom M W
2014-01-01
Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks, clustering and multidimensional scaling have been developed and applied to tree samples. This paper describes a stochastic algorithm for constructing a principal geodesic or line through treespace which is analogous to the first principal component in standard principal components analysis. A principal geodesic summarizes the most variable features of a sample of trees, in terms of both tree topology and branch lengths, and it can be visualized as an animation of smoothly changing trees. The algorithm performs a stochastic search through parameter space for a geodesic which minimizes the sum of squared projected distances of the data points. This procedure aims to identify the globally optimal principal geodesic, though convergence to locally optimal geodesics is possible. The methodology is illustrated by constructing principal geodesics for experimental and simulated data sets, demonstrating the insight into samples of trees that can be gained and how the method improves on a previously published approach. A java package called GeoPhytter for constructing and visualizing principal geodesics is freely available from www.ncl.ac.uk/ ntmwn/geophytter.
Geodesic models generated by Lie symmetries
Abebe, G Z; Govinder, K S
2014-01-01
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
A geodesic model in conformal superspace
Gomes, Henrique de A
2016-01-01
In this paper, I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. Conformal superspace is a stratified manifold, with different strata corresponding to different isometry groups. Choosing space to be (homeomorphic to) $S^3$, conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point -- corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geome...
Drift effects on electromagnetic geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)
2015-02-15
A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)
Geodesic motion in a stationary dihole spacetime
Dubeibe, F L
2016-01-01
The knowledge of the properties of the different exact solutions modeling binary systems, is a necessary step towards the classification of physically suitable solutions and its corresponding limits of applicability. In the present paper, we perform an analysis of the geodesics around two counter--rotating Kerr--Newman black holes endowed with opposite electric charges, which achieve equilibrium by means of a strut between their constituents. We find that bounded and unbounded orbits are possible. However, test particles may cross between the black holes only if their angular momentum equals zero, otherwise, there exist a repulsive potential, which prohibits such orbits. Two important aspects are pointed out for these trajectories: ({\\it i}) the motion of photons is affected once crossing the strut; and ({\\it ii}) massive particles exhibit oscillatory motion, as a first analog of the Sitnikov problem in general relativity. The radius of the innermost stable circular orbit as a function of the physical paramet...
On the Morris - Thorne wormhole geodesics
Culetu, Hristu
2014-01-01
The properties of a particular Misner - Thorne wormhole are investigated. The "exotic stress-energy" needed to maintain the wormhole open corresponds to a massless scalar field whose Lagrangean density contains a negative kinetic term. While the Komar energy of the spacetime is vanishing due to the negative energy density and radial pressure, the ADM energy is (minus) the Planck energy. The timelike geodesics are hyperbolae and any static observer is inertial. The null radial trajectories are also hyperbolae and Lorentz invariant as Coleman- de Luccia expanding bubble or Ipser-Sikivie domain wall. Using a different equation of state for the fluid on the dynamic wormhole throat of Redmount and Suen, we reached an equation of motion for the throat (a hyperbola) that leads to a negative surface energy density and the throat expands with the same acceleration $2\\pi |\\sigma|$ as the Ipser-Sikivie domain wall.
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian...... Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically....
A Visualization of Null Geodesics for the Bonnor Massive Dipole
Oliva-Mercado, Guillermo Andree; Cordero-García, Iván; Frutos-Alfaro, Francisco
2015-01-01
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
A visualization of null geodesics for the bonnor massive dipole
Directory of Open Access Journals (Sweden)
G. Andree Oliva Mercado
2015-08-01
Full Text Available In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro; Tamaoka, Kotaro
2017-05-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using a conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show that our construction agrees with the known result of the conformal partial waves.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro
2016-01-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construction agrees with the known result of the conformal partial waves.
Geodesic Motion in a Charged 2D Stringy Blackhole Spacetime
Uniyal, Rashmi; Purohit, K D
2014-01-01
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacetime.
de Sitter geodesics: reappraising the notion of motion
Pereira, J G
2011-01-01
de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined by any one of these geodesics. By taking into account the appropriate transitivity properties, a new family of geodesics is obtained whose trajectories are able to connect any two points of the de Sitter spacetime. They are, furthermore, consistent with the de Sitter momentum conservation. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may be important at very-high energies, where conformal symmetry plays a significant role.
Spin-geodesic deviations in the Kerr spacetime
Bini, D.; Geralico, A.
2011-11-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Spin-geodesic deviations in the Kerr spacetime
Bini, Donato
2014-01-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Closed timelike geodesics in a gas of cosmic strings
Grøn, Ø; Gron, Oyvind; Johannesen, Steinar
2007-01-01
We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.
Geodesic motion on closed spaces: Two numerical examples
Energy Technology Data Exchange (ETDEWEB)
Müller, Daniel, E-mail: muller@fis.unb.br [Universidade de Brasília, Instituto de Física, Cxp 04455, Asa Norte, 70919-900, Brasília, DF (Brazil)
2012-01-09
The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy–momentum tensor in Universes with non-trivial topology. The purpose of this work is to provide concrete numerical examples of geodesic flows. Two manifolds with genus g=0 are given. In one the chaotic regions, form sets of negligible or zero measure. In the second example the geodesic flow shows the presence of measurable chaotic regions. The approach is “experimental”, numerical, and there is no attempt to an analytical calculation. -- Highlights: ► Elementary differential geometry of surfaces and the Gauss–Bonnet theorem. ► The geodesic equation is numerically solved for two metrics on the sphere. ► With the Poincare surface, chaotic and regular regions are identified. ► Chaotic regions increase as the curvature fluctuation of the manifold increases.
Lie symmetries of the geodesic equations and projective collineations
Energy Technology Data Exchange (ETDEWEB)
Tsamparlis, Michael; Paliathanasis, Andronikos, E-mail: mtsampa@phys.uoa.g, E-mail: paliathanasis@gmail.co [Department of Physics, Section Astrophysics Astronomy Mechanics, University of Athens, University of Athens, Zografos 15783, Athens (Greece)
2009-10-01
We study the Lie symmetries of the geodesic equations in a Riemannian space and show that they coincide with the projective symmetries of the Riemannian metric. We apply the result to the spaces of constant curvature.
A Note on Geodesically Bounded ℝ-Trees
Directory of Open Access Journals (Sweden)
W. A. Kirk
2010-01-01
Full Text Available It is proved that a complete geodesically bounded R-tree is the closed convex hull of the set of its extreme points. It is also noted that if X is a closed convex geodesically bounded subset of a complete R-tree Y, and if a nonexpansive mapping T:X→Y satisfies inf{d(x,T(x:x∈X}=0, then T has a fixed point. The latter result fails if T is only continuous.
The Lorentzian oscillator group as a geodesic orbit space
Energy Technology Data Exchange (ETDEWEB)
Batat, W. [Ecole Normale Superieure d' Enseignement Technologique d' Oran, Departement de Mathematiques et Informatique, B.P. 1523, El M' Naouar, Oran (Algeria); Gadea, P. M. [Instituto de Fisica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid (Spain); Oubina, J. A. [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela (Spain)
2012-10-15
We prove that the four-dimensional oscillator group Os, endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so, in particular, null-geodesic) orbit space with some of its homogeneous descriptions corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in d-dimensional supergravity with at least 24 of the 32 possible supersymmetries.
GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION
Directory of Open Access Journals (Sweden)
Serge Beucher
2011-05-01
Full Text Available The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstruction supposes the use of a marker function f which is not necessarily related to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristic regions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy to handle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in image reconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of the function reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.
Geodesics and Acceleration in Influence Theory
Walsh, James; Knuth, Kevin
Influence theory is concerned with a foundational approach where it is assumed that particles influence one another in a discrete one-to-one fashion. This results in a partially ordered set of influence events, called the influence network, where particles are represented by totally ordered chains of events. Information physics considers physical laws to result from consistent quantification of physical phenomena. Knuth and Bahreyni (2014) demonstrated that the mathematics of spacetime emerges from consistent quantification of influence events by embedded coordinated observers. Knuth (2014) showed that in 1 +1 dimensions observer-based predictions about a free (uninfluenced) particle result in the Dirac equation. Here, we show that when a particle in 1 +1 dimensions is influenced, it is uniquely and consistently described in terms of relativistic acceleration for constant rate of influence and in general obeys equations of the form of the geodesic equations of general relativity. This suggests that Influence Theory can also account for forces (like gravity), which give rise to well-known relativistic effects such as time dilation.
A Finsler geodesic spray paradigm for wildfire spread modelling
DEFF Research Database (Denmark)
Markvorsen, Steen
2015-01-01
represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... sensitive - geodesic solutions to the wildfire spread problem. The methods presented here stem directly from first principles of 2-dimensional Finsler geometry, and they can be readily extracted from the seminal monographs [10] and [11], but we will take special care to introduce and exemplify the necessary...... framework for the implementation of the geometric machinery into this new application - not least in order to facilitate and support the dialog between geometers and the wildfire modelling community. The ‘integration’ part alluded to above is obtained via the geodesics of the ensuing Finsler metric which...
Geodesics on Surfaces with Helical Symmetry: Cavatappi Geometry
Jantzen, Robert T
2013-01-01
A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface of revolution like the torus which it contains as a special case. It serves as a simple example of helically symmetric surfaces which are the generalizations of surfaces of revolution in which an initial plane curve is screw-revolved around an axis in its plane. The physics description of geodesic motion on these surfaces requires a slightly more involved effective potential approach than the torus case due to the nonorthogonal coordinate grid necessary to describe this problem. Amazingly this discussion allows one to very nicely describe the geodesics of the surface of the more complicated ridged cavatappi pasta.
Null geodesics in a magnetically charged stringy black hole spacetime
Kuniyal, Ravi Shankar; Uniyal, Rashmi; Nandan, Hemwati; Purohit, K. D.
2016-04-01
We study the null geodesics of a four-dimensional magnetic charged black hole spacetime arising in string theory. The behaviour of effective potential in view of the different values of black hole parameters are analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results are compared to those obtained for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime in general relativity.
Coherent states and geodesics cut locus and conjugate locus
Berceanu, S
1997-01-01
The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point $0$ is equal to the set of coherent vectors orthogonal to $\\vert 0>$. A simple method to calculate the conjugate locus in Hermitian symmetric spaces with significance in the coherent state approach is presented. The results are illustrated on the complex Grassmann manifold.
An Efficient Geodesic Path Solution for Prolate Spheroids
1979-07-01
unit tangent vector is determinr 4, the other relevant parameter in the ray analysis , namely, the unit binprmal vector 6 can readily be obtained via...geodesic shown in Fig. S . Recall that the unit tangent vectors for the geodesic are given by Equations (1l)-(15). Assuming at a particular point (e )on the...Aeronautics and Space Adi&inistration, ’,,ashington, D.C. 20546. [3] M.M. Lipschutz, Theory and Problems of Di-fferentia-l_(eni ret-rv, Schaums Outline
Global structure and geodesics for Koenigs superintegrable systems
Valent, Galliano
2016-09-01
We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their superintegrability (SI) and most of them are shown to be globally defined on either ℝ2 or ℍ2. Their geodesic flows are easily determined thanks to their quadratic integrals. Using Carter (or minimal) quantization, we show that the formal SI is preserved at the quantum level and for two metrics, for which all of the geodesics are closed, it is even possible to compute the classical action variables and the point spectrum of the quantum Hamiltonian.
Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points
Institute of Scientific and Technical Information of China (English)
Fei LIU; Fang WANG
2016-01-01
In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
A Few Endpoint Geodesic Restriction Estimates for Eigenfunctions
Chen, Xuehua; Sogge, Christopher D.
2014-07-01
We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a TT* argument, simply by using the L 2-boundedness of the Hilbert transform on , we are able to improve the corresponding L 2-restriction bounds of Burq, Gérard and Tzvetkov (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009). Also, in the case of 2-dimensional compact manifolds with nonpositive curvature, we obtain improved L 4-estimates for restrictions to geodesics, which, by Hölder's inequality and interpolation, implies improved L p -bounds for all exponents p ≥ 2. We do this by using oscillatory integral theorems of Hörmander (Ark Mat 11:1-11, 1973), Greenleaf and Seeger (J Reine Angew Math 455:35-56, 1994) and Phong and Stein (Int Math Res Notices 4:49-60, 1991), along with a simple geometric lemma (Lemma 3.2) about properties of the mixed-Hessian of the Riemannian distance function restricted to pairs of geodesics in Riemannian surfaces. We are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that, in this case, there are many totally geodesic submanifolds.
Integrability of Invariant Geodesic Flows on n-Symmetric Spaces
Jovanovic, Bozidar
2010-01-01
In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata $n$-symmetric spaces $K^n/\\diag(K)$, where $K$ is a semisimple (respectively, simple) compact Lie group.
Monodromic vs geodesic computation of Virasoro classical conformal blocks
Directory of Open Access Journals (Sweden)
Konstantin Alkalaev
2016-03-01
Full Text Available We compute 5-point classical conformal blocks with two heavy, two light, and one superlight operator using the monodromy approach up to third order in the superlight expansion. By virtue of the AdS/CFT correspondence we show the equivalence of the resulting expressions to those obtained in the bulk computation for the corresponding geodesic configuration.
Thermodynamic Geodesics of a Reissner Nordstr\\"om Black Hole
Farrugia, Christine
2016-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordstr\\"om black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems. It can be deduced that the relation which the geodesics establish between the entropy $S$ and electric charge $Q$ of the black hole extremises changes in the black hole's mass. Indeed, at any given point along a geodesic, the value of $\\text{d}S/\\text{d}Q$ is of the same order of magnitude as the rate at which entropy changes with charge during a constant-mass perturbation. Our claim is further justified by the fact that the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation.
On the regularity of geodesic rays associated to test configurations
Phong, D. H.; Sturm, Jacob
2007-01-01
Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation. Geometrically, this is accomplished by the use a positive line bundle on the resolution which is trivial outside of the exceptional divisor.
Geodesics in the space of K\\"ahler cone metrics
Calama, Simone
2012-01-01
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\\"ahler cone metrics.
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan;
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....
Geodesic atlas-based labeling of anatomical trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2015-01-01
We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...
Analytical solutions for geodesics in black hole spacetimes
Hackmann, Eva
2015-01-01
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general timelike and lightlike motion is also presented.
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees...
Geodesic flow, connecting orbits and almost full foliation
Institute of Scientific and Technical Information of China (English)
CHENG; Jian; MENG; Long
2006-01-01
We study in this article a special dynamical behavior of geodesic flow on T2.Our example shows that there is an area-preserving monotone twist map for which all minimal periodic orbits can be connected,and at the same time for a certain rational rotation number the minimal set is almost an invariant curve.
Non-Minimally Coupled Cosmology as Geodesic Motion
Elias, L A; Elias, Luciana A.; Saa, Alberto
2007-01-01
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
LIU; Chungen
2002-01-01
［1］Klingenberg, W., Riemannian Geometry, Berlin: Walter de Gruyter, 1982.［2］Morse, M., The Calculus of Variations in the Large, Vol. 18,New York: Colloquium Publ., 1934.［3］Long, Y., Bott formula of the Maslov_type index theory, Pacific J. Math., 1999, 187: 113-149.［4］Hingston, N., On the lengths of closed geodesics on a two_sphere, Proc. Amer. Math. Soc., 1997, 125(10): 3099-3106.［5］Hingston, N., On the growth of the number of closed geodesics on the two_sphere, Inter. Math. Res. Notices, 1993, 9: 253-262.［6］Ballmann, W., Thorberrgsson, G., Ziller, W., Closed geodesics on positively curved manifolds, Annals of Math., 1982, 116: 213-247.［7］Bott, R., On the iteration of closed geodesics and the Sturm intersection theory, Commun. Pure Appl. Math., 1956, 9: 171-206.［8］Yakubovich, V., Starzhinskii, V., Linear Differential Equations with Periodic Ceofficients, New York: John Wiley & Sons, 1975.［9］Long, Y., Zhu, C., Closed characteristics on compact convex hypersurfaces in R2n, Nankai Inst. of Math., Preprint Series, No. 1999_M_002, Revised Dec. 2000.［10］Rademacher, H. _B., On the average indices of closed geodesics, J. Diff. Geom., 1989, 29: 65-83.［11］Liu, C., Long, Y., Iteration inequalities of the Maslov_type index theory with applications, J. Diff. Equa., 2000, 165: 355-376.［12］Liu, C., Long, Y., An optimal increasing estimate of the iterated Maslov_type indices, Chinese Science Bulletin, 1997, 42: 2275-2277.［13］Long, Y., Precise iteration formula of the Maslov_type index theory and ellipticity of closed characteristics,Advances in Math., 2000, 154: 76-131.［14］Bangert, V., On the existence of closed geodesics on two_spheres, Inter. J. of Math., 1993, 4: 1-10.［15］Bao, D., Chern, S. S., Shen, Z., An Introduction to Riemann_Finsler Geometry, New York: Springer_Verlag, 2000.［16］Bott, R., Lectures on More theory, old and new, Bull. Amer. Math. Soc., 1982, 7(2): 331-358.［17］Franks, J., Geodesics on S2 and
Haustral loop extraction for CT colonography using geodesics.
Liu, Yongkai; Duan, Chaijie; Liang, Jerome; Hu, Jing; Lu, Hongbing; Luo, Mingyue
2017-03-01
The human colon has complex geometric structures because of its haustral folds, which are thin flat protrusions on the colon wall. The haustral loop is the curve (approximately triangular in shape) that encircles the highly convex region of the haustral fold, and is regarded as the natural landmark of the colon, intersecting the longitude of the colon in the middle. Haustral loop extraction can assist in reducing the structural complexity of the colon, and the loops can also serve as anatomic markers for computed tomographic colonography (CTC). Moreover, haustral loop sectioning of the colon can help with the performance of precise prone-supine registration. We propose an accurate approach of extracting haustral loops for CT virtual colonoscopy based on geodesics. First, the longitudinal geodesic (LG) connecting the start and end points is tracked by the geodesic method and the colon is cut along the LG. Second, key points are extracted from the LG, after which paired points that are used for seeking the potential haustral loops are calculated according to the key points. Next, for each paired point, the shortest distance (geodesic line) between the paired points twice is calculated, namely one on the original surface and the other on the cut surface. Then, the two geodesics are combined to form a potential haustral loop. Finally, erroneous and nonstandard potential loops are removed. To evaluate the haustral loop extraction algorithm, we first utilized the algorithm to extract the haustral loops. Then, we let the clinicians determine whether the haustral loops were correct and then identify the missing haustral loops. The extraction algorithm successfully detected 91.87% of all of the haustral loops with a very low false positive rate. We believe that haustral loop extraction may benefit many post-procedures in CTC, such as supine-prone registration, computer-aided diagnosis, and taenia coli extraction.
Null Geodesics in a Magnetically Charged Stringy Black Hole Spacetime
Kuniyal, Ravi Shankar; Nandan, Hemwati; Purohit, K D
2015-01-01
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of black hole parameters is analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in detail in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results obtained are then compared with those for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime. It is observed that there exists no stable circular orbit outside the event horizon for massless test particles.
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
Geodesic acoustic modes with poloidal mode couplings ad infinitum
Singh, Rameswar; Garbet, X; Hennequin, P; Vermare, L; Morel, P; Singh, R
2015-01-01
Geodesic acoustic modes (GAMs) are studied, for the first time, including all poloidal mode $(m)$ couplings using drift reduced fluid equations. The nearest neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number $k_{r}$. The infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fractions. Convergence study of linear GAM dispersion with respect to $k_{r}$ and the $m$-spectra confirms that high m couplings become increasingly important with $k_{r}$. The radially sorted roots overlap with experimentally measured GAM frequency profile in low collisionality shots in Tore Supra thus explaining the reduced frequency of GAM in Tore Supra.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, Kuantay; Abutalip, Marzhan; Kalymova, Zhanerke; Suleymanova, Sharara
2015-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
Detecting Einstein geodesics: Einstein metrics in projective and conformal geometry
Gover, A Rod
2013-01-01
Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the existence of such a metric, and in generic settings the vanishing of these is also sufficient. We also obtain results for the problem of metrisability (without the Einstein condition): We show that the odd Chern type invariants of an affine connection are projective invariants that obstruct the existence of a projectively related Levi-Civita connection. In addition we discuss a concrete link between projective and conformal geometry and the application of this to the projective-Einstein problem.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, K. A.; Quevedo, H.; Abutalip, M. S.; Kalymova, Zh. A.; Suleymanova, Sh. S.
2016-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
Embedding spacetime via a geodesically equivalent metric of Euclidean signature
Jonsson, Rickard
2001-01-01
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent, or dual, metric can be embedded in ordinary Euclidean space. On the embedded surface freely falling particles move on the shortest path. Thus one can visualize how acceleration in a gravitational field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature, even the weak gravity of our Earth. This may provide a nice pedagogical tool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions. In an addendum I extend the analysis concerning the shape of an embedding of the dual spacetime of a line through a planet of constant proper density.
Geodesic flows and their deformations in Bertrand spacetimes
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
In this article we will discuss some features of a particular spacetime called Bertrand space-time of Type II (BST-II). This spacetime is associated with multiple real parameters. The various energy conditions and geodesic equations of BST-II are used to find the limits of these parameters which can result in a meaningful and physical space-time. It will be shown that in certain circumstances where the weak and strong energy conditions hold BST-II can be thought of as a physically interesting spacetime. Further, the talk discusses about the ESR parameters in this spacetime. The properties of these parameters are nemerically analyzed keeping an eye on the focussing property of radial timelike and radial null geodesics.
van Vleck determinants geodesic focussing and defocussing in Lorentzian spacetimes
Visser, M
1993-01-01
The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.
Quantization of black hole entropy from unstable circular null geodesics
Wei, Shao-Wen; Liu, Yu-Xiao; Fu, Chun-E.
2016-04-01
The quasinormal mode frequencies can be understood from the massless particles trapped at the unstable circular null geodesics and slowly leaking out to infinity. Based on this viewpoint, in this paper, we semiclassically construct the entropy spectrum of the static and stationary black holes from the null geodesics. The result shows that the spacing of the entropy spectrum only depends on the property of the black hole in the eikonal limit. Moreover, for a black hole far from the extremal case, the spacing is found to be smaller than 2πħ for any dimension, which is very different from the result of the previous work by using the usual quasinormal mode frequencies.
Polyaffine parametrization of image registration based on geodesic flows
DEFF Research Database (Denmark)
Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.
2012-01-01
Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....... is very similar to existing methods, we show that we can find an analytical solution. This solution converges exponentially to the true solution, and the gradients may be determined similarly. We compare to existing prominent methods; the log-euclidean polyaffine framework, and the DARTEL implementation...
Do electromagnetic waves always propagate along null geodesics?
Asenjo, Felipe A
2016-01-01
We find exact solutions to Maxwell equations written in terms of four-vector potentials in non--rotating, as well as in G\\"odel and Kerr spacetimes. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non--rotating spherical symmetric spacetimes, electromagnetic plane waves travel along null geodesics. However, electromagnetic plane waves on G\\"odel and Kerr spacetimes do not exhibit that behavior.
Geodesic motion of test particles in Korkina-Grigoryev metric
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under whi...
Landau damping of geodesic acoustic mode in toroidally rotating tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment, The Collaborative Innovation Center for Advanced Fusion Energy and Plasma Science, and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Cao, Jintao [Bejing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-06-15
Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary toroidal Mach number is analytically derived. The effects of toroidal rotation on the GAM frequency and damping rate do not depend on the orientation of equilibrium flow. It is shown that the toroidal Mach number M increases the GAM frequency and dramatically decreases the Landau damping rate.
Lens rigidity with trapped geodesics in two dimensions
Croke, Christopher B
2011-01-01
We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat M\\"obius strip are determined by their lens data. We also see by example that the flat M\\"obius strip is not determined by it's scattering data. We then consider the case of negatively curved cylinders with convex boundary and show that they are lens rigid.
A Continuum Mechanical Approach to Geodesics in Shape Space
2010-01-01
A CONTINUUM MECHANICAL APPROACH TO GEODESICS IN SHAPE SPACE By Benedikt Wirth Leah Bar Martin Rumpf and Guillermo Sapiro IMA Preprint Series # 2295...Benedikt Wirth† Leah Bar‡ Martin Rumpf† Guillermo Sapiro‡ †Institute for Numerical Simulation, University of Bonn, Germany ‡Department of Electrical and...mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Firmly nonexpansive mappings in classes of geodesic spaces
Ariza-Ruiz, David; Lopez-Acedo, Genaro
2012-01-01
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, as (uniformly convex) $W$-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic egularity for the Picard iterations.
Geodesic completeness in a wormhole spacetime with horizons
Olmo, Gonzalo J; Sanchez-Puente, A
2015-01-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
A Dynamical Systems Approach to Schwarzschild Null Geodesics
Belbruno, Edward
2011-01-01
The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular m...
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
2016-01-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Adaptive geodesic transform for segmentation of vertebrae on CT images
Gaonkar, Bilwaj; Shu, Liao; Hermosillo, Gerardo; Zhan, Yiqiang
2014-03-01
Vertebral segmentation is a critical first step in any quantitative evaluation of vertebral pathology using CT images. This is especially challenging because bone marrow tissue has the same intensity profile as the muscle surrounding the bone. Thus simple methods such as thresholding or adaptive k-means fail to accurately segment vertebrae. While several other algorithms such as level sets may be used for segmentation any algorithm that is clinically deployable has to work in under a few seconds. To address these dual challenges we present here, a new algorithm based on the geodesic distance transform that is capable of segmenting the spinal vertebrae in under one second. To achieve this we extend the theory of the geodesic distance transforms proposed in1 to incorporate high level anatomical knowledge through adaptive weighting of image gradients. Such knowledge may be provided by the user directly or may be automatically generated by another algorithm. We incorporate information 'learnt' using a previously published machine learning algorithm2 to segment the L1 to L5 vertebrae. While we present a particular application here, the adaptive geodesic transform is a generic concept which can be applied to segmentation of other organs as well.
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
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.
Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
Sokołowski, Leszek M
2016-01-01
We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by $\\Lambda$, lying on a Euclidean two--plane. Then we outline an alternative proof for $AdS_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.
Symmetries of geodesic motion in G\\"{o}del-type spacetimes
Camci, U
2014-01-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for $\\dot{t}, \\dot{r}, \\dot{\\phi}$ and $\\dot{z}$ of each classes I-IV which depends essentially on two independent parameters $m$ and $w$, we explicitly integrated the geodesic equations of motion for the corresponding G\\"{o}del-type spacetimes.
Simple computation of null-geodesics, with applications to vortex boundary detection
Serra, Mattia; Haller, George
2016-11-01
Recent results show that boundaries of coherent vortices (elliptic coherent structures) can be computed as closed null-geodesics of appropriate Lorentzian metrics defined on the physical domain of the underlying fluid. Here we derive a new method for computing null-geodesics of general Lorentzian metrics, founded on the geometry of geodesic flows. We also derive the correct set of initial conditions for the computation of closed null-geodesics, based on simple topological properties of planar closed curves. This makes the computation of coherent vortex boundaries fully automated, simpler and more accurate compared to the existing procedure. As an illustration, we compute objective coherent vortex boundaries in Oceanic and Atmospheric Flows.
Divided Spheres Geodesics and the Orderly Subdivision of the Sphere
Popko, Edward S
2012-01-01
This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.
Tifinagh Character Recognition Using Geodesic Distances, Decision Trees & Neural Networks
Directory of Open Access Journals (Sweden)
O.BENCHAREF
2011-09-01
Full Text Available The recognition of Tifinagh characters cannot be perfectly carried out using the conventional methods which are based on the invariance, this is due to the similarity that exists between some characters which differ from each other only by size or rotation, hence the need to come up with new methods to remedy this shortage. In this paper we propose a direct method based on the calculation of what is called Geodesic Descriptors which have shown significant reliability vis-à-vis the change of scale, noise presence and geometric distortions. For classification, we have opted for a method based on the hybridization of decision trees and neural networks.
A Mean Value Theorem for Closed Geodesics on Congruence Surfaces
Lukianov, Vladimir
2005-01-01
We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics of the eigenvalues of the Laplacian on the surface. In the case of the modular domain, E. Bogomolny, F. Leyvraz and C. Schmit gave a formula for the mean square, which was rigorously proved by M. Peter. In this paper we...
3+1 geodesic equation and images in numerical spacetimes
Vincent, Frederic H; Novak, Jérôme
2012-01-01
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.
Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature
Mangoubi, Oren; Smith, Aaron
2016-01-01
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\\mathcal{M}$, which we call the $\\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 < \\mathfrak{m}_{2} \\leq C_{x}(u,v) \\leq \\mathfrak{M}_2 < \\infty$ is $\\mathcal{O}^*\\left(\\frac{\\mathfrak{M}_2}{\\mathfrak{m}_2}\\right)$. In particular, this bound on the mixing time does not depend expli...
Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2012-01-01
Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.
Dome, Sweet Dome--Geodesic Structures Teach Math, Science, and Technology Principles
Shackelford, Ray; Fitzgerald, Michael
2007-01-01
Today, geodesic domes are found on playgrounds, homes, over radar installations, storage facilities, at Disney's Epcot Center, and at World's Fairs. The inventor of the design, Buckminster Fuller, thought that geodesic domes could be used to cover large areas and even designed one to cover all of New York's Manhattan Island. This article details…
Optimal three-dimensional biped walking pattern generation based on geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2017-03-01
Full Text Available The innovative three-dimensional humanoid biped gait planning method using geodesics is introduced in this article. In order to control three-dimensional walking, the three-dimensional linear inverted pendulum model is studied in our energy-optimal gait planning based on geodesics. The kinetic energy of the three-dimensional linear inverted pendulum model is calculated at first. Based on this kinetic energy model, the Riemannian metric is defined and the Riemannian surface is further determined by this Riemannian metric. The geodesic is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the center of gravity because the kinetic energy along the geodesic is invariant according to the geometric property of geodesics and the walking is energy-saving. Finally, a simulation experiment using a 12-degree-of-freedom biped robot model is implemented. The gait sequences of the simulated RoboErectus humanoid robot are obtained in the ROS (Robot Operating System Gazebo environment. The proposed geodesics approach is compared with the traditional sinusoidal interpolation method by analyzing the torque feedback of each joint of both legs, and our geodesics optimization gait planning method for three-dimensional linear inverted pendulum model walking control is verified by the assessment results.
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Y.N.; Risager, Morten
2005-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on a random set of homology classes and certain arithmetic sets. We explain the analogues for free groups, conjugacy classes...
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Yiannis N.; Risager, Morten S.
2008-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any set with asymptotic density with respect to a specific norm. We explain the analogues for free groups, conjugacy classes...
Spectral segmentation via midlevel cues integrating geodesic and intensity.
Lu, Huchuan; Zhang, Ruixuan; Li, Shifeng; Li, Xuelong
2013-12-01
Image segmentation still remains as a challenge in image processing and pattern recognition when involving complex natural scenes. In this paper, we present a new affinity model for spectral segmentation based on midlevel cues. In contrast to most existing methods that operate directly on low-level cues, we first oversegment the image into superpixel images and then integrate the geodesic line edge and intensity cue to form the similarity matrix W so that it more accurately describes the similarity between data. The geodesic line edge could avoid strong boundary and represent the true boundary between two superpixels while the mean red green blue vector could describe the intensity of superpixels better. As far as we know, this is a totally new kind of affinity model to represent superpixels. Based on this model, we use the spectral clustering in the superpixel level and then achieve the image segmentation in the pixel level. The experimental results show that the proposed method performs steadily and well on various natural images. The evaluation comparisons also prove that our method achieves comparable accuracy and significantly performs better than most state-of-the-art algorithms.
Ricci magnetic geodesic motion of vortices and lumps
Alqahtani, L S
2014-01-01
Ricci magnetic geodesic (RMG) motion in a k\\"ahler manifold is the analogue of geodesic motion in the presence of a magnetic field proportional to the ricci form. It has been conjectured to model low-energy dynamics of vortex solitons in the presence of a Chern-Simons term, the k\\"ahler manifold in question being the $n$-vortex moduli space. This paper presents a detailed study of RMG motion in soliton moduli spaces, focusing on the cases of hyperbolic vortices and spherical $\\mathbb{C}P^1$ lumps. It is shown that RMG flow localizes on fixed point sets of groups of holomorphic isometries, but that the flow on such submanifolds does not, in general, coincide with their intrinsic RMG flow. For planar vortices, it is shown that RMG flow differs from an earlier reduced dynamics proposed by Kim and Lee, and that the latter flow is ill-defined on the vortex coincidence set. An explicit formula for the metric on the whole moduli space of hyperbolic two-vortices is computed (extending an old result of Strachan's), an...
Maxwell Fields and Shear-Free Null Geodesic Congruences
Newman, E
2004-01-01
We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the world-line. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, it can be given the following strange interpretation. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x^a take complex values, i.e., x^a => z^a=x^a+iy^a with co...
Cold Scalar-Tensor Black Holes Causal Structure, Geodesics, Stability
Bronnikov, K A; Constantinidis, C P; Fabris, J C
1998-01-01
We study the structure and stability of spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant $\\omega$. These solutions split into two classes, depending on finite (B1) or infinite (B2) proper time needed for an infalling particle to reach the horizon. Class B1 metrics can be extended through the horizon only for discrete values of mass and scalar charge, depending on two integers m and n. For even m-n, the space-time is globally regular; for odd m, the metric changes its signature on the horizon but remains Lorentzian. Geodesics are smoothly continued across the horizon, but for odd m timelike geodesics become spacelike and vice versa. Causality problems, arising in some cases, are discussed. Tidal forces are shown to grow infinitely near type B1 horizons. All vacuum static, spherically symmetric solutions of the Brans-Dicke theory with $\\omega<-3/2$ are found to be linearly stable again...
Black-Box Optimization Using Geodesics in Statistical Manifolds
Directory of Open Access Journals (Sweden)
Jérémy Bensadon
2015-01-01
Full Text Available Information geometric optimization (IGO is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a Riemannian manifold, defining a parametrization-invariant first order differential equation and, thus, yielding an approximately parametrization-invariant algorithm (up to second order in the step size. We define the geodesic IGO update, a fully parametrization-invariant algorithm using the Riemannian structure, and we compute it for the manifold of Gaussians, thanks to Noether’s theorem. However, in similar algorithms, such as CMA-ES (Covariance Matrix Adaptation - Evolution Strategy and xNES (exponential Natural Evolution Strategy, the time steps for the mean and the covariance are decoupled. We suggest two ways of doing so: twisted geodesic IGO (GIGO and blockwise GIGO. Finally, we show that while the xNES algorithm is not GIGO, it is an instance of blockwise GIGO applied to the mean and covariance matrix separately. Therefore, xNES has an almost parametrization-invariant description.
Dynamic realization of the Unruh effect for a geodesic observer
Lochan, Kinjalk; Padmanabhan, T
2016-01-01
We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\\to\\infty$) observers, around $x\\to\\infty$ and $x\\to-\\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity witness a thermal radiation, without experiencing any change of spacetime geometry all along their trajectories. They remain geodesic observers in a flat region of spacetime. Thus these observers measure a late time thermal radiation, with exactly the same temperature as measured by the observers at right null infinity, despite moving geodesically in flat spacetime throughout their trajectories. However such radia...
A thermodynamic study of zatrikean geodesics resulting from a discrete-geometry model
Geroyannis, V. S.; Dallas, T. G.
We attempt a connection between thermodynamics and zatrikean pregeometry, i.e., a chess-like pregeometry (Geroyannis 1993, hereafter G93). In zatrikean pregeometry space is represented by the abacus, a discrete chessboard-like structure consisting of a sufficiently large number of plaquettes called geobits. The particles move on the abacus from one geobit to the next following certain rules that resemble the game of chess. The sets of rules imposed on the motions of particles on the abacus are called premetrics. There is a variety of paths (called subabaces) leading from one geobit to another, and there is a class consisting of subabaces with the minimum number of geobits. These are called alyssoids (respectively, class of alyssoids) for the particular premetric, while those alyssoids with minimum length are called geodesics (respectively, class of geodesics) for the particular premetric. The so-called zatrikean geodesic was originally defined in G93 (Section 2) as the geodesic most closely following the line segment joining the two geobits. It is also called algorithmic geodesic since it is drawn with the assistance of four simple algorithms. This is a rectifiable curve; and a connection between rectifiable curves and thermodynamics is already available (DuPain, Kamae and Mendes-France 1986). Consequently, the so-called thermodynamic geodesic is defined as the particular member of the class of geodesics with maximum entropy. Since it does not necessarily correspond to the algorithmic geodesic, a new algorithm is devised that draws the geodesic with maximum entropy. Furthermore, the probability of each member of the class of geodesics can be determined as the difference of its entropy from the entropy of the thermodynamicgeodesic.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F.; Armano, M.; Audley, H.; Auger, G.; Benedetti, M.; Binetruy, P.; Boatella, C.; Bogenstahl, J.; Bortoluzzi, D.; Bosetti, P.; Brandt, N.; Caleno, M.; Cavalleri, A.; Cesa, M.; Chmeissani, M.; Ciani, G.; Conchillo, A.; Congedo, G.; Cristofolini, I.; Cruise, M.; Danzmann, K.; De Marchi, F.; Diaz-Aguilo, M.; Diepholz, I.; Dixon, G.; Dolesi, R.; Dunbar, N.; Fauste, J.; Ferraioli, L.; Fertin, D.; Fichter, W.; Fitzsimons, E.; Freschi, M.; García Marin, A.; García Marirrodriga, C.; Gerndt, R.; Gesa, L.; Giardini, D.; Gibert, F.; Grimani, C.; Grynagier, A.; Guillaume, B.; Guzmán, F.; Harrison, I.; Heinzel, G.; Hewitson, M.; Hollington, D.; Hough, J.; Hoyland, D.; Hueller, M.; Huesler, J.; Jeannin, O.; Jennrich, O.; Jetzer, P.; Johlander, B.; Killow, C.; Llamas, X.; Lloro, I.; Lobo, A.; Maarschalkerweerd, R.; Madden, S.; Mance, D.; Mateos, I.; McNamara, P. W.; Mendes, J.; Mitchell, E.; Monsky, A.; Nicolini, D.; Nicolodi, D.; Nofrarias, M.; Pedersen, F.; Perreur-Lloyd, M.; Perreca, A.; Plagnol, E.; Prat, P.; Racca, G. D.; Rais, B.; Ramos-Castro, J.; Reiche, J.; Romera Perez, J. A.; Robertson, D.; Rozemeijer, H.; Sanjuan, J.; Schleicher, A.; Schulte, M.; Shaul, D.; Stagnaro, L.; Strandmoe, S.; Steier, F.; Sumner, T. J.; Taylor, A.; Texier, D.; Trenkel, C.; Tombolato, D.; Vitale, S.; Wanner, G.; Ward, H.; Waschke, S.; Wass, P.; Weber, W. J.; Zweifel, P.
2011-05-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Energy Technology Data Exchange (ETDEWEB)
Antonucci, F; Cavalleri, A; Congedo, G [Dipartimento di Fisica, Universita di Trento and INFN, Gruppo Collegato di Trento, 38050 Povo, Trento (Italy); Armano, M [European Space Astronomy Centre, European Space Agency, Villanueva de la Canada, 28692 Madrid (Spain); Audley, H; Bogenstahl, J [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik und Universitaet Hannover, 30167 Hannover (Germany); Auger, G; Binetruy, P [APC UMR7164, Universite Paris Diderot, Paris (France); Benedetti, M [Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Boatella, C [CNES, DCT/AQ/EC, 18 Avenue Edouard Belin, 31401 Toulouse, Cedex 9 (France); Bortoluzzi, D; Bosetti, P; Cristofolini, I [Dipartimento di Ingegneria Meccanica e Strutturale, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Brandt, N [Astrium GmbH Claude-Dornier-Strasse, 88090 Immenstaad (Germany); Caleno, M; Cesa, M [European Space Technology Centre, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk (Netherlands); Chmeissani, M [IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona (Spain); Ciani, G [Department of Physics, University of Florida, Gainesville, FL 32611-8440 (United States); Conchillo, A [ICE-CSIC/IEEC, Facultat de Ciencies, E-08193 Bellaterra, Barcelona (Spain); Cruise, M, E-mail: Stefano.Vitale@unitn.it [Department of Physics and Astronomy, University of Birmingham, Birmingham (United Kingdom)
2011-05-07
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
Timelike geodesics around a charged spherically symmetric dilaton black hole
Directory of Open Access Journals (Sweden)
Blaga C.
2015-01-01
Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
Geodesic motion of test particles in Korkina-Grigoryev metric
Bormotova, Irina
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under which the finite motion of particles occurs. From the behavior of the potential curves the radii of both stable and unstable circular orbits around a black hole are found, as well as the corresponding energies of the test particles. The effective-potential curves for the Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are compared. It is shown, that in the case of the Korkina-Grigoryev metric the stable orbits eventually vanish with increasing charge.
About some diophantine equation and the resulting chaos in geodesics
Perrine, Serge
2001-06-01
We announce results about a complete Markoff theory for the diophantine equation: x2+y2+z2=3xyz+2x All its solutions can be computed. For positive integers, they are organized in two trees. With them, we build a new tree thanks to related continued fractions, and associated binary quadratic forms. In an infinite number of cases, the corresponding approximation and Markoff constants have the form: ((m-2)/√9m2-4 ) For other cases, we conjecture the expression of the constants. All of them converge towards (1/3) by lower values, similarly but differently from the classical Markoff theory. We conclude considering very briefly the link between such equations and geodesics on some Riemann surfaces.
Geodesic acoustic mode in anisotropic plasma with heat flux
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2015-10-15
Geodesic acoustic mode (GAM) in an anisotropic tokamak plasma is investigated in fluid approximation. The collisionless anisotropic plasma is described within the 16-momentum magnetohydrodynamic (MHD) fluid closure model, which takes into account not only the pressure anisotropy but also the anisotropic heat flux. It is shown that the GAM frequency agrees better with the kinetic result than the standard Chew-Goldberger-Low (CGL) MHD model. When zeroing the anisotropy, the 16-momentum result is identical with the kinetic one to the order of 1/q{sup 2}, while the CGL result agrees with the kinetic result only on the leading order. The discrepancies between the results of the CGL fluid model and the kinetic theory are well removed by considering the heat flux effect in the fluid approximation.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking.
van Aart, Evert; Sepasian, Neda; Jalba, Andrei; Vilanova, Anna
2011-01-01
Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Interpreting spacetimes of any dimension using geodesic deviation
Podolsky, Jiri
2012-01-01
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corres...
Geodesic deviation in Kundt spacetimes of any dimension
Svarc, Robert
2012-01-01
Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type III, and type N purely transverse effects corresponding to gravitational waves with D(D-3)/2 independent polarization states. We explicitly study the most important examples, namely exact pp-waves, gyratons, and VSI spacetimes. This analysis helps us to clarify the geometrical and physical interpretation of the Kundt class of nonexpanding, nontwisting and shearfree geometries.
Rational first integrals of geodesic equations and generalised hidden symmetries
Aoki, Arata; Tomoda, Kentaro
2016-01-01
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O'Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking
Directory of Open Access Journals (Sweden)
Evert van Aart
2011-01-01
Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Fanizza, Giuseppe
2016-01-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
2016-06-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F; Audley, H; Auger, G; Benedetti, M; Binetruy, P; Boatella, C; Bogenstahl, J; Bortoluzzi, D; Bosetti, P; Brandt, N; Caleno, M; Cavalleri, A; Cesa, M; Chmeissani, M; Ciani, G; Conchillo, A; Congedo, G; Cristofolini, I; Cruise, M; Danzmann, K; De Marchi, F; Diaz-Aguilo, M; Diepholz, I; Dixon, G; Dolesi, R; Dunbar, N; Fauste, J; Ferraioli, L; Fertin, D; Fichter, W; Fitzsimons, E; Freschi, M; Marin, A García; Marirrodriga, C García; Gerndt, R; Gesa, L; Giardini, D; Gibert, F; Grimani, C; Grynagier, A; Guillaume, B; Guzmán, F; Harrison, I; Heinzel, G; Hewitson, M; Hollington, D; Hough, J; Hoyland, D; Hueller, M; Huesler, J; Jeannin, O; Jennrich, O; Jetzer, P; Johlander, B; Killow, C; Llamas, X; Lloro, I; Lobo, A; Maarschalkerweerd, R; Madden, S; Mance, D; Mateos, I; McNamara, P W; Mendestì, J; Mitchell, E; Monsky, A; Nicolini, D; Nicolodi, D; Nofrarias, M; Pedersen, F; Perreur-Lloyd, M; Perreca, A; Plagnol, E; Prat, P; Racca, G D; Rais, B; Ramos-Castro, J; Reiche, J; Perez, J A Romera; Robertson, D; Rozemeijer, H; Sanjuan, J; Schleicher, A; Schulte, M; Shaul, D; Stagnaro, L; Strandmoe, S; Steier, F; Sumner, T J; Taylor, A; Texier, D; Trenkel, C; Tombolato, D; Vitale, S; Wanner, G; Ward, H; Waschke, S; Wass, P; Weber, W J; Zweifel, P
2010-01-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware and flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor two of the LISA requirement at 1 mHz and within a factor 10 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement, that will guarantee the LISA performance.
On the applicability of the geodesic deviation equation in General Relativity
Philipp, Dennis; Laemmerzahl, Claus
2016-01-01
Within the theory of General Relativity we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. The deviation equation is used to model satellite orbit constellations around the earth. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity. The deviation of nearby orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in Schwarzschild spacetime.
Powers of the space forms curvature operator and geodesics of the tangent bundle
Saharova, Yelena; Yampolsky, Alexander
2005-01-01
It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all its geodesic curvatures constant. In this paper we consider the case of tangent (sphere) bundle over the real, complex and quaternionic space form and give a unified proof of the following property: all geodesic curvatures of projected curve are zero starting from k_3,k_6 and k_{10} for the real, complex and quaternio...
On the number and location of short geodesics in moduli space
Leininger, Christopher J
2011-01-01
A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
National Research Council Canada - National Science Library
Huang, Wei-Xian; Wu, Hua-Jing-Ling; Wang, Guo-Jin
2013-01-01
In order to explore a new approach to construct surfaces bounded by geodesics or lines of curvature, a method of surface modeling based on fourth-order partial differential equations (PDEs) is presented...
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas.
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-30
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Thermodynamic geodesics of a Reissner Nordström black hole
Farrugia, Christine; Sultana, Joseph
2017-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordström black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems (Phys Rev D 41:1142-1151, 1990). It can be deduced that the relation which the geodesics establish between the entropy S and electric charge Q of the black hole extremises changes in the black hole's mass. Indeed, the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation. We also find that in certain cases, the geodesics describe the evolution brought about by the constant emission of Hawking radiation and charged-particle pairs.
Energy Technology Data Exchange (ETDEWEB)
Rowland, D R [Student Support Services, University of Queensland, Brisbane QLD 4072 (Australia)
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Are eikonal quasinormal modes linked to the unstable circular null geodesics?
Konoplya, R. A.; Stuchlík, Z.
2017-08-01
In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.
Proper Accelerations of Time-Like Curves near a Null Geodesic
Institute of Scientific and Technical Information of China (English)
田贵花; 赵峥
2003-01-01
It is well known that when given a null geodesic γ0(λ) with a point r in (p, q) conjugate to p along γ0(λ), there will be a variation of γ0(λ) which can give a time-like curve from p to q. Here we prove that the time-like curves coming from the above-mentioned variation (with the second derivative β2 ≠ 0) have a proper acceleration A = √AaAa which approaches infinity as the time-like curve approaches the null geodesic. Because the curve obtained from variation of the null geodesic must be everywhere time-like, we also discuss the constraint of the vector field Za on the null geodesic γ0(λ) cannot be zero.
Menon, Govind
2008-01-01
The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.
Physical meaning of the conserved quantities on anti-de Sitter geodesics
Cotǎescu, Ion I.
2017-05-01
The geodesic motion on anti-de Sitter spacetimes is studied, pointing out how the trajectories are determined by the ten independent conserved quantities associated with the specific S O (2 ,3 ) isometries of these manifolds. The new result is that there are two conserved S O (3 ) vectors which play the same role as the Runge-Lenz vector of the Kepler problem, determining the major and minor semiaxes of the ellipsoidal anti-de Sitter geodesics.
On the Mass Neutrino Phase calculations along the geodesic line and the null line
Zhang, C. M.; Beesham, A.
2000-01-01
On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting error--factor of 2 when comparing the geodesic phase with the null phase. For the mass neutrino propagation in the flat spacetime, we study the neutrino interference phase calculation in the Minkowski diagram and find that the double counting effect originates from despising the velocity difference between two mass neutrinos. Moreover, we compare the phase cal...
A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole
Soroushfar, Saheb; Jafari, Afsaneh
2015-01-01
This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.
Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes
Flathmann, Kai
2016-01-01
In this article we derive the geodesic equations in the $\\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\\sigma$-function and in special cases in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.
Geometry of Cyclic Quotients; 1, Knotted Totally Geodesic Submanifolds in Positively Curved Spheres
Reznikov, A G
1994-01-01
We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic projective plane with Euler number four. Surpisingly, the technique borrows a lot from the Mostow-Siu-Gromov-Thurston constuction of exotic negatively curved manifolds.
Flathmann, Kai
2015-01-01
In this article we study the geodesic motion of test particles and light in the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types.
Finsler geodesics in the presence of a convex function and their applications
Energy Technology Data Exchange (ETDEWEB)
Caponio, Erasmo; Masiello, Antonio [Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari (Italy); Javaloyes, Miguel Angel [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada (Spain)], E-mail: caponio@poliba.it, E-mail: ma.javaloyes@gmail.com, E-mail: majava@ugr.es, E-mail: masiello@poliba.it
2010-04-24
In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.
Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem
Krishnaswami, Govind S.; Senapati, Himalaya
2016-10-01
The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation isometries in addition to scaling isometries for the inverse-square potential with zero energy E. The geodesic flow on the full configuration space ℂ3 (with collision points excluded) leads to corresponding flows on its Riemannian quotients: the center of mass configuration space ℂ2 and shape space ℝ3 (as well as 𝕊3 and the shape sphere 𝕊2 for the inverse-square potential when E = 0). The corresponding Riemannian submersions are described explicitly in "Hopf" coordinates which are particularly adapted to the isometries. For equal masses subject to inverse-square potentials, Montgomery shows that the zero-energy "pair of pants" JM metric on the shape sphere is geodesically complete and has negative gaussian curvature except at Lagrange points. We extend this to a proof of boundedness and strict negativity of scalar curvatures everywhere on ℂ2, ℝ3, and 𝕊3 with collision points removed. Sectional curvatures are also found to be largely negative, indicating widespread geodesic instabilities. We obtain asymptotic metrics near collisions, show that scalar curvatures have finite limits, and observe that the geodesic reformulation "regularizes" pairwise and triple collisions on ℂ2 and its quotients for arbitrary masses and allowed energies. For the Newtonian potential with equal masses and zero energy, we find that the scalar curvature on ℂ2 is strictly negative though it could have either sign on ℝ3. However, unlike for the inverse-square potential, geodesics can encounter curvature singularities at collisions in finite geodesic time.
Geodesic active fields--a geometric framework for image registration.
Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe
2011-05-01
In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to
Solar performance of an electrochromic geodesic dome roof
Energy Technology Data Exchange (ETDEWEB)
Porta-Gandara, M.A. [Centro de Investigaciones Biologicas del Noroeste, BCS (Mexico); Gomez-Munoz, V. [Centro Interdisciplinario de Ciencas Marinas, BCS (Mexico)
2005-10-01
A Fuller type geodesic dome was modeled in terms of the variation of the solar energy that passes to the interior when the dome is covered with electrochromic glazing (ECG), compared with common glass, by means of two different solar control strategies: one discrete and the other continuous. With the discrete strategy, when a solar beam strikes any ECG pane at any angle, it is darkened to its maximum level. In the continuous strategy, each ECG pane is darkened by using a direct function of solar beam radiation. The results demonstrate the advantages of solar control achieved with the former strategy. For the discrete strategy, the daily reduction in solar energy intake, with respect to the ordinary glass, was around 86% for all considered latitudes along the year. The optimum values for the continuous strategy occurred during the equinoxes with a maximum reduction of 69% for all latitudes. During the summer solstice, the reduction percentages increase with the latitude from 52 to 57%. During the winter solstice, the energy reduction with the continuous strategy decreases with the latitude from 52% in the Equator to 46% at 40{sup o} north latitude. (author)
On geodesic dynamics in deformed black-hole fields
Semerák, Oldřich
2015-01-01
"Almost all" seems to be known about isolated stationary black holes in asymptotically flat space-times and about the behaviour of {\\em test} matter and fields in their backgrounds. The black holes likely present in galactic nuclei and in some X-ray binaries are commonly being represented by the Kerr metric, but actually they are not isolated (they are detected only thanks to a strong interaction with the surroundings), they are not stationary (black-hole sources are rather strongly variable) and they also probably do not live in an asymptotically flat universe. Such "perturbations" may query the classical black-hole theorems (how robust are the latter against them?) and certainly affect particles and fields around, which can have observational consequences. In the present contribution we examine how the geodesic structure of the static and axially symmetric black-hole space-time responds to the presence of an additional matter in the form of a thin disc or ring. We use several different methods to show that ...
Perfect imaging analysis of the spherical geodesic waveguide
González, Juan C.; Benítez, Pablo; Miñano, Juan C.; Grabovičkić, Dejan
2012-12-01
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to λ/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.
Extreme super-resolution using the spherical geodesic waveguide
Miñano, Juan Carlos; González, Juan Carlos; Benítez, Pablo; Grabovičkić, Dejan
2012-06-01
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.
Circuital model for the spherical geodesic waveguide perfect drain
González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.
2012-08-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.
Geodesic family of spherical instantons and cosmic quantum creation
Lapiedra, Ramon
2015-01-01
The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\\^{\\i}}tre-Tolman-Bondi family and for a general $\\Lambda$-Friedmann-Lema{\\^{\\i}}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $\\Lambda$FLRW model is quantically creatable while the open and flat model...
Self-gravitating stellar collapse: explicit geodesics and path integration
Directory of Open Access Journals (Sweden)
Jayashree Balakrishna
2016-11-01
Full Text Available We extend the work of Oppenheimer-Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Computation of the shortest path between two curves on a parametric surface by geodesic-like method
Chen, Wen-Haw
2010-01-01
In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in $\\mathbb{R}^3$. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.
The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths
Institute of Scientific and Technical Information of China (English)
Chun Gen LIU
2005-01-01
In this paper, we consider the relation of the Morse index of a closed geodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closed geodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), we construct a symplectic path γ(t) starting from identity I and ending at P, such that the Morse index of the closed geodesic c equals the Maslov-type index of γ. As an application of this result, we study the parity of the Morse index of any closed geodesic.
Geodesic distance on a Grassmannian for monitoring the progression of Alzheimer's disease.
Gui, Liangyan; Tang, Xiaoying; Moura, José M F
2017-02-01
We propose a geodesic distance on a Grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi, amygdalas, and lateral ventricles in healthy control (HC), mild cognitive impairment (MCI), and Alzheimer's disease (AD). Longitudinal magnetic resonance imaging (MRI) scans of 754 subjects (3092 scans in total) were used in this study. Longitudinally, the geodesic distance was found to be proportional to the elapsed time separating the two scans in question. Cross-sectionally, utilizing a linear mixed-effects statistical model, we found that each structure's annualized rate of change in the geodesic distance followed the order of AD>MCI>HC, with statistical significance being reached in every case. In addition, for each of the six structures of interest, within the same time interval (e.g., from baseline to the 6th month), we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the ADAS-cog increase and the MMSE decrease. Furthermore, as the disease progresses over time, this linkage between the inter-shape geodesic distance and the cognitive decline becomes considerably stronger and more significant.
3D Facial Similarity Measure Based on Geodesic Network and Curvatures
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.
Exact solutions to the geodesic equations of linear dilaton black holes
Hamo, A H H
2015-01-01
In this paper, we analyze the geodesics of the 4-dimensional ($4D$) linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. LDBHs have non-asymptotically flat (NAF) geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange (EL) equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the WeierstrassP-function ($\\wp$-function), which is an elliptic-type special function.
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole
2011-01-01
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant......-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine...... that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE...
The Poincar\\'e reduction problem for geodesics on deformed spheres
Sinitsyn, D O
2011-01-01
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation theory with the view of obtaining a topological classification of the set of geodesics on a manifold. To that end we use the X-ray transform familiar in the integral geometry, and obtain the system of averaged equations of motion, which turns out to be a Hamiltonian one. The system serves an asymptotic reduction of the initial exact system of 2n-2 equations to that of 2n-4 equations on the Grassmann manifold G(2,n). The Poisson brackets of the reduction system are determined by the Lie algebra of the group SO(n). In the important cases of two-dimensional and a range of three-dimensional hypersurfaces it allows a topological classification of the set of geodesics.
Educational Facilities Labs., Inc., New York, NY.
A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…
A numerical study of the correspondence between paths in a causal set and geodesics in the continuum
Ilie, R; Thompson, G B; Ilie, Raluca; Reid, David D.; Thompson, Gregory B.
2006-01-01
This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.
Directory of Open Access Journals (Sweden)
Kun-Lin Wu
2016-01-01
Full Text Available In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, Marcelo B.
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical...
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, M B
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
A Fortran code for null geodesic solutions in the Lemaître-Tolman-Bondi spacetime
Ribeiro, Marcelo B.
2002-10-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaître-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
Kazempour, Sobhan; Soroushfar, Saheb
2016-01-01
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.
Impact of Energetic-Particle-Driven Geodesic Acoustic Modes on Turbulence
Zarzoso, D.; Sarazin, Y.; Garbet, X.; Dumont, R.; Strugarek, A.; Abiteboul, J.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-03-01
The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.
On geodesics with negative energies in the ergoregions of dirty black holes
Zaslavskii, O B
2014-01-01
We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov, and V. D. Vertogradov, Mod. Phys. Lett. 29, 1450110 (2014) [arXiv:1304.7360].
Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb
2017-03-01
A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.
Geodesic Structures of Lifshitz Black Holes in 2+1 Dimensions
Cruz, Norman; Villanueva, J R
2013-01-01
We present an study of the geodesic equations of a black hole spacetime which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev.{\\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non radial geodesics are given in terms of the Weierstrass elliptic $\\wp$, $\\sigma$, and $\\zeta$ functions.
Soroushfar, Saheb; Saffari, Reza; Sahami, Ehsan
2016-07-01
In this paper, we consider the timelike and null geodesics around the static (GMGHS, magnetically charged GMGHS, electrically charged GMGHS) and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained results we study astrophysical applications.
Paiva, F M
2011-01-01
In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular motion with constant velocity, particularly closed timelike curves, and time travel of a voyager. ------------------- ^Ce la ^Generala Relativeco, en homogena metriko de Som-Raychaudhuri, ni studas geodeziojn de la tri tipoj: tempa, nula, kaj spaca, speciale la malmulte konatajn samtempajn geodeziojn. Ni anka^u studas ne-geodezian cirklan movadon kun konstanta rapido, speciale fermitajn kurbojn de tempa tipo, kaj movadon de voja^ganto al estinto.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James;
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots ...
Santoprete, Manuele
2002-01-01
Resorting to classical techniques of Riemannian geometry we develop a geometrical method suitable to investigate the nonintegrability of geodesic flows and of natural Hamiltonian systems. Then we apply such method to the Anisotropic Kepler Problem (AKP) and we prove that it is not analytically integrable.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces Y
Visinescu, Mihai
2017-01-01
We use action-angle variables to describe the geodesic motions in the 5-dimensional Sasaki-Einstein spaces Y. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequencies is zero, indicating chaotic behavior when the system is perturbed.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz. PMID:28134324
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots...
Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections
Institute of Scientific and Technical Information of China (English)
SHI Bing-Ren; LI Ji-Quan; DONG Jia-Qi
2005-01-01
@@ The geodesic acoustic mode in general toroidally axisymmetric plasmas such as Tokamak and spherical torus is studied in detail. The mode structure is found and the dispersion equation is derived and solved for arbitrary toroidally axi-symmetric plasmas. Besides the finite aspect ratio, effects of elongation and triangularity on this mode are clarified.
On Geodesic Flows and Their Deformations in Bertrand Space-times
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
We study the energy conditions and geodesic equations of Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the parameter space where the weak and strong energy conditions hold. We further compute the ESR parameters for a class of such space-times and analyze them numerically.
Null geodesics in the Reissner-Nordstr\\"om Anti-de Sitter black holes
Cruz, Norman; Saavedra, Joel; Villanueva, J R
2011-01-01
In this work we address the study of null geodesics in the background of Reissner-Nordstr\\"om Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.
Integrability of geodesics and action-angle variables in Sasaki-Einstein space T{sup 1,1}
Energy Technology Data Exchange (ETDEWEB)
Visinescu, Mihai [National Institute of Physics and Nuclear Engineering, Department Theoretical Physics, Magurele, Bucharest (Romania)
2016-09-15
We briefly describe the construction of Staekel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T{sup 1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed. (orig.)
Waterline extraction in optical images and InSAR coherence maps based on the geodesic time concept
Soares, Fernando; Nico, Giovanni
2010-10-01
An algorithm for waterline extraction from SAR images is presented based on the estimation of the geodesic path, or minimal path (MP) between two pixels on the waterline. For two given pixels, geodesic time is determined in terms of the time shortest path, between them. The MP is determined by estimating the mean value for all pairs of neighbor pixels that can be part of a possible path connecting the initial given pixels. A MP is computed as the sum of those two geodesic image functions. In general, a MP is obtained with the knowledge of two end pixels. Based on the 2-dimensional spreading of the estimated geodesic time function, the concepts of propagation energy and strong pixels are introduced and tested for the waterline extraction by marking only one pixel in the image.
Soroushfar, Saheb; Kazempour, Sobhan; Grunau, Saskia; Kunz, Jutta
2016-01-01
We study the geodesic equations in the space time of a rotating charged black hole in $f(R)$ gravity. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\\wp$, $\\zeta$ and $\\sigma$ functions as well as the Kleinian $\\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types.
On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
Ortiz, Néstor; Zannias, Thomas
2015-01-01
Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.
Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime
Müller, Thomas
2011-01-01
The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first course in general relativity to give them a deeper inside in the calculation of non-affinely parametrized null and time-like geodesics and a straightforward approach to determine the gravitational lensing effect due to curved spacetime by means of the Jacobi equation. Both topics are necessary for a thorough discussion of the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. The visual effects of the traveller can be reproduced with an interactive Java application.
Geodesic-length functions and the Weil-Petersson curvature tensor
Wolpert, Scott A
2010-01-01
An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower bound for sectional curvature in terms of the systole is presented. The curvature tensor expansion is applied to establish continuity properties at the frontier strata of the augmented Teichm\\"{u}ller space. The curvature tensor has the asymptotic product structure already observed for the metric and covariant derivative. The product structure is combined with the earlier negative sectional curvature results to establish a classification of asymptotic flats. Furthermore, tangent subspaces of more than half the dimension of Teichm\\"{u}ller space contain sections with a definite amount of negative curvature. Proofs combine estimates for uniformization group exponential-distance sums and potential theory bounds.
Vacuum non-expanding horizons and shear-free null geodesic congruences
Adamo, T M
2009-01-01
We investigate the geometry of a particular class of null surfaces in space-time called vacuum Non-Expanding Horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex world-line in a complex four dimensional space, each such choice induces a CR structure on the horizon, and a particular world-line (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.
Singh, Nikhil; Hinkle, Jacob; Joshi, Sarang; Fletcher, P Thomas
2013-04-01
This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a closed-form update for template estimation in both the geodesic regression and atlas estimation problems. While we show that the theoretical optimal solution is equivalent to the scalar momenta case, the simplification of the optimization problem leads to more stable and efficient estimation in practice. We demonstrate the effectiveness of our method for atlas estimation and geodesic regression using synthetically generated shapes and 3D MRI brain scans.
Geodesic mode instability driven by electron and ion fluxes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Elfimov, A. G., E-mail: elfimov@if.usp.br; Camilo de Souza, F.; Galvão, R. M. O. [Institute of Physics, University of São Paulo, São Paulo 05508-090 (Brazil)
2015-11-15
The effect of the parallel electron current and plasma flux on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current and plasma flow, modeled by shifted Maxwell distributions of electrons and ions, may overcome the ion Landau damping generating the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity of sidebands, Rqω. The instability is driven by the electron current and the parallel ion flux cross term. Possible applications to tokamak experiments are discussed. The existence of the geodesic ion sound mode due to plasma flow is shown.
Hackmann, Eva
2015-01-01
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer Anomaly is addressed. The periastron shift and its post--Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space--times.
Geodesic least squares regression for scaling studies in magnetic confinement fusion
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2015-01-13
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
Equatorial geodesics of dyonic Kerr-Newman black hole pierced by a cosmic string
Sharif, M.; Iftikhar, Sehrish
2016-12-01
This paper is devoted to study the circular geodesics of the dyonic Kerr-Newman black hole with a cosmic string passing through it. We investigate circular geodesics of null and timelike particle. In this context, we find the circular photon orbit as well as the innermost stable circular orbit. The angular velocity and time period for the timelike particle are calculated. The effect of electric and magnetic charge as well as of the cosmic string parameter on the effective potential is analyzed numerically. Finally, we discuss the role of these parameters on the energy extraction by the Penrose process. We conclude that the string parameter does not affect the gain energy of the particle but it decreases with respect to charge.
AdS/CFT prescription for angle-deficit space and winding geodesics
Aref'eva, Irina Ya
2016-01-01
We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS$_3$ space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical Green functions for a scalar field in the bulk with conical defect and use them to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of $\\mathbb{Z}_r$-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.
Single Past Null Geodesic in the Lemaitre-Tolman-Bondi Cosmology
Nogueira, Felipe A M G
2013-01-01
This work provides a general discussion of the spatially inhomogeneous Lema\\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift. As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, comparing it to the spatially homogeneous Einstein-de Sitter cosmology. The results obtained indicate that the standard model, in this case represented by the Einstein-de Sitter cosmology, can be equivalently described by a fractal distribution of matter, as we found that different single fractal dimensions describe different scale ranges of the parabolic LTB matter distribution. It is shown that at large ranges the parabolic LTB model with fractal dimension equal to 0.5 approximates the matter distribution of the Einstein-de Sitter univers...
The Differential of the Exponential Map, Jacobi Fields and Exact Principal Geodesic Analysis
Sommer, Stefan; Nielsen, Mads
2010-01-01
The importance of manifolds and Riemannian geometry in mathematics is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry. The transfer of interest has created demand for methods for computing classical constructs of geometry on manifolds occurring in practical applications. This paper develops initial value problems for the computation of the differential of the exponential map and Jacobi fields on parametrically and implicitly represented manifolds. It is shown how the solution to these problems allow for determining sectional curvatures and provides upper bounds for injectivity radii. In addition, when combined with the second derivative of the exponential map, the initial value problems allow for solving the problem of computing Principal Geodesic Analysis, a non-linear version of the Principal Component Analysis procedure for estimating variability in datasets. The paper develops algorithms for computing Principal Geodesic Analysis with...
Models of rotating boson stars and geodesics around them: New type of orbits
Grandclément, Philippe; Somé, Claire; Gourgoulhon, Eric
2014-07-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number k=3 and k=4, as well as the first determination of the maximum mass of free-field boson stars with k=2. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for k=1, 2 and 3. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbit: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
Ortaggio, M
2007-01-01
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.
Models of rotating boson stars and geodesics around them: new type of orbits
Grandclement, Philippe; Gourgoulhon, Eric
2014-01-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, $2$ and $3$. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbits: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
On the determination of shifting operators along geodesics on a surface
Directory of Open Access Journals (Sweden)
Drašković Zoran
2013-01-01
Full Text Available A procedure to obtain a closed form of the shifting operators along a known geodesic line on a surface as a solution of a system of linear algebraic equations is proposed. Its correctness is numerically demonstrated in the case of a helicoid surface and a spherical one. The future use of these operators in finite element approximations of tensor fields in non-Euclidean spaces is announced.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$
Visinescu, Mihai
2016-01-01
We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequency is zero indicating a chaotic behavior when the system is perturbed.
Multi-focal spherical media and geodesic lenses in geometrical optics
Sarbort, Martin
2013-01-01
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains.
Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation
Herrera, L; Ospino, J
2015-01-01
Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution, unless the dissipative flux vanishes. In this latter case the vorticity also must vanish, and the resulting spacetime is Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational radiation.
Space-time Geodesics of the 5D Schwarzschild field and its deformation retract
Ahmed, Nasr
2014-01-01
In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.
Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation
Lacquaniti, V; Vietri, F; 10.1007/s10714-009-0853-3
2009-01-01
In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $\\phi=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $\\phi$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.
Geodesic motions of test particles in a relativistic core-shell spacetime
Liu, Lei; Wu, Xin; Huang, Guoqing
2017-02-01
In this paper, we discuss the geodesic motions of test particles in the intermediate vacuum between a monopolar core and an exterior shell of dipoles, quadrupoles and octopoles. The radii of the innermost stable circular orbits at the equatorial plane depend only on the quadrupoles. A given oblate quadrupolar leads to the existence of two innermost stable circular orbits, and their radii are larger than in the Schwarzschild spacetime. However, a given prolate quadrupolar corresponds to only one innermost stable circular orbit, and its radius is smaller than in the Schwarzschild spacetime. As to the general geodesic orbits, one of the recently developed extended phase space fourth order explicit symplectic-like methods is efficiently applicable to them although the Hamiltonian of the relativistic core-shell system is not separable. With the aid of both this fast integrator without secular growth in the energy errors and gauge invariant chaotic indicators, the effect of these shell multipoles on the geodesic dynamics of order and chaos is estimated numerically.
A triangulation-invariant method for anisotropic geodesic map computation on surface meshes.
Yoo, Sang Wook; Seong, Joon-Kyung; Sung, Min-Hyuk; Shin, Sung Yo; Cohen, Elaine
2012-10-01
This paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner.
Geodesics of McVittie Spacetime with a Phantom Cosmological Background
Antoniou, Ioannis
2016-01-01
We investigate the geodesics of a Schwarzschild spacetime embedded in an isotropic expanding cosmological background (McVittie metric). We focus on bound particle geodesics in a background including matter and phantom dark energy with constant dark energy equation of state parameter $w<-1$ involving a future Big Rip singularity at a time $t_{\\ast}$. Such geodesics have been previously studied in the Newtonian approximation and found to lead to dissociation of bound systems at a time $t_{rip}
Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows
Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch
2017-09-01
Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.
Derivation of Geodesic Flow Fields and Spectrum in Digital Topographic Basins
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Sin Liang Lim
2008-01-01
Full Text Available We present a framework to characterize terrestrial functions—surficial and bottom topographic regions that are represented, respectively, as raster digital elevation models (DEMs and digital bathymetric models (DBMs—through analysis of flow fields that are simulated via geodesic morphology. Characterization of such functions is done via a new descriptor. Computation of this new descriptor involves the following steps: (i basin in digital form representing topographic fluctuations as an input, (ii threshold decomposition of basin—that consists of channelized and nonchannelized regions—into sets, (iii proper indexing of these sets to decide the marker set(s and its (their corresponding mask set(s, (iv performing geodesic propagation that provides basic flow field structures, and (v finally providing a new basin descriptor—geodesic spectrum. We demonstrated this five-step framework on five different synthetic and/or realistic DEMs and/or DBMs. This study provides potentially invaluable insights to further study the travel-time flood propagation within basins of both fluvial and tidal systems.
Small scale structure of spacetime: van Vleck determinant and equi-geodesic surfaces
Stargen, D Jaffino
2015-01-01
It has recently been argued that if spacetime $\\mathcal M$ possesses non-trivial structure at small scales, an appropriate semi-classical description of it should be based on non-local bi-tensors instead of local tensors such as the metric $g_{ab}$. Two most relevant bi-tensors in this context are Synge's World function $\\Omega(p,p_0)$ and the van Vleck determinant (VVD) $\\Delta(p,p_0)$, as they encode the metric properties of spacetime and (de)focussing behaviour of geodesics. They also characterize the leading short distance behavior of two point functions of the d'Alembartian $_{p_0} \\square_p$. We begin by discussing the intrinsic and extrinsic geometry of equi-geodesic surfaces $\\Sigma_{G,p_0}$ defined by $\\Omega(p,p_0)=constant$ in a geodesically convex neighbourhood of an event $p_0$, and highlight some elementary identities relating the VVD with geometry of these surfaces. As an aside, we also comment on the contribution of $\\Sigma_{G,p_0}$ to the surface term in the Einstein-Hilbert (EH) action and s...
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
Benvenuti, S; Benvenuti, Sergio; Kruczenski, Martin
2006-01-01
The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analisys simplifies for the special case of the Lpqq models, which are shown to correspond to the known "generalized conifolds". These geometries can break conformal invariance through toric deformations of the c...
A dynamical system's approach to Schwarzschild null geodesics
Energy Technology Data Exchange (ETDEWEB)
Belbruno, Edward [Courant Institute of Mathematical Sciences, New York University, NY (United States); Pretorius, Frans, E-mail: belbruno@Princeton.edu, E-mail: fpretori@Princeton.edu [Department of Physics, Princeton University, Princeton, NJ (United States)
2011-10-07
The null geodesics of a Schwarzschild black hole are studied from a dynamical system's perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of the four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L| > |L{sub c}|, (1) the set that flow outward from the white hole, turn around, and then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L| < |L{sub c}|, (3) the set that flow outward from the white hole and continue to future null infinity and (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum L{sub c} corresponds to the unstable circular orbit at r = 3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r = 0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is that a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the L {yields} {infinity} limit, as described in Schwarzschild coordinates, these geodesics begin at r = 0, flow along t = constant lines, turn around at r = 2M, and then continue to r = 0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Directory of Open Access Journals (Sweden)
Timothy M. Adamo
2009-09-01
Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Directory of Open Access Journals (Sweden)
Timothy M. Adamo
2012-01-01
Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Verdoolaege, G.; Shabbir, A.; Hornung, G.
2016-11-01
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field
Zimdahl, Winfried
2014-01-01
We investigate a Boltzmann gas in equilibrium with its center of mass moving on a circular geodesics in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the solar system as well as to strong-field configurations of neutron stars and black holes.
Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field
Zimdahl, Winfried; Kremer, Gilberto M.
2015-01-01
We investigate a Boltzmann gas at equilibrium with its center of mass moving on a circular geodesic in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the Solar System as well as to strong-field configurations of neutron stars and black holes.
A Brief Comment on Geodesic Deviation Equation in f(R) Gravity
Guarnizo, Alejandro; Tejeiro, Juan M
2014-01-01
In the context of metric $f(R)$ gravity, the Geodesic Deviation Equation (GDE) was first studied in arXiv:1010.5279v3, giving a general expression and studying a particular case, the FLRW universe. Recently, a new work appears arXiv:1312.2022v1 making a similar analysis. However, there is a discrepancy in the expressions for the null vector field case. Here we make explicit the contribution of the different operators in the GDE, finding the differences with our previous result.
Geodesic Motions in AdS Soliton Background Space-time
Shi, Han-qing
2016-01-01
We study both massive and massless particle's geodesic motion in the background of general dimensional AdS-Sol space-time. We find that the massive particles oscillate along the radial direction, while massless particles experience one-time bouncing as they approach the "horizon" line of the soliton. Our results provide a direct way to understand the negative energy/masses leading to the AdS-Sol geometry. As a potential application, we extend the point particle to a 3-brane and fix the background as a 5+1 dimension AdS-Sol, thus obtain a very natural bouncing/cyclic cosmological model.
Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
Manno, Gianni; Pavlov, Maxim V.
2017-03-01
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.
On the Possibility of Non-Geodesic Motion of the Massless Spinning Top
Armaza, Cristóbal; Koch, Benjamin; Zalaquett, Nicolás
2016-01-01
The motion of spinning massless particles in gravitationally curved backgrounds is revisited by considering new types of constraints. Those constraints guarantee zero mass ($P_\\mu P^\\mu=0$) and they allow for the possibility of trajectories which are not simply null geodesics. To exemplify this previously unknown possibility, the equations of motion are solved for radial motion in Schwarzschild background. It is found that the particle experiences a spin-induced energy shift, which is proportional to the Hawking temperature of the black hole background.
Becerril, Ricardo; Valdez-Alvarado, Susana; Nucamendi, Ulises
2016-12-01
The mass parameters of compact objects such as boson stars, Schwarzschild, Reissner-Nordström, and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred , zblue ) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We find bounds for the values of (zred , zblue ) that may be observed. For the case of the Kerr black hole, recent observational estimates of Sgr A* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
Effective potential and geodesic motion in Kerr-de Sitter space-time
Poudel, P C
2013-01-01
In the present work, geodesic trajectories in Kerr-de Sitter geometry is analyzed. From the mathematical solution of Lagrangian formalism appropriate to motions in the equatorial plane (for which 'theta' = 0 and 'theta' = (constant)= pi/2) can give potential energy of massive and massless particles for rotating axisymetric black hole. From this, for a particular value of cosmological constant, Kerr parameter, mass, angular momentum and impact parameter; variation of potential with distance can be found. Similarly, for a particular value of cosmological constant, mass and Kerr parameter; variation of velocity with distance can be found.
Finite-orbit-width effects on the geodesic acoustic mode in the toroidally rotating tokamak plasma
Ren, Haijun
2016-01-01
The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating tokamak plasma is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical result is shown to agree well with the numerical solution. The dependence of the damping rate on the toroidal Mach number $M$ relies on $k_r \\rho_i$. For sufficiently small $k_r \\rho_i$, the damping rate monotonically decreases with $M$. For relatively large $k_r \\rho_i$, the damping rate increases with $M$ until approaching the maximum and then decreases with $M$.
On the realizable topology of a manifold with attractors of geodesics
Fenille, Marcio Colombo
2017-01-01
We discuss the so-called realizable topology of a Riemannian manifold with attractors of geodesics, which we understand as its topological properties, mainly that related to its fundamental group, investigated from a viewpoint that may be considered realizable in a sense. In the special approach in which the manifold is understood as a model physical universe, we conclude that its realizable fundamental group is isomorphic to the classical fundamental group of its observable portion. For a universe of dimension at least three whose unobservable components are all contractible, this conclusion ensures the possibility to get real inferences about its classical fundamental group through observational methods.
The properties and geodesics related to the NUT-Taub-like spacetime
Institute of Scientific and Technical Information of China (English)
Wu Ya-Bo; Zhao Guo-Ming; Deng Xue-Mei; Yang Xiu-Yi; Lü Jian-Bo; Li Song
2006-01-01
Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m* = 0 and m* < M,respectively.
Energy Technology Data Exchange (ETDEWEB)
Saito, Ryo [APC, (CNRS-Université Paris 7), 10 rue Alice Domon et Léonie Duquet, 75205 Paris (France); Naruko, Atsushi [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan); Hiramatsu, Takashi; Sasaki, Misao, E-mail: rsaito@apc.univ-paris7.fr, E-mail: naruko@th.phys.titech.ac.jp, E-mail: hiramatz@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-10-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.
Saito, Ryo; Hiramatsu, Takashi; Sasaki, Misao
2014-01-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.
Euclidean geodesic loops on high-genus surfaces applied to the morphometry of vestibular systems.
Xin, Shi-Qing; He, Ying; Fu, Chi-Wing; Wang, Defeng; Lin, Shi; Chu, Winnie C W; Cheng, Jack C Y; Gu, Xianfeng; Lui, Lok Ming
2011-01-01
This paper proposes a novel algorithm to extract feature landmarks on the vestibular system (VS), for the analysis of Adolescent Idiopathic Scoliosis (AIS) disease. AIS is a 3-D spinal deformity commonly occurred in adolescent girls with unclear etiology. One popular hypothesis was suggested to be the structural changes in the VS that induce the disturbed balance perception, and further cause the spinal deformity. The morphometry of VS to study the geometric differences between the healthy and AIS groups is of utmost importance. However, the VS is a genus-3 structure situated in the inner ear. The high-genus topology of the surface poses great challenge for shape analysis. In this work, we present a new method to compute exact geodesic loops on the VS. The resultant geodesic loops are in Euclidean metric, thus characterizing the intrinsic geometric properties of the VS based on the real background geometry. This leads to more accurate results than existing methods, such as the hyperbolic Ricci flow method. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than. We applied our algorithm to the VS of normal and AIS subjects. The promising experimental results demonstrate the efficacy of our method and reveal more statistically significant shape difference in the VS between right-thoracic AIS and normal subjects.
Saini, Sahil; Singh, Parampreet
2016-12-01
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.
Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
Alkalaev, K B
2016-01-01
We study the semiclassical holographic correspondence between 2d CFT n-point conformal blocks and massive particle configurations in the asymptotically AdS3 space. On the boundary we use the heavy-light approximation in which case two of primary operators are the background for the other (n-2) operators considered as fluctuations. In the bulk the particle dynamics can be reduced to the hyperbolic time slice. Although lacking exact solutions we nevertheless show that for any n the classical n-point conformal block is equal to the length of the dual geodesic network connecting n-3 cubic vertices of worldline segments. To this end, both the bulk and boundary systems are reformulated as potential vector fields. Gradients of the conformal block and geodesic length are given respectively by accessory parameters of the monodromy problem and particle momenta of the on-shell worldline action represented as a function of insertion points. We show that the accessory parameters and particle momenta are constrained by two...
Implementation of a PMN-PT piezocrystal-based focused array with geodesic faceted structure.
Qiu, Zhen; Qiu, Yongqiang; Demore, Christine E M; Cochran, Sandy
2016-07-01
The higher performance of relaxor-based piezocrystals compared with piezoceramics is now well established, notably including improved gain-bandwidth product, and these materials have been adopted widely for biomedical ultrasound imaging. However, their use in other applications, for example as a source of focused ultrasound for targeted drug delivery, is hindered in several ways. One of the issues, which we consider here, is in shaping the material into the spherical geometries used widely in focused ultrasound. Unlike isotropic unpoled piezoceramics that can be shaped into a monolithic bowl then poled through the thickness, the anisotropic structure of piezocrystals make it impossible to machine the bulk crystalline material into a bowl without sacrificing performance. Instead, we report a novel faceted array, inspired by the geodesic dome structure in architecture, which utilizes flat piezocrystal material and maximizes fill factor. Aided by 3D printing, a prototype with f#≈ 1.2, containing 96 individually addressable elements was manufactured using 1-3 connectivity PMN-PT piezocrystal-epoxy composite. The fabrication process is presented and the array was connected to a 32-channel controller to shape and steer the beam for preliminary performance demonstration. At an operating frequency of 1MHz, a focusing gain around 30 was achieved and the side lobe intensities were all at levels below -12dB compared to main beam. We conclude that, by taking advantage of contemporary fabrication techniques and driving instrumentation, the geodesic array configuration is suitable for focused ultrasound devices made with piezocrystal.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-05-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-01-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Geodesic motion in the space-time of a non-compact boson star
Eilers, Keno; Kagramanova, Valeria; Schaffer, Isabell; Toma, Catalin
2013-01-01
We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -- depending on the scalar field's mass -- can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular, can -- however -- only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particle's energy and angular momentum. The space-time of a boson star approaches the Schwarzschild space-time asymptotically, however deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions ...
Zhang, Zhijun; Liu, Feng; Deng, Fuqin; Tsui, Hungtat
2014-11-01
Due to the variance between subjects, there is usually ambiguity in intensity-based intersubject registration. The topological constraint in the brain cortical surface might be violated because of the highly convolved nature of the human cortical cortex. We propose an intersubject brain registration method by combining the intensity and the geodesic closest point-based similarity measurements. Each of the brain hemispheres can be topologically equal to a sphere and a one-to-one mapping of the points on the spherical surfaces of the two subjects can be achieved. The correspondences in the cortical surface are obtained by searching the geodesic closest points in the spherical surface. The corresponding features on the cortical surfaces between subjects are then used as anatomical landmarks for intersubject registration. By adding these anatomical constraints of the cortical surfaces, the intersubject registration results are more anatomically plausible and accurate. We validate our method by using real human datasets. Experimental results in visual inspection and alignment error show that the proposed method performs better than the typical joint intensity- and landmark-distance-based methods.
Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
Energy Technology Data Exchange (ETDEWEB)
Alkalaev, Konstantin [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky ave. 53, Moscow, 119991 (Russian Federation); Department of General and Applied Physics, Moscow Institute of Physics and Technology, 7 Institutskiy per., Dolgoprudnyi, Moscow region, 141700 (Russian Federation)
2016-12-15
We study the semiclassical holographic correspondence between 2d CFT n-point conformal blocks and massive particle configurations in the asymptotically AdS{sub 3} space. On the boundary we use the heavy-light approximation in which case two of primary operators are the background for the other (n−2) operators considered as fluctuations. In the bulk the particle dynamics can be reduced to the hyperbolic time slice. Although lacking exact solutions we nevertheless show that for any n the classical n-point conformal block is equal to the length of the dual geodesic network connecting n−3 cubic vertices of worldline segments. To this end, both the bulk and boundary systems are reformulated as potential vector fields. Gradients of the conformal block and geodesic length are given respectively by accessory parameters of the monodromy problem and particle momenta of the on-shell worldline action represented as a function of insertion points. We show that the accessory parameters and particle momenta are constrained by two different algebraic equation systems which nevertheless have the same roots thereby guaranteeing the correspondence.
Directory of Open Access Journals (Sweden)
El-Nabulsi Rami Ahmad
2016-07-01
Full Text Available Starting with an extended complex backwardforward derivative operator in differential geometry which is motivated from non-local-in-time Lagrangian dynamics, higher-order geodesic equations are obtained within classical differential geometrical settings. We limit our analysis up to the 2nd-order derivative where some applications are discussed and a number of features are revealed accordingly.
Ahangari, Fatemeh
2017-01-01
Scalar-field cosmology can be regarded as one of the significant fields of research in recent years. This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory. The mentioned string inspired Friedmann-Robertson-Lamai ^tre-Walker (FRLW) solution is one of the noteworthy solutions of Einstein field equations. For this purpose, first of all the Christoffel symbols and the corresponding system of geodesic equations are computed and then the associated Lie symmetries are totally analyzed. Moreover, the algebraic structure of the Lie algebra of local symmetries is briefly investigated and a complete classification of the symmetry subalgebras is presented. Besides by applying the resulted symmetry operators the invariant solutions of the system of geodesic equations are discussed. In addition, the Noether symmetries and the Killing vector fields of the geodesic Lagrangian are determined and the corresponding optimal system of one-dimensional subalgebras is constructed. Mainly, an entire set of local conservation laws is computed for our analyzed scalar-field cosmological solution. For this purpose, two distinct procedures are applied: the celebrated Noether's theorem and the direct method which is fundamentally based on a systematic application of Euler differential operators which annihilate any divergence expression identically.
Directory of Open Access Journals (Sweden)
Wafaa Batat
2010-02-01
Full Text Available In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
Giambo', R; Piccione, P
2010-01-01
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous Seifert conjecture (formulated in 1948) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level.
Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics
Finch, Tehani K.
2015-01-01
We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.
Study of Geodesics and the Frame-dragging effect in a Rotating Traversable Wormhole
Pradhan, Parthapratim
2016-01-01
The complete equatorial causal geodesic structure of a rotating traversable wormhole is analyzed and it has been shown that the ISCO (Innermost Stable Circular Orbit) coincides at the throat of the wormhole for the retrograde rotation. By studying the effective potential we also find the radius of the circular photon orbit. The Periastron precession frequency and the nodal precession frequency have been derived for both of the direct and retrograde rotation. Moreover, we derive the exact Lense-Thirring precession frequency of a test gyro for the said wormhole and we show that this frequency is inversely proportional to the angular momentum $(a)$ of the wormhole along the pole in a certain range of $r \\,\\, (r < 16a^2)$ whereas it is directly proportional to the angular momentum of the spacetime for the other compact objects like black holes and pulsars.
Toroidal symmetry of the geodesic acoustic mode zonal flow in a tokamak plasma.
Zhao, K J; Lan, T; Dong, J Q; Yan, L W; Hong, W Y; Yu, C X; Liu, A D; Qian, J; Cheng, J; Yu, D L; Yang, Q W; Ding, X T; Liu, Y; Pan, C H
2006-06-30
The toroidal symmetry of the geodesic acoustic mode (GAM) zonal flows is identified with toroidally distributed three step Langmuir probes at the edge of the HuanLiuqi-2A (commonly referred to as HL-2A) tokamak plasmas for the first time. High coherence of both the GAM and the ambient turbulence for the toroidally displaced measurements along a magnetic field line is observed, in contrast with the high coherence of the GAM but low coherence of the ambient turbulence when the toroidally displaced measurements are not along the same field line. The radial and poloidal features of the flows are also simultaneously determined. The nonlinear three wave coupling between the high frequency turbulent fluctuations and the flows is demonstrated to be a plausible formation mechanism of the flows.
Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
Bini, Donato
2013-01-01
The deviation from geodesic motion of the world line of an extended body endowed with multipolar structure up to the mass quadrupole moment is studied in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The properties of the quadrupole tensor are clarified by identifying the relevant components which enter the equations of motion, leading to the definition of an effective quadrupole tensor sharing its own algebraic symmetries, but also obeying those implied by the Mathisson-Papapetrou-Dixon model itself. The equations of motion are then solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables in comparison with the one associated with the background curvature and under special assumptions on body's structure and motion. The resulting quasi-circular orbit is parametrized in a Keplerian-like form, so that temporal, radial and azimuthal eccentricities as well as semi-major axis, period and periastron advance are e...
Second--order hyperbolic Fuchsian systems. Asymptotic behavior of geodesics in Gowdy spacetimes
Beyer, Florian
2011-01-01
Recent work by the authors led to the development of a mathematical theory dealing with `second--order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this theory which provides one with a new tool to tackle the Einstein equations of general relativity (under certain symmetry assumptions). Specifically, we formulate the `Fuchsian singular initial value problem' and apply our general analysis to the broad class of vacuum Gowdy spacetimes with spatial toroidal topology. Our main focus is on providing a detailed description of the asymptotic geometry near the initial singularity of these inhomogeneous cosmological spacetimes and, especially, analyzing the asymptotic behavior of causal geodesics ---which represent the trajectories of freely falling observers. In particular, we numerically construct here Gowdy spacetimes which contain a black hole--like region together with a flat Minkowski--like region. By using the Fuchsian techn...
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Breton, N
2016-01-01
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for singular, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparison is shown with the QNMs of the linear electromagnetic counterpart, their Reissner-Nordstr\\"{o}m black hole.
Rigidity of geodesic completeness in the Brinkmann class of gravitational wave spacetimes
Silva, Ivan P Costa e; Herrera, Jonatan
2016-01-01
We consider restrictions placed by geodesic completeness on spacetimes possessing a null parallel vector field, the so-called Brinkmann spacetimes. This class of spacetimes includes important idealized gravitational wave models in General Relativity, namely the plane-fronted waves with parallel rays, or pp-waves, which in turn have been intensely and fruitfully studied in the mathematical and physical literatures for over half a century. More concretely, we prove a restricted version of a conjectural analogue for Brinkmann spacetimes of a rigidity result obtained by M.T. Anderson for stationary spacetimes. We also highlight its relation with a long-standing 1962 conjecture by Ehlers and Kundt. Indeed, it turns out that the subclass of Brinkmann spacetimes we consider in our main theorem is enough to settle an important special case of the Ehlers-Kundt conjecture in terms of the well known class of Cahen-Wallach spaces.
Energy Technology Data Exchange (ETDEWEB)
Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Singh, Rameswar; Morel, P. [Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, UPMC, UPSud, 91128 Palaiseau (France); Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Ghendrih, P. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Görler, T. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany)
2015-06-15
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
Storelli, A.; Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Görler, T.; Singh, Rameswar; Morel, P.; Grandgirard, V.; Ghendrih, P.
2015-06-01
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane
2016-12-01
The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
Evolution of geodesic congruences in a gravitationally collapsing scalar field background
Shaikh, Rajibul; DasGupta, Anirvan
2014-01-01
The evolution of timelike and null geodesic congruences in a non-static, inhomogeneous spacetime representing the gravitational collapse of a massless scalar field, is investigated in detail. We show explicitly how the initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature along the congruence, influence the evolution and focusing of trajectories in different ways. The role of initial conditions on the focusing time is explored and highlighted. In certain specific cases, the expansion scalar is found to exhibit a finite jump (from negative to positive value) before focusing. The issue of singularity formation and the effect of the central inhomogeneity in the spacetime, on the evolution of the kinematic variables, is discussed. In summary, our analysis does seem to throw some light on how a family of trajectories evolve in a specific model of gravitational collapse.
Schottky-type groups and minimal sets of horocycle and geodesic flows
Kulikov, M. S.
2004-02-01
In the first part of the paper the following conjecture stated by Dal'bo and Starkov is proved: the geodesic flow on a surface M=\\mathbb H^2/\\Gamma of constant negative curvature has a non-compact non-trivial minimal set if and only if the Fuchsian group \\Gamma is infinitely generated or contains a parabolic element. In the second part interesting examples of horocycle flows are constructed: 1) a flow whose restriction to the non-wandering set has no minimal subsets, and 2) a flow without minimal sets.In addition, an example of an infinitely generated discrete subgroup of \\operatorname{SL}(2,\\mathbb R) with all orbits discrete and dense in \\mathbb R^2 is constructed.
Excitation of kinetic geodesic acoustic modes by drift waves in nonuniform plasmas
Energy Technology Data Exchange (ETDEWEB)
Qiu, Z. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Chen, L. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Dept. Physics and Astronomy, Univ. of California, Irvine, California 92697-4575 (United States); Zonca, F. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Associazione Euratom-ENEA sulla Fusione, C.P. 65 - I-00044 - Frascati (Italy)
2014-02-15
Effects of system nonuniformities and kinetic dispersiveness on the spontaneous excitation of Geodesic Acoustic Mode (GAM) by Drift Wave (DW) turbulence are investigated based on nonlinear gyrokinetic theory. The coupled nonlinear equations describing parametric decay of DW into GAM and DW lower sideband are derived and then solved both analytically and numerically to investigate the effects on the parametric decay process due to system nonuniformities, such as nonuniform diamagnetic frequency, finite radial envelope of DW pump, and kinetic dispersiveness. It is found that the parametric decay process is a convective instability for typical tokamak parameters when finite group velocities of DW and GAM associated with kinetic dispersiveness and finite radial envelope are taken into account. When, however, nonuniformity of diamagnetic frequency is taken into account, the parametric decay process becomes, time asymptotically, a quasi-exponentially growing absolute instability.
Synchronization of Geodesic Acoustic Modes and Magnetic Fluctuations in Toroidal Plasmas
Zhao, K. J.; Nagashima, Y.; Diamond, P. H.; Dong, J. Q.; Itoh, K.; Itoh, S.-I.; Yan, L. W.; Cheng, J.; Fujisawa, A.; Inagaki, S.; Kosuga, Y.; Sasaki, M.; Wang, Z. X.; Wei, L.; Huang, Z. H.; Yu, D. L.; Hong, W. Y.; Li, Q.; Ji, X. Q.; Song, X. M.; Huang, Y.; Liu, Yi.; Yang, Q. W.; Ding, X. T.; Duan, X. R.
2016-09-01
The synchronization of geodesic acoustic modes (GAMs) and magnetic fluctuations is identified in the edge plasmas of the HL-2A tokamak. Mesoscale electric fluctuations (MSEFs) having components of a dominant GAM, and m /n =6 /2 potential fluctuations are found at the same frequency as that of the magnetic fluctuations of m /n =6 /2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m /n =6 /2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. Such nonlinear synchronization may also contribute to low-frequency zonal flow formation, reduction of turbulence level, and thus confinement regime transitions.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Bretón, Nora; López, L. A.
2016-11-01
The expressions for the quasinormal modes (QNM) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNM of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNM of four nonlinear electromagnetic black holes, two singular and two regular, namely, from Euler-Heisenberg and Born-Infeld theories, for singular ones, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparing with the QNM of the linear electromagnetic counterpart, their Reissner-Nordström black hole is done.
A Unified Spatiotemporal Prior based on Geodesic Distance for Video Object Segmentation.
Wang, Wenguan; Shen, Jianbing; Yang, Ruigang; Porikli, Fatih
2017-01-31
Video saliency, aiming for estimation of a single dominant object in a sequence, offers strong object-level cues for unsupervised video object segmentation. In this paper, we present a geodesic distance based technique that provides reliable and temporally consistent saliency measurement of superpixels as a prior for pixel-wise labeling. Using undirected intra-frame and inter-frame graphs constructed from spatiotemporal edges or appearance and motion, and a skeleton abstraction step to further enhance saliency estimates, our method formulates the pixel-wise segmentation task as an energy minimization problem on a function that consists of unary terms of global foreground and background models, dynamic location models, and pairwise terms of label smoothness potentials. We perform extensive quantitative and qualitative experiments on benchmark datasets. Our method achieves superior performance in comparison to the current state-of-the-art in terms of accuracy and speed.
From geodesics of the multipole solutions to the perturbed Kepler problem
Hernandez-Pastora, J L; 10.1103/PhysRevD.82.104001
2010-01-01
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the Monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2$^4$-pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.
Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
Ritter, P; Spallicci, A; Cordier, S
2015-01-01
The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT.
Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi
2015-07-01
This work aims to develop a robust and efficient method to track the fuzzy borders between liver and the abutted organs where automatic liver segmentation usually suffers, and to investigate its applications in automatic liver segmentation on noncontrast-enhanced planning computed tomography (CT) images. In order to track the fuzzy liver-chestwall and liver-heart borders where oversegmentation is often found, a starting point and an ending point were first identified on the coronal view images; the fuzzy border was then determined as a geodesic curve constructed by minimizing the gradient-weighted path length between these two points near the fuzzy border. The minimization of path length was numerically solved by fast-marching method. The resultant fuzzy borders were incorporated into the authors' automatic segmentation scheme, in which the liver was initially estimated by a patient-specific adaptive thresholding and then refined by a geodesic active contour model. By using planning CT images of 15 liver patients treated with stereotactic body radiation therapy, the liver contours extracted by the proposed computerized scheme were compared with those manually delineated by a radiation oncologist. The proposed automatic liver segmentation method yielded an average Dice similarity coefficient of 0.930 ± 0.015, whereas it was 0.912 ± 0.020 if the fuzzy border tracking was not used. The application of fuzzy border tracking was found to significantly improve the segmentation performance. The mean liver volume obtained by the proposed method was 1727 cm(3), whereas it was 1719 cm(3) for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. The proposed method was shown to provide accurate segmentation for liver in the planning CT images where contrast agent is not applied. The authors' results also clearly demonstrated that the application of tracking the fuzzy
Juxta-vascular nodule segmentation based on flow entropy and geodesic distance.
Sun, Shenshen; Guo, Yang; Guan, Yubao; Ren, Huizhi; Fan, Linan; Kang, Yan
2014-07-01
Computed aided diagnosis of lung CT data is a new quantitative analysis technique to distinguish malignant nodules from benign ones. Nodule growth rate is a key indicator to discriminate between benign and malignant nodules. Accurate nodule segmentation is the essential for calculating the nodule growth rate. However, it is difficult to segment juxta-vascular nodules, due to the similar gray levels in nodule and attached blood vessels. To distinguish the nodule region from the adjacent vessel region, a flowing direction feature, referred to as the direction of the normal vector for a pixel, is introduced. Since blood is flowing in one single direction through a vessel, the normal vectors of pixels in the vessel region typically point in similar orientations while the directions of those in the nodule region can be viewed as disorganized. The entropy value of the flowing direction features in a neighboring region for a vessel pixel is smaller than that for a nodule pixel. Moreover, vessel pixels typically have a larger geodesic distance to the nodule center than nodule pixels. Based on k -means clustering method, the flow entropy, combined with the geodesic distance, is used to segment vessel attached nodules. The validation of the proposed segmentation algorithm was carried out on juxta-vascular nodules, identified in the Chinalung-CT screening trial and on Lung Image Database Consortium (LIDC) dataset. In fully automated mode, accuracies of 92.9% (26/28), 87.5%(7/8), and 94.9% (149/157) are reached for the outlining of juxta-vascular nodules in the Chinalung-CT, and the first and second datasets of LIDC, respectively. Furthermore, it is demonstrated that the proposed method has low time complexity and high accuracies.
Geodesic chromaticity diagram based on variances of color matching by 14 normal observers.
Macadam, D L
1971-01-01
A nonlinear transformation of the CIE x,y chromaticity coordinates has been derived from the combined color-matching-variance data of 14 normal observers. In the resulting diagram, the series of equiluminous chromaticities entailing the least number of standard deviations of color matching (sigma-units) between any two-terminal, equiluminous chromaticities is the straight line drawn between the points that represent those terminal colors. The total number of sigma-unit differences between those terminal colors is the euclidean distance between those two points. According to Schrödinger's hypothesis, the loci of constant hue are the straight lines (geodesics) radiating from the point that represents hueless colors in this diagram. The horizontal coordinate in the geodesic chromaticity diagram is xi = 3751a(2) - 10a(4) - 520b(2) + 13295b(3) + 32327ab - 25491a(2)b - 41672ab(2) + 10a(3)b - 5227a((1/2)) + 2952(4)a((1/4)), where a = 10x/(2.4x + 34y + 1) and b = 10y/(2.4x + 34y + 1). The vertical coordinate in the geodesic chromaticity diagram is eta = 404b - 185b(2) + 52b(3) + 69a(1 - b(2)) - 3a(2)b + 30ab(2), where a = 10x/(4.2y - x + 1) and b = 10y/(4.2y - x + 1). These formulas were obtained by use of averages of data for two observers whose individual data were published in 1949 and the weighted averages for 12 young observers, which were published in 1957, together with the data for the single observer, PGN, whose data were published in 1942-45. On the basis of extensive studies of these data, the PGN data were assigned 30% weight in the derivation of the new xi,eta diagram. The 1949 data were assigned 44% weight, or 22% per observer, and the 1957 data were assigned 26%, or about 2.2% per observer. The best fit was found by assuming that the over-all mean of the standard deviation of color matching according to the 1949 data was 1.2 times as much as the standard deviation for PGN, and that the weighted-mean standard deviation for the 12 observers was 1.04 times the
Directory of Open Access Journals (Sweden)
Geert Verdoolaege
2015-07-01
Full Text Available In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS is the most popular. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS. The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.
Wang, Xiaoting; Allegra, Michele; Jacobs, Kurt; Lloyd, Seth; Lupo, Cosmo; Mohseni, Masoud
2015-05-01
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
Kabirzadeh, Rasoul
The GEODESIC sounding rocket encountered hundreds of localized, VLF-wave-filled density depletions in an auroral return current region at altitudes between 900--1000 km. While these are similar to well-studied lower-hybrid "spikelets", which are electrostatic, many of the GEODESIC events exhibited strong VLF magnetic field enhancements as well. In the present study we show that these magnetic field fluctuations can be interpreted as the result of geomagnetic field-aligned electron currents driven by fluctuating electric fields parallel to the geomagnetic field lines. This observation suggests that the electromagnetic wave-filled cavities are signatures of unstable filaments of return current fluctuating at VLF frequencies. We argue that the cavities' spatial dimensions, their location inside the return current region and their total radiated power are consistent with the properties of VLF saucer source regions inferred from earlier satellite observations taken at higher altitudes.
Circular geodesics of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
Stuchlik, Zdenek
2015-01-01
We study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and non-linear electrodynamics. They both are characterized by the mass parameter $m$ and the charge parameter $g$. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be sorrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter $g/m > 2$ can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phe...
Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi; Sasaki, Misao
2014-01-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a per...
Geodesic Motion in the Spacetime Of a SU(2)-Colored (A)dS Black Hole in Conformal Gravity
Hoseini, Bahareh; Soroushfar, Saheb
2016-01-01
In this paper we are interested to study the geodesic motion in the spacetime of a SU(2)-colored (A)dS black hole solving in conformal gravity. Using Weierstrass elliptic and Kleinian {\\sigma} hyperelliptic functions, we derive the analytical solutions for the equation of motion of test particles and light rays. Also, we classify the possible orbits according to the particle's energy and angular momentum.
Flux Tensor Constrained Geodesic Active Contours with Sensor Fusion for Persistent Object Tracking
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Filiz Bunyak
2007-08-01
Full Text Available This paper makes new contributions in motion detection, object segmentation and trajectory estimation to create a successful object tracking system. A new efficient motion detection algorithm referred to as the flux tensor is used to detect moving objects in infrared video without requiring background modeling or contour extraction. The flux tensor-based motion detector when applied to infrared video is more accurate than thresholding ”hot-spots”, and is insensitive to shadows as well as illumination changes in the visible channel. In real world monitoring tasks fusing scene information from multiple sensors and sources is a useful core mechanism to deal with complex scenes, lighting conditions and environmental variables. The object segmentation algorithm uses level set-based geodesic active contour evolution that incorporates the fusion of visible color and infrared edge informations in a novel manner. Touching or overlapping objects are further refined during the segmentation process using an appropriate shapebased model. Multiple object tracking using correspondence graphs is extended to handle groups of objects and occlusion events by Kalman filter-based cluster trajectory analysis and watershed segmentation. The proposed object tracking algorithm was successfully tested on several difficult outdoor multispectral videos from stationary sensors and is not confounded by shadows or illumination variations.
Fractional Brownian Motion and Geodesic Rao Distance for Bone X-ray Image Characterization.
El Hassouni, Mohammed; Tafraouti, Abdessamad; Toumi, Hechmi; Lespessailles, Eric; Jennane, Rachid
2016-10-19
Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the Probability Density Function (PDF) of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in that a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an Area Under Curve (AUC) rate of 97% was achieved.
Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
Adamo, T M; Newman, E T
2009-01-01
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtai...
Automatic sulcal line extraction on cortical surfaces using geodesic path density maps.
Le Troter, A; Auzias, G; Coulon, O
2012-07-16
We present here a method that is designed to automatically extract sulcal lines on the mesh of any cortical surface. The method is based on the definition of a new function, the Geodesic Path Density Map (GPDM), within each sulcal basin (i.e. regions with a negative mean curvature). GPDM indicates at each vertex the likelihood that a shortest path between any two points of the basins boundary goes through that vertex. If the distance used to compute shortest path is anisotropic and constrained by a geometric information such as the depth, the GPDM indicates the likelihood that a vertex belongs to the sulcal line in the basin. An automatic GPDM adaptive thresholding procedure is proposed and sulcal lines are then defined. The process has been validated on a set of 25 subjects by comparing results to the manual segmentation from an expert and showed an average error below 2mm. It is also compared to our previous reference method in the context of inter-subject cortical surface registration and shows an significant improvement in performance. Copyright © 2012 Elsevier Inc. All rights reserved.
Negative refractive perfect lens vs Spherical geodesic lens. Perfect Imaging comparative analysis
Gonzalez, Juan C; Minano, Juan C; Grabovickic, Dejan
2012-01-01
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electric field, emitted by the object surface, towards the image surface producing the same field distribution in both surfaces. In particular, a Dirac delta electric field in the object surface is focused without diffraction limit to the Dirac delta electric field in the image surface. The Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to Wavelength/500, they cannot be compared to the NRL, since the concept of the object and image surface is not esta...
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
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Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Balankin, Alexander S.; Mena, Baltasar; Martínez Cruz, M. A.
2017-09-01
In this work, we prove that the topological Hausdorff dimension of critical percolation cluster (CPC) in two dimensions is equal to DtH =Drb + 1 = 7 / 4, where Drb is the Hausdorff dimension of the set of red bonds. Hence, the CPC is infinitely ramified. We also argue that the mapping from the Euclidean metric to the geodesic metric on the CPC is governed by the Hausdorff dimension of the cluster skeleton Dsc =DH /dℓ >dmin, where DH, dℓ, and dmin are the Hausdorff and the connectivity (chemical) dimensions of the CPC and the fractal dimension of the minimum path, respectively. Then we introduce the notion of the topological connectivity dimension dtℓ. This allows us to establish the exact upper and lower bounds for the connectivity dimension dℓ of the CPC in d = 2. The upper and lower bounds for some other dimension numbers were established using the relations between dimension numbers. Narrow ranges defined by these bounds are much smaller than the error bars of numerical estimates reported in literature. Accordingly, the exact values of some dimension numbers are conjectured.
Decay of geodesic acoustic modes due to the combined action of phase mixing and Landau damping
Biancalani, A; Angioni, C; Bottino, A; Zonca, F
2016-01-01
Geodesic acoustic modes (GAMs) are oscillations of the electric field whose importance in tokamak plasmas is due to their role in the regulation of turbulence. The linear collisionless damping of GAMs is investigated here by means of analytical theory and numerical simulations with the global gyrokinetic particle-in-cell code ORB5. The combined effect of the phase mixing and Landau damping is found to quickly redistribute the GAM energy in phase-space, due to the synergy of the finite orbit width of the passing ions and the cascade in wave number given by the phase mixing. When plasma parameters characteristic of realistic tokamak profiles are considered, the GAM decay time is found to be an order of magnitude lower than the decay due to the Landau damping alone, and in some cases of the same order of magnitude of the characteristic GAM drive time due to the nonlinear interaction with an ITG mode. In particular, the radial mode structure evolution in time is investigated here and reproduced quantitatively by ...
iPGA: Incremental Principal Geodesic Analysis with Applications to Movement Disorder Classification★
Salehian, Hesamoddin; Vaillancourt, David
2014-01-01
The nonlinear version of the well known PCA called the Principal Geodesic Analysis (PGA) was introduced in the past decade for statistical analysis of shapes as well as diffusion tensors. PGA of diffusion tensor fields or any other manifold-valued fields can be a computationally demanding task due to the dimensionality of the problem and thus establishing motivation for an incremental PGA (iPGA) algorithm. In this paper, we present a novel iPGA algorithm that incrementally updates the current Karcher mean and the principal sub-manifolds with any newly introduced data into the pool without having to recompute the PGA from scratch. We demonstrate substantial computational and memory savings of iPGA over the batch mode PGA for diffusion tensor fields via synthetic and real data examples. Further, we use the iPGA derived representation in an NN classifier to automatically discriminate between controls, Parkinson’s Disease and Essential Tremor patients, given their HARDI brain scans. PMID:25485449
Geodesic motion in equal angular momenta Myers-Perry-AdS spacetimes
Delsate, Térence; Santarelli, Raphael
2015-01-01
We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-AdS black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable spherical orbits (ISSOs) for these asymptotically anti-de Sitter (AdS) spacetimes, as well as the location of null spherical orbits. We find that the ISSO dives below the ergosurface for black holes rotating close to extremality and merges with the event horizon exactly at extremality, in analogy with the four-dimensional Kerr case. For sufficiently massive black holes in AdS there exists a spin parameter range in which the background spacetime...
Kong, D. F.; Liu, A. D.; Lan, T.; Yu, C. X.; Cheng, J.; Qiu, Z. Y.; Zhao, H. L.; Shen, H. G.; Yan, L. W.; Dong, J. Q.; Xu, M.; Zhao, K. J.; Duan, X. R.; Liu, Y.; Chen, R.; Zhang, S. B.; Sun, X.; Xie, J. L.; Li, H.; Liu, W. D.
2017-04-01
Coexisting dual kinetic geodesic acoustic modes (KGAMs) with similar characteristics have been observed with Langmuir probe arrays in the edge plasma of HL-2A tokamak with low density Ohmic discharge. The dual KGAMs are named a low-frequency GAM (LFGAM) and a high-frequency GAM (HFGAM), respectively. By changing the line averaged density from 1.0× {{10}19}~{{\\text{m}}-3} to 0.7× {{10}19}~{{\\text{m}}-3} , the study of n e and T e profiles indicate that collision damping rate plays a crucial role on exciting of dual KGAMs, especially for the higher frequency branch (HFGAM). With the application of modulating techniques, we provide direct proof that nonlinear interactions between GAMs and ambient turbulence (AT) show great difference at different radial positions. At the exciting position of GAM, the amplitude modulation of AT is dominant, indicating that GAM is generated in the energy-conserving triad interaction. After the exciting of GAMs, they will propagate both inward and outward. During the propagation, the phase modulation of AT is dominant, GAMs can rarely gain energy from AT, yet they can give back-reactions on AT through shearing effect.
Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma
Ren, Haijun
2017-01-01
Energetic particle (EP) driven geodesic acoustic modes (EGAMs) in toroidally rotating tokamak plasmas are analytically investigated using the hybrid kinetic-fluid model and gyrokinetic equations. By ignoring high-order terms and ion Landau damping, the kinetic dispersion relation is reduced to the hybrid one in the large safety factor limit. There is one high-frequency branch with a frequency larger than {ωt0} , the transit frequency of EPs with initial energy, which is always stable. Two low-frequency solutions with a frequency smaller than {ωt0} are complex conjugates in the hybrid limit. In the presence of ion Landau damping, the growth rate of the unstable branch is decreased and the damping rate of the damped branch is increased. The toroidal Mach number is shown to increase {{ Ω }\\text{r}} , the normalized real frequency of both branches. Although not affecting the instability critical condition, the Mach number decreases the growth rate when {{ Ω }\\text{r}} is larger than a critical value Ω \\text{r}\\text{cri} and enlarges the growth rate when {{ Ω }\\text{r}}Landau damping effect is negligible for large M. But the discrepancy between the kinetic dispersion relation and the hybrid one becomes ignorable only for q≳ 7 .
La Nave, Gabriele
2016-01-01
We show explicitly that the full structure of IIB string theory is needed to remove the non-localities that arise in boundary conformal theories that border hyperbolic spaces on AdS$_5$. Specifically, using the Caffarelli/Silvestri\\cite{caffarelli}, Graham/Zworski\\cite{graham}, and Chang/Gonzalez\\cite{chang:2010} extension theorems, we prove that the boundary operator conjugate to bulk p-forms with negative mass in geodesically complete metrics is inherently a non-local operator, specifically the fractional conformal Laplacian. The non-locality, which arises even in compact spaces, applies to any degree p-form such as a gauge field. We show that the boundary theory contains fractional derivatives of the longitudinal components of the gauge field if the gauge field in the bulk along the holographic direction acquires a mass via the Higgs mechanism. The non-locality is shown to vanish once the metric becomes incomplete, for example, either 1) asymptotically by adding N transversely stacked Dd-branes or 2) exact...
Unberath, Mathias; Taubmann, Oliver; Hell, Michaela; Achenbach, Stephan; Maier, Andreas
2017-08-10
The performance of many state-of-the-art coronary artery centerline reconstruction algorithms in rotational angiography heavily depends on accurate two-dimensional centerline information that, in practice, is not available due to segmentation errors. To alleviate the need for correct segmentations, we propose generic extensions to symbolic centerline reconstruction algorithms that target symmetrization, outlier rejection, and topology recovery on asymmetrically reconstructed point clouds. Epipolar geometry- and graph cut-based reconstruction algorithms are used to reconstruct three-dimensional point clouds from centerlines in reference views. These clouds are input to the proposed methods that consist of (a) merging of asymmetric reconstructions, (b) removal of inconsistent three-dimensional points using the reprojection error, and (c) projection domain-informed geodesic computation. We validate our extensions in a numerical phantom study and on two clinical datasets. In the phantom study, the overlap measure between the reconstructed point clouds and the three-dimensional ground truth increased from 68.4 ± 9.6% to 85.9 ± 3.3% when the proposed extensions were applied. In addition, the averaged mean and maximum reprojection error decreased from 4.32 ± 3.03 mm to 0.189 ± 0.182 mm and from 8.39 ± 6.08 mm to 0.392 ± 0.434 mm. For the clinical data, the mean and maximum reprojection error improved from 1.73 ± 0.97 mm to 0.882 ± 0.428 mm and from 3.83 ± 1.87 mm to 1.48 ± 0.61 mm, respectively. The application of the proposed extensions yielded superior reconstruction quality in all cases and effectively removed erroneously reconstructed points. Future work will investigate possibilities to integrate parts of the proposed extensions directly into reconstruction. © 2017 American Association of Physicists in Medicine.
Computational Analysis of Natural Ventilation Flows in Geodesic Dome Building in Hot Climates
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Zohreh Soleimani
2016-08-01
Full Text Available For centuries, dome roofs were used in traditional houses in hot regions such as the Middle East and Mediterranean basin due to its thermal advantages, structural benefits and availability of construction materials. This article presents the computational modelling of the wind- and buoyancy-induced ventilation in a geodesic dome building in a hot climate. The airflow and temperature distributions and ventilation flow rates were predicted using Computational Fluid Dynamics (CFD. The three-dimensional Reynolds-Averaged Navier-Stokes (RANS equations were solved using the CFD tool ANSYS FLUENT15. The standard k-epsilon was used as turbulence model. The modelling was verified using grid sensitivity and flux balance analysis. In order to validate the modelling method used in the current study, additional simulation of a similar domed-roof building was conducted for comparison. For wind-induced ventilation, the dome building was modelled with upper roof vents. For buoyancy-induced ventilation, the geometry was modelled with roof vents and also with two windows open in the lower level. The results showed that using the upper roof openings as a natural ventilation strategy during winter periods is advantageous and could reduce the indoor temperature and also introduce fresh air. The results also revealed that natural ventilation using roof vents cannot satisfy thermal requirements during hot summer periods and complementary cooling solutions should be considered. The analysis showed that buoyancy-induced ventilation model can still generate air movement inside the building during periods with no or very low wind.
Timelike and null equatorial geodesics in the Bonnor-Sackfield relativistic disk
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Guillermo A. González
2011-06-01
Full Text Available A study of timelike and null equatorial geodesics in the BonnorSackfield relativistic thin disk is presented. The motion of test particles in the equatorial plane is analyzed, both for the newtonian thin disk model as for the corresponding relativistic disk. The nature of the possible orbits is studied by means of a qualitative analysis of the effective potential and by numerically solving the motion equation for radial and non-radial equatorial trajectories. The existence of stable, unstable and marginally stable circular orbits is analyzed, both for the newtonian and relativistic case. Examples of the numerical results, obtained with some simple values of the parameters, are presented. Resumen. En este trabajo se presenta un estudio de las geodésicas temporales y nulas en el disco delgado relativista y newtoniano de Bonnor-Sackfield. Se analiza el movimiento de las partículas de prueba en el plano ecuatorial, tanto para el modelo newtoniano del disco delgado como para el disco relativista correspondiente. La naturaleza de las órbitas posibles se estudia por medio de un análisis cualitativo del potencial efectivo, y numéricamente mediante la solución de la ecuación de movimiento de las trayectorias ecuatorial radial y no radial: Se analiza la existencia de órbitas estables, circulares inestables y estables marginalmente, tanto para el caso newtoniano, como el relativista. Se presentan ejemplos de los resultados numéricos obtenidos con algunos valores de los parámetros simples.
La Nave, Gabriele; Phillips, Philip W.
2016-12-01
We show explicitly that the full structure of IIB string theory is needed to remove the nonlocalities that arise in boundary conformal theories that border hyperbolic spaces on AdS5 . Specifically, using the Caffarelli/Silvestri [1], Graham/Zworski [2], and Chang/Gonzalez [3] extension theorems, we prove that the boundary operator conjugate to bulk p-forms with negative mass in geodesically complete metrics is inherently a nonlocal operator, specifically the fractional conformal Laplacian. The nonlocality, which arises even in compact spaces, applies to any degree p-form such as a gauge field. We show that the boundary theory contains fractional derivatives of the longitudinal components of the gauge field if the gauge field in the bulk along the holographic direction acquires a mass via the Higgs mechanism. The nonlocality is shown to vanish once the metric becomes incomplete, for example, either (1) asymptotically by adding N transversely stacked Dd-branes or (2) exactly by giving the boundary a brane structure and including a single transverse Dd-brane in the bulk. The original Maldacena conjecture within IIB string theory corresponds to the former. In either of these proposals, the location of the Dd-branes places an upper bound on the entanglement entropy because the minimal bulk surface in the AdS reduction is ill-defined at a brane interface. Since the brane singularities can be circumvented in the full 10-dimensional spacetime, we conjecture that the true entanglement entropy must be computed from the minimal surface in 10-dimensions, which is of course not minimal in the AdS5 reduction.
Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
Stuchlík, Zdeněk; Schee, Jan
2015-12-01
In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.
Local, Non-Geodesic, Timelike Currents in the Force-Free Magnetosphere of a Kerr Black Hole
Menon, Govind
2014-01-01
In this paper, we use previously developed exact solutions to present some of the curious features of a force-free magnetosphere in a Kerr background. More precisely, we obtain a hitherto unseen timelike current in the force-free magnetosphere that does not flow along a geodesic. The electromagnetic field in this case happens to be magnetically dominated. This too is a feature that has entered the literature for the first time. Changing the sign of a single parameter in our solutions generates a spacelike current that creates an electromagnetic field that is electrically dominated.
Becerril, Ricardo; Nucamendi, Ulises
2016-01-01
The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA\\* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
Energy Technology Data Exchange (ETDEWEB)
JH Mather; DA Randall; CJ Flynn
2008-06-30
In 2008, the Atmospheric Radiation Measurement (ARM) Program and the Climate Change Prediction Program (CCPP) have been asked to produce joint science metrics. For CCPP, the metrics will deal with a decade-long control simulation using geodesic grid-coupled climate model. For ARM, the metrics will deal with observations associated with the 2006 deployment of the ARM Mobile Facility (AMF) to Niamey, Niger. Specifically, ARM has been asked to deliver data products for Niamey that describe cloud, aerosol, and dust properties. This report describes the aerosol optical depth (AOD) product.
GEODESIC MONITORING OF VERTICAL MOVEMENT OF JSC «GRODNO AZOT» BUILDINGS USING DIGITAL DNA 03 LEVEL
Directory of Open Access Journals (Sweden)
V. I. Mikhailov
2010-01-01
Full Text Available The paper presents peculiar features and methodology pertaining to application of digital DNA 03 level for monitoring vertical movement of load-carrying structures in the workshops and foundations of various capacities, exhaust pipes and granulation towers having height from 100 to150 meters. The proposed methods presuppose usage of the results of engineering and geological investigations and highly accurate geodesic measurements considered in the process of hydro- and pneumatic tests of an isothermic storage of liquid ammonia and a production “Ammonia” shop taken as an example.
Dorn, H
2003-01-01
Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of AdS sub 5 xS sup 5 and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all AdS sub 5 xS sup 5 and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of AdS sub 5 xS sup 5 to that of the plane wave is studied in detail. At each point these null geodesics of AdS sub 5 xS sup 5 form a cone which degenerates in the limit. (author)
Geodesic Distance for Support Vector Machines%基于测地距离的支持向量机分类算法
Institute of Scientific and Technical Information of China (English)
全勇; 杨杰
2005-01-01
When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into classification method at hand. A very common type of prior knowledge is many data sets are on some kinds of manifolds. Distance based classification methods can make use of this by a modified distance measure called geodesic distance.We introduce a new kind of kernels for support vector machines which incorporate geodesic distance and therefore are applicable in cases such transformation invariance is known. Experiments results show that the performance of our method is comparable to that of other state-of-the-art method.
Guha, Sarbari; Bhattacharya, Pinaki
2010-01-01
In this paper, we have studied the timelike and null geodesics in the vicinity of a non-rotating, charged black hole in a five-dimensional Reissner-Nordstrom Anti-de Sitter spacetime. Here the solutions are uniquely characterized by their mass, charge and the cosmological constant. The line element and the horizon function has been defined and it is found that only one horizon is physically admissible. The spherical symmetry of the geometry helps us to reduce the problem to a study of three geodesic equations. In our analysis, we have used both the method of effective Newtonian orbit calculations and the dynamical systems method to analyze the particle trajectories. The equation of motion of a particle of unit mass is found. The effective potential under which any test particle moves with a given angular momentum at a given distance from the black hole, depends only on the mass and charge of the black hole and the cosmological constant. This equation is used to study radial motion and the corresponding stabil...
Kayran, A.; İbrahimoǧlu, C. S.
2014-12-01
During last twenty years, wind turbine manufacturers took the path of building larger machines to generate more electricity. However, the bigger the size became, the more material was required to support the loads, leading to great weight increases. Larger turbines and higher hub heights also resulted in larger tower base diameters which are limited considering their logistics. In many countries, the limit for transports with special permits maximizes the diameter to 4.5 metres. Considering this fact, the wind turbine market dominated by welded steel shell towers is looking for new structural solutions for their future turbines. Although, composite materials are not used as the structural material in the towers of today's turbines, the demand for larger wind turbines forces engineers to seek for alternative material systems with high specific strength and stiffness ratios to be used in towers. Inspired by the applicability of filament winding in tower production, in the present article we investigated the effect of semi-geodesic winding on the winding angle, thickness, stiffness coefficients and vibration characteristics of filament wound composite conical shells of revolution which simulate wind turbine towers at the structural level. Present study showed that the preset friction applied during semi-geodesic winding is an important design parameter which can be controlled to obtain gradually increasing thickness from tower top to the base of the tower, and favourably alter the dynamic characteristics of the composite towers.
Kerr black hole parameters in terms of red/blue shifts of photons emitted by geodesic particles
Herrera-Aguilar, Alfredo
2015-01-01
We are motivated by the recently reported dynamical evidence of stars with short orbital periods moving around the center of the Milky Way and the corresponding hypothesis about the existence of a supermassive black hole hosted at its center. In this paper we show how the mass and rotation parameters of a Kerr black hole (assuming that the putative supermassive black hole is of this type), as well as the distance that separates the black hole from the Earth, can be estimated in a relativistic way in terms of i) the red and blue shifts of photons that are emitted by geodesic massive particles (stars and galactic gas) and travel along null geodesics towards a distant observer, and ii) the radius of these star/gas orbits. As a concrete example and as a first step towards a full relativistic analysis of the above mentioned star orbits around the center of our galaxy, we consider stable equatorial circular orbits of stars and express their corresponding red/blue shifts in terms of the metric parameters (mass and a...
Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Ho\\v{r}ava's gravity
Vieira, Ronaldo S S; Kluźniak, W\\lodek; Stuchlík, Zdeněk; Abramowicz, Marek
2013-01-01
We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric. For any value of the Ho\\v{r}ava parameter $\\omega$, there are values of the gravitational mass $M$ for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasi-static spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of $M$, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordstr\\"om naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.
Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity
Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek
2014-07-01
We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.
Directory of Open Access Journals (Sweden)
Yamill Santiago Campos Pérez
2015-01-01
Full Text Available A geodesic dome is a mesh of bars and nodes arranged along the edges and vertices of a polyhedron on a surface that can be in the form of a sphere, parabola or ellipse. From knowing the advantages of this type of structure, they have been widely used in various constructions such as: housing, commercial offices, greenhouses, fair stand, fixed ceilings fuel storage tanks, among others. Many researchers have studied modeling and geometry of geodesic domes. The purpose of this paper is to present, from the review and compilation of information from several researches, an algorithm for generating a wireframe model of a geodesic dome for fixed roofs of spherical fuel storage tanks, for a further analysis of resistance by the method of finite elements. In this paper, we describe in detail the procedure and geometric expressions that were used. Finally, a computer program was developed in order to evaluate mathematical expressions and the procedure described in this paper and also to have a tool for generating computational model of a geodesic dome.
H. Bogunović; J.M. Pozo; M.C. Villa-Uriol; C.B.L.M. Majoie; R. van den Berg; H.A.F.G. van Andel; J.M. Macho; J. Blasco; L.S. Román; A.F. Frangi
2011-01-01
Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D x-ray reconstruction angiography (3DRA) and time of flight magnetic resonance angiography (TOF-MRA) images
Isometry group and geodesics of the Wagner lift of a riemannian metric on two-dimensional manifold
B., José Ricardo Arteaga
2010-01-01
In this paper we construct a functor from the category of two-dimensional Riemannian manifolds to the category of three-dimensional manifolds with generalized metric tensors. For each two-dimensional oriented Riemannian manifold $(M,g)$ we construct a metric tensor $\\hat g$ (in general, with singularities) on the total space $SO(M,g)$ of the principal bundle of the positively oriented orthonormal frames on $M$. We call the metric $\\hat g$ the Wagner lift of $g$. We study the relation between the isometry groups of $(M,g)$ and $(SO(M,g),\\hat g)$. We prove that the projections of the geodesics of $(SO(M,g),\\hat g)$ onto $M$ are the curves which satisfy the equation \\begin{equation*} \
A conformal boundary for space-times based on light-like geodesics: The 3-dimensional case
Bautista, A.; Ibort, A.; Lafuente, J.; Low, R.
2017-02-01
A new causal boundary, which we will term the l-boundary, inspired by the geometry of the space of light rays and invariant by conformal diffeomorphisms for space-times of any dimension m ≥3 , proposed by one of the authors [R. J. Low, The Space of Null Geodesics (and a New Causal Boundary), Lecture Notes in Physics 692 (Springer, 2006), pp. 35-50] is analyzed in detail for space-times of dimension 3. Under some natural assumptions, it is shown that the completed space-time becomes a smooth manifold with boundary and its relation with Geroch-Kronheimer-Penrose causal boundary is discussed. A number of examples illustrating the properties of this new causal boundary as well as a discussion on the obtained results will be provided.
Gallo, Emanuel
2015-01-01
In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically symmetric black holes. As applications of these results we give a universal upper bound for the real part of quasinormal modes in the WKB limit and a universal lower bound for the position of the first relativistic image in the strong lensing regime produced by these type of black holes. For the axially-symmetric case, we also make some general comments (independent of the underlying gravitational theory) on the relation between circular null geodesics and the fastest way to circle a black hole.
A note on circular geodesics in the equatorial plane of an extreme Kerr-Newman black hole
Ulbricht, Sebastian
2015-01-01
We examine the behaviour of circular geodesics describing orbits of neutral test particles around an extreme Kerr-Newman black hole. It is well known that the radial Boyer-Lindquist coordinates of the prograde photon orbit $r=r_{\\rm ph}$, marginally bound orbit $r=r_{\\rm mb}$ and innermost stable orbit $r=r_{\\rm ms}$ of the extreme Kerr black hole all coincide with the event horizon's value $r=r_+$. We find that the same property holds for the extreme Kerr-Newman black hole with mass $M$, angular momentum $J$ and electric charge $Q=\\pm\\sqrt{M^2-J^2/M^2}$ ($|J|\\le M^2$) if and only if $|J|$ is greater than or equal to $M^2/2$, $M^2/\\sqrt{3}$ and $M^2/\\sqrt{2}$, respectively.
Araki, Keisuke
2016-01-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Examinations of the stabilities of the hydrodynamic (HD, $\\alpha=0$) and magnetohydrodynamic (MHD, $\\alpha\\to0$) motions and the $O(\\alpha)$ Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where {\\alpha} represents the Hall-term strength parameter. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Els\\"asser variables (GEVs). It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the po...
Simpson, J. J.; Taflove, A.
2005-12-01
We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A
Energy Technology Data Exchange (ETDEWEB)
Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I. [National Research Centre Kurchatov Institute (Russian Federation); Konovaltseva, L. V. [Peoples’ Friendship University of Russia (Russian Federation)
2015-12-15
A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.
Computation of approximate geodesics on point cloud%点云模型上近似测地线的计算
Institute of Scientific and Technical Information of China (English)
杨斌; 范媛媛; 王继东
2011-01-01
In order to compute approximate geodesic efficiently between two points on point cloud, a weighted graph was constructed by splitting point cloud along the Cartesian coordinate axes, thus initial approximate geodesic between any two given points could be computed out using Dijkstra's algorithm. Then the conjugate gradient method was adopted to minimize the energy function defined; finally, approximate geodesic could be obtained after some iterative steps. This proposed algorithm avoids meshing or reconstructing the point cloud to be local or global surface, and it is suitable for computing geodesic on large scale point cloud.%为了有效计算点云模型上任意两点间的近似测地线,将点云模型沿着直角坐标系中三坐标轴方向进行空间栅格划分后,建立表示点云模型的带权图,采用Dijkstra算法计算带权图上任意给定两点间的最短路径作为初始测地线;然后通过使能量函数最小化,用共轭梯度方法对初始测地线迭代优化,计算得到点云模型上任意给定两点间的近似测地线.该算法无需对点云模型进行网格化,无需对点云模型进行局部或全局的曲面重建,适合大规模点云模型上测地线的计算.
Energy Technology Data Exchange (ETDEWEB)
JH Mather; DA Randall; CJ Flynn
2008-09-30
In 2008, the Atmospheric Radiation Measurement (ARM) Program and the Climate Change Prediction Program (CCPP) have been asked to produce joint science metrics. For CCPP, the metrics will deal with a decade-long control simulation using geodesic grid-coupled climate model. For ARM, the metrics will deal with observations associated with the 2006 deployment of the ARM Mobile Facility (AMF) to Niamey, Niger. Specifically, ARM has been asked to deliver data products for Niamey that describe cloud, aerosol, and dust properties. The first quarter milestone was the initial formulation of the algorithm for retrieval of these properties. The second quarter milestone included the time series of ARM-retrieved cloud properties and a year-long CCPP control simulation. The third quarter milestone included the time series of ARM-retrieved aerosol optical depth and a three-year CCPP control simulation. This final fourth quarter milestone includes the time-series of aerosol and dust properties and a decade-long CCPP control simulation.
Andersson, F
2000-01-01
By the method of rho-integration we obtain all Lanczos potentials L_{ABCA'}of the Weyl spinor that, in a certain sense, are aligned to a geodesicshear-free expanding null congruence. We also obtain all spinorsH_{ABA'B'}=Q_{AB}o_{A'}o_{B'}, Q_{AB}=Q_{(AB)} satisfyingnabla_{(A}{}^{B'}H_{BC)A'B'}=L_{ABCA'}. We go on to prove that H_{ABA'B'} canbe chosen so that Gamma_{ABCA'}=nabla_{(A}{}^{B'} H_{B)CA'B'} defines a metricasymmetric curvature-free connection such that L_{ABCA'}=Gamma_{(ABC)A'} is aLanczos potential that is aligned to the geodesic shear-free expandingcongruence. These results are a generalization to a large class ofalgebraically special spacetimes (including all vacuum ones for which theprincipal null direction is expanding) of the curvature-free connection of theKerr spacetime found by Bergqvist and Ludvigsen, which was used in aconstruction of quasi-local momentum.
Jurcak, V; Fripp, J; Engstrom, C; Walker, D; Salvado, O; Ourselin, S; Crozier, S
2008-01-01
This study presents a novel method for the automatic segmentation of the quadratus lumborum (QL) muscle from axial magnetic resonance (MR) images using a hybrid scheme incorporating the use of non-rigid registration with probabilistic atlases (PAs) and geodesic active contours (GACs). The scheme was evaluated on an MR database of 7mm axial images of the lumbar spine from 20 subjects (fast bowlers and athletic controls). This scheme involved several steps, including (i) image pre-processing, (ii) generation of PAs for the QL, psoas (PS) and erector spinae+multifidus (ES+MT) muscles and (iii) segmentation, using 3D GACs initialized and constrained by the propagation of the PAs using non-rigid registration. Pre-processing of the images involved bias field correction based on local entropy minimization with a bicubic spline model and a reverse diffusion interpolation algorithm to increase the slice resolution to 0.98 x 0.98 x 1.75mm. The processed images were then registered (affine and non-rigid) and used to generate an average atlas. The PAs for the QL, PS and ES+MT were then generated by propagation of manual segmentations. These atlases were further analysed with specialised filtering to constrain the QL segmentation from adjacent non-muscle tissues (kidney, fat). This information was then used in 3D GACs to obtain the final segmentation of the QL. The automatic segmentation results were compared with the manual segmentations using the Dice similarity metric (DSC), with a median DSC for the right and left QL muscles of 0.78 (mean = 0.77, sd=0.07) and 0.75 (mean =0.74, sd=0.07), respectively.
Energy Technology Data Exchange (ETDEWEB)
Fritscher, Karl D., E-mail: Karl.Fritscher@umit.at; Sharp, Gregory [Department for Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts 02114 (United States); Peroni, Marta [Paul Scherrer Institut, Villigen 5232 (Switzerland); Zaffino, Paolo; Spadea, Maria Francesca [Department of Experimental and Clinical Medicine, Magna Graecia University, Catanzaro 88100 (Italy); Schubert, Rainer [Institute for Biomedical Image Analysis, Private University of Health Sciences, Medical Informatics and Technology, Hall in Tirol 6060 (Austria)
2014-05-15
Purpose: Accurate delineation of organs at risk (OARs) is a precondition for intensity modulated radiation therapy. However, manual delineation of OARs is time consuming and prone to high interobserver variability. Because of image artifacts and low image contrast between different structures, however, the number of available approaches for autosegmentation of structures in the head-neck area is still rather low. In this project, a new approach for automated segmentation of head-neck CT images that combine the robustness of multiatlas-based segmentation with the flexibility of geodesic active contours and the prior knowledge provided by statistical appearance models is presented. Methods: The presented approach is using an atlas-based segmentation approach in combination with label fusion in order to initialize a segmentation pipeline that is based on using statistical appearance models and geodesic active contours. An anatomically correct approximation of the segmentation result provided by atlas-based segmentation acts as a starting point for an iterative refinement of this approximation. The final segmentation result is based on using model to image registration and geodesic active contours, which are mutually influencing each other. Results: 18 CT images in combination with manually segmented labels of parotid glands and brainstem were used in a leave-one-out cross validation scheme in order to evaluate the presented approach. For this purpose, 50 different statistical appearance models have been created and used for segmentation. Dice coefficient (DC), mean absolute distance and max. Hausdorff distance between the autosegmentation results and expert segmentations were calculated. An average Dice coefficient of DC = 0.81 (right parotid gland), DC = 0.84 (left parotid gland), and DC = 0.86 (brainstem) could be achieved. Conclusions: The presented framework provides accurate segmentation results for three important structures in the head neck area. Compared to a
Ciller Ruiz, Carlos
2012-01-01
[ANGLÈS] This work presents an analysis and optimization, both in terms of optimal parameters and speed, of the novel geodesic active fields framework for surface image registration on the sphere, presented by Zosso, Dominique in his PhD thesis at the École Polytechnique Fédérale de Lausanne. The relevance of surface registration to medical imaging is that there is a lot of anatomical information in the form of collected surface points, giving information about the cortical folding pattern. H...
On Geodesic Exponential Kernels
DEFF Research Database (Denmark)
Lauze, François; Hauberg, Søren
2015-01-01
This extended abstract summarizes work presented at CVPR 2015 [1]. Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes...
基于2DUGDP的戴眼镜人脸识别%Glasses-faces Recognition Based on 2D Unsupervised Geodesic Discriminant Projection
Institute of Scientific and Technical Information of China (English)
宋彩芳; 尹宝才; 孙艳丰; 陈尚佑
2011-01-01
A novel glasses-faces recognition method based on the 2D unsupervised geodesic discriminant projection (2DUGDP) technique is presented in this paper. Based on the virtual samples, discriminable features will be obtained by analyzing the difference of faces with variety eyeglasses. This feature characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. The projection ensures the distance of samples remain close for near samples, and separate for far samples. Face space is regarded as a nonlinear instructure embedded in the high dimensional space. Geodesic distance is employed to model the intrinsic structure of the manifold. The method is applied to glasses-faces recognition and examination using the CAS-PEAL, FERET face databases. Results show that 2DUDP outperforms other methods.%针对戴眼镜人脸识别问题,提出了二维非监督测地线判别投影(2D unsupervised geodesic discriminant projection,2DUGDP)方法.该方法在扩充虚拟样本库的基础上,分析戴眼镜人脸图像和不戴眼镜人脸图像的差异及戴不同眼镜人睑图像的差异,提取判别特征用于识别.该特征考虑局部特征的同时考虑非局部特征,寻找一种最优投影在最大化非局部散度矩阵的同时最小化局部散度矩阵,使得距离近的数据投影后仍然近,距离远的数据投影后仍然远.考虑到人脸是非线性的流形结构,文中采用测地线距离表示样本间的差异.在FERET人脸库和CAS-PEAL人脸库上分别进行了实验,实验结果表明,该方法相比较其他方法更能提高戴眼镜人脸的识别率.
Marchenko, V. S.; Panwar, A.; Reznik, S. N.; Ryu, C. M.
2017-09-01
In a recent work, we have shown that the plasma flow around the magnetic island can excite the beta-induced Alfvén eigenmode (BAE) (Marchenko et al 2016 Nucl. Fusion 56 106021). In the present communication, it is shown that coupling of this primary BAE and magnetic island generates secondary geodesic acoustic mode (GAM), which has the frequency and mode structure identical to those of the primary BAE. The fixed GAM/BAE amplitude ratio, determined by the plasma neutrality, is comparable with the plasma/magnetic pressure ratio. This nonlinear coupling can be responsible for axis-symmetric modes, which accompany island-driven Alfvénic modes observed on HL-2A tokamak (Chen et al 2013 Nucl. Fusion 53 113010).
Araki, Keisuke
2017-06-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Elsässer variables (GEVs). Examinations of the stabilities of the hydrodynamic (HD, α=0 ) and magnetohydrodynamic (MHD, α\\to0 ) motions and the O(α) Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where α represents the Hall-term strength parameter. It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the positive (stable) and negative (unstable) values, while that of the HD system between two complex helical waves was observed to be negative definite. Moreover, for the MHD case, negative sectional curvatures were found to occur only when mode interaction was ‘local’, i.e. the wavenumber moduli of the main flow (say p) and perturbation (say k) were relatively close to each other. However, in the nonlocal limit (k\\ll p or k\\gg p ), the sectional curvatures were always positive. This result leads to the conjecture that the MHD interactions mainly excite wavy or non-growing motions; however, some local interactions cause dynamical instability that leads to chaotic or turbulent plasma motions. Additionally, it was found that the tendencies of the O(α) effects are opposite between the ion cyclotron and whistler modes. Comparison with the energy-Casimir method is also discussed using a remarkable constant of motion which relates the Riemannian curvature to the second variation of the
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)
2010-05-15
Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F{<=}f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less
Demczuk, Piotr; Rodzik, Jan; Superson, Józef; Mroczek, Przemysław
2017-04-01
The dissection of loess covers by Neoholocene gullies in east Poland particularly depends on relative heights. In the case of height differences not exceeding 30 m, gullies hardly exist. In areas with height differences exceeding 50 m, gullies develop a network with a density of several km km-2 of the catchment, and locally even more than 10 km·km-2. Systems of dissections called badlands are then abundant, as well as piping landforms with no surface runoff. The gullies are covered by forest vegetation - particularly dry-ground forest Tilio-carpinetum. In such conditions, it is difficult to accurately mark the gullies on a map, and perform geodesic measurements in the field. Even the measurement of the length and calculation of the density of the gullies is problematic. Due to the diversity of their types and shapes, the calculation of the volume of the gullies, and therefore the determination of the total amount of gully erosion, is approximate, particularly in many kilometres long branched out systems. An additional difficulty is posed by the agricultural use of some slopes and bottoms of the gullies in the past. This considerably changed the features of such landforms, making them resemble Late Pleistocene trough valleys. The determination of their genesis requires conducting pedological research. For the above reasons, calculations of the volume of the gully and its erosion balance were performed for a small gully catchment with an area of 0.19 km2. The total length of gullies in the catchment amounts to approximately 2 km, and their density exceeds 11 km·km-2. The studied gully dissects the left slope of the Bystra River valley near Celejów on the Nałęczów Plateau, a loess mesoregion constituting a fragment of the western part of the Lublin Upland. The difference in height between the valley floor and the plateau amounts to 58 m (204-146 m a.s.l.). Nine height difference and soil transects were performed within the analysed system, and geodesic
Qiu, Wu; Yuan, Jing; Rajchl, Martin; Kishimoto, Jessica; Chen, Yimin; de Ribaupierre, Sandrine; Chiu, Bernard; Fenster, Aaron
2015-09-01
Intraventricular hemorrhage (IVH) or bleed within the cerebral ventricles is a common condition among very low birth weight pre-term neonates. The prognosis for these patients is worsened should they develop progressive ventricular dilatation, i.e., post-hemorrhagic ventricle dilatation (PHVD), which occurs in 10-30% of IVH patients. Accurate measurement of ventricular volume would be valuable information and could be used to predict PHVD and determine whether that specific patient with ventricular dilatation requires treatment. While the monitoring of PHVD in infants is typically done by repeated transfontanell 2D ultrasound (US) and not MRI, once the patient's fontanels have closed around 12-18months of life, the follow-up patient scans are done by MRI. Manual segmentation of ventricles from MR images is still seen as a gold standard. However, it is extremely time- and labor-consuming, and it also has observer variability. This paper proposes an accurate multiphase geodesic level-set segmentation algorithm for the extraction of the cerebral ventricle system of pre-term PHVD neonates from 3D T1 weighted MR images. The proposed segmentation algorithm makes use of multi-region segmentation technique associated with spatial priors built from a multi-atlas registration scheme. The leave-one-out cross validation with 19 patients with mild enlargement of ventricles and 7 hydrocephalus patients shows that the proposed method is accurate, suggesting that the proposed approach could be potentially used for volumetric and morphological analysis of the ventricle system of IVH neonatal brains in clinical practice. Copyright © 2015 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Bogunovic, Hrvoje; Pozo, Jose Maria; Villa-Uriol, Maria Cruz [Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra (UPF) and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine - CIBER-BBN, Barcelona 08018 (Spain); and others
2011-01-15
Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D x-ray reconstruction angiography (3DRA) and time of flight magnetic resonance angiography (TOF-MRA) images available in the clinical routine. Methods: Three aspects of the GAR method have been improved: execution time, robustness to variability in imaging protocols, and robustness to variability in image spatial resolutions. The improved GAR was retrospectively evaluated on images from patients containing intracranial aneurysms in the area of the Circle of Willis and imaged with two modalities: 3DRA and TOF-MRA. Images were obtained from two clinical centers, each using different imaging equipment. Evaluation included qualitative and quantitative analyses of the segmentation results on 20 images from 10 patients. The gold standard was built from 660 cross-sections (33 per image) of vessels and aneurysms, manually measured by interventional neuroradiologists. GAR has also been compared to an interactive segmentation method: isointensity surface extraction (ISE). In addition, since patients had been imaged with the two modalities, we performed an intermodality agreement analysis with respect to both the manual measurements and each of the two segmentation methods. Results: Both GAR and ISE differed from the gold standard within acceptable limits compared to the imaging resolution. GAR (ISE) had an average accuracy of 0.20 (0.24) mm for 3DRA and 0.27 (0.30) mm for TOF-MRA, and had a repeatability of 0.05 (0.20) mm. Compared to ISE, GAR had a lower qualitative error in the vessel region and a lower quantitative error in the aneurysm region. The repeatability of GAR was superior to manual measurements and ISE. The intermodality agreement was similar between GAR and the manual measurements. Conclusions: The improved GAR method outperformed ISE qualitatively as well as
Minati, Ludovico; Cercignani, Mara; Chan, Dennis
2013-10-01
Graph theory-based analyses of brain network topology can be used to model the spatiotemporal correlations in neural activity detected through fMRI, and such approaches have wide-ranging potential, from detection of alterations in preclinical Alzheimer's disease through to command identification in brain-machine interfaces. However, due to prohibitive computational costs, graph-based analyses to date have principally focused on measuring connection density rather than mapping the topological architecture in full by exhaustive shortest-path determination. This paper outlines a solution to this problem through parallel implementation of Dijkstra's algorithm in programmable logic. The processor design is optimized for large, sparse graphs and provided in full as synthesizable VHDL code. An acceleration factor between 15 and 18 is obtained on a representative resting-state fMRI dataset, and maps of Euclidean path length reveal the anticipated heterogeneous cortical involvement in long-range integrative processing. These results enable high-resolution geodesic connectivity mapping for resting-state fMRI in patient populations and real-time geodesic mapping to support identification of imagined actions for fMRI-based brain-machine interfaces.
Perfect imaging with geodesic waveguides
Miñano, Juan C.; Benítez, Pablo; González, Juan C.
2010-12-01
Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radially polarized modes (i.e. the electric field is only radial) with the same perfect focusing properties as the Maxwell fish-eye (MFE) lens. An approximate version of that device, comprising a thin waveguide with a homogeneous core, paves the way to experimentally attaining perfect imaging in the MFE lens.
Geodesics of Spherical Dilaton Spacetimes
Institute of Scientific and Technical Information of China (English)
ZENG Yi; L(U) Jun-Li; WANG Yong-Jiu
2006-01-01
The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesies. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant a are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for a≠0.
Analytical time-like geodesics
Kostic, Uros
2012-01-01
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r=r(\\lambda), t=t(\\chi), and \\tau=\\tau(\\chi), where \\lambda\\ is the true anomaly and \\chi\\ is a parameter along the orbit. A very simple relation between \\lambda\\ and \\chi\\ is also shown. These solutions are very useful for modeling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.
Interactive Manipulation and Reuse of Geodesic B-spline Curves on Meshes%网格曲面上测地B样条曲线交互操作与重用
Institute of Scientific and Technical Information of China (English)
刘斌; 韩林; 林俊义; 黄常标; 江开勇
2012-01-01
针对现有曲面上自由曲线设计重用方法的不足,提出一种流形网格曲面上曲线几何变换方法,达到曲线重用与再设计的目的.网格曲面上的曲线用测地B样条表示,具有与欧氏空间中传统B样条相一致的明确数学模型；引入对数映射理论将给定的源曲线控制顶点映射到切空间,获得它们的法坐标,按照曲线迁移前后控制顶点法坐标保持不变的原则,建立曲线迁移前后控制顶点的对应关系,实现类似于欧氏空间中的平移、旋转和缩放等几何变换.以网格曲面上离散对数映射理论为基础,将欧氏空间中的对称定义拓展到曲面空间,提出曲面上曲线的广义镜像概念并给出具体的算法实现.法坐标很好地保持了控制顶点之间的测地距离和相对位置关系,因而也保证了曲线迁移重用过程中的形状保持性.试验结果表明,所介绍方法健壮、有效,能满足曲面上曲线的交互设计要求.%In allusion to the deficiencies of the existing methods of reuse designing free curve on the surface, a geometric transformation method of curves on Manifold triangulation surface is proposed to achieve the aim of curves reuse and redesign. The curve on the mesh surface is represented as Geodesic B- spline curve, which has the clear uniform mathematical model with the classical B-spline curves in Euclidean space; by introduction of the logarithmic mapping theory, the control points of source curves can be mapped into tangent space and its Normal Coordinates can be obtained. According to the principle of those Normal Coordinates of remained unchanged, establishing the corresponding relation between pre and post transfer of curves, and curve's translation, rotation and scaling could be realized similaring to its geometric transformation in Euclidean space. The symmetry definition in Euclidean space is expand to curved space based on discrete logarithmic mapping theory, the generalized mirror
Riemann Curvature Tensor and Closed Geodesic Paths
Morganstern, Ralph E.
1977-01-01
Demonstrates erroneous results obtained if change in a vector under parallel transport about a closed path in Riemannian spacetime is made in a complete circuit rather than just half a circuit. (Author/SL)
On Regularity of Abnormal Subriemannian Geodesics
Tan, Kanghai
2012-01-01
We prove the smoothness of abnormal minimizers of subriemannian manifolds of step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4 admit no strictly abnormal minimizers. For any subriemannian manifolds of step less than 7, we show all abnormal minimizers have no corner type singularities, which partly generalize the main result of Leonardi-Monti.
On certain geodesic conjugacies of flat cylinders
Indian Academy of Sciences (India)
C S ARAVINDA; H A GURURAJA
2017-06-01
We prove $C^0$-conjugacy rigidity of any flat cylinder among two different classes of metrics on the cylinder, namely among the class of rotationally symmetric metrics and among the class of metrics without conjugate points.
Institute of Scientific and Technical Information of China (English)
刘力军; 马玉梅; 孟佳娜
2014-01-01
Using the same topology as that of Oja-Brockett-Xu parallel neural network,a novel dual purpose adaptive algorithm for principal and minor component extraction was proposed by the optimization framework of a weighted Ray-leigh quotient on the compact Stiefel manifold. By taking the right translation invariant Killing metric on orthogonal ma-trix group and search along the geodesic emanating from identity by means of exponential map,a novel dual learning al-gorithm for principal and minor component analysis was proposed. The proposed algorithm could switch from PCA (Principal Component Analysis)to MCA(Minor Component Analysis)with a simple sign change of its stepsize pa-rameter. Moreover,orthonormality of the weight matrix was guaranteed at any iteration step. The effectiveness of the proposed algorithm was further verified in the section of numerical simulation.%神经网络在线提取子分量并不成功。基于 Oja-Brockett-Xu 并行神经网络拓扑结构，通过紧致 Stiefel 流形上加权 Rayleigh 商目标函数的优化框架，提出一个通过改变搜索方向并行提取主分量和子分量的自适应对偶学习算法。在正交矩阵群上采用基于右平移不变的 Killing 度量，通过在单位元处基于指数映射的测地线搜索，得到Stiefel 流形上主（子）分量分析的对偶学习算法，提出的算法通过简单的变换步长参数符号，从主分量分析切换至子分量分析，权值矩阵在任意迭代时刻保持正交归一性。数值仿真验证了该算法的有效性。
Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity
Directory of Open Access Journals (Sweden)
Luis Acedo
2015-11-01
Full Text Available We consider a parametrized torsion gravity model for Riemann–Cartan geometry around a rotating axisymmetric massive body. In this model, the source of torsion is given by a circulating vector potential following the celestial parallels around the rotating object. Ours is a variant of the Mao, Tegmark, Guth and Cabi (MTGC model in which the total angular momentum is proposed as a source of torsion. We study the motion of bodies around the rotating object in terms of autoparallel trajectories and determine the leading perturbations of the orbital elements by using standard celestial mechanics techniques. We find that this torsion model implies new gravitational physical consequences in the Solar system and, in particular, secular variations of the semi-major axis of the planetary orbits. Perturbations on the longitude of the ascending node and the perihelion of the planets are already under discussion in the astronomical community, and if confirmed as truly non-zero effects at a statistically significant level, we might be at the dawn of an era of torsion phenomenology in the Solar system.
A simple intrinsic reduced-observer for geodesic flow
Bonnabel, Silvere
2008-01-01
Aghannan and Rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. The observer is based on the Riemannian structure of the configuration manifold endowed with the kinetic energy metric and is intrinsic. They proved local convergence. When the system is conservative, we propose a globally convergent intrinsic reduced-observer based on the Jacobi metric. For non-conservative syste...
Geodesic deviation in a nonlinear gravitational wave spacetime
Culetu, Hristu
2016-01-01
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\\xi^{v}$ and $\\xi^{u}$ of the separation vector behave as in flat space but the transversal components $\\xi^{x}$ and $\\xi^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
Near real-time stereo matching using geodesic diffusion.
De-Maeztu, Leonardo; Villanueva, Arantxa; Cabeza, Rafael
2012-02-01
Adaptive-weight algorithms currently represent the state of the art in local stereo matching. However, due to their computational requirements, these types of solutions are not suitable for real-time implementation. Here, we present a novel aggregation method inspired by the anisotropic diffusion technique used in image filtering. The proposed aggregation algorithm produces results similar to adaptive-weight solutions while reducing the computational requirements. Moreover, near real-time performance is demonstrated with a GPU implementation of the algorithm.
Superintegrability of Geodesic Motion on the Sausage Model
Arutyunov, G; Medina-Rincon, D
2016-01-01
Reduction of the $\\eta$-deformed sigma model on ${\\rm AdS}_5 \\times {\\rm S}^5$ to the two-dimensional squashed sphere $({\\rm S}^2)_{\\eta}$ can be viewed as a special case of the Fateev sausage model where the coupling constant $\
Extraction of sandy bedforms features through geodesic morphometry
Debese, Nathalie; Jacq, Jean-José; Garlan, Thierry
2016-09-01
State-of-art echosounders reveal fine-scale details of mobile sandy bedforms, which are commonly found on continental shelfs. At present, their dynamics are still far from being completely understood. These bedforms are a serious threat to navigation security, anthropic structures and activities, placing emphasis on research breakthroughs. Bedform geometries and their dynamics are closely linked; therefore, one approach is to develop semi-automatic tools aiming at extracting their structural features from bathymetric datasets. Current approaches mimic manual processes or rely on morphological simplification of bedforms. The 1D and 2D approaches cannot address the wide ranges of both types and complexities of bedforms. In contrast, this work attempts to follow a 3D global semi-automatic approach based on a bathymetric TIN. The currently extracted primitives are the salient ridge and valley lines of the sand structures, i.e., waves and mega-ripples. The main difficulty is eliminating the ripples that are found to heavily overprint any observations. To this end, an anisotropic filter that is able to discard these structures while still enhancing the wave ridges is proposed. The second part of the work addresses the semi-automatic interactive extraction and 3D augmented display of the main lines structures. The proposed protocol also allows geoscientists to interactively insert topological constraints.
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren
2010-01-01
and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...
Automatic extraction of sulcal lines on cortical surfaces based on anisotropic geodesic distance.
Seong, Joon-Kyung; Im, Kiho; Yoo, Sang Wook; Seo, Sang Won; Na, Duk L; Lee, Jong-Min
2010-01-01
Analyzing cortical sulci is important for studying cortical morphology and brain functions. Although sulcal lines on cortical surfaces can be defined in various ways, it is critical in a neuroimaging study to define a sulcal line along the valley of a cortical surface with a high curvature within a sulcus. To extract the sulcal lines automatically, we present a new geometric algorithm based on the computation of anisotropic skeletons of sulcal regions. Because anisotropic skeletons are highly adaptive to the anisotropic nature of the surface shape, the resulting sulcal lines lie accurately on the valleys of the sulcal areas. Our sulcal lines remain unchanged under local shape variabilities in different human brains. Through experiments, we show that the errors of the sulcal lines for both synthetic data and real cortical surfaces were nearly as constant as the function of random noise. By measuring the changes in sulcal shape in Alzheimer's disease (AD) patients, we further investigated the effectiveness of the accuracy of our sulcal lines using a large sample of MRI data. This study involved 70 normal controls (n [men/women]: 29/41, age [mean+/-SD]: 71.7+/-4.9 years), and 100 AD subjects (37/63, 72.3+/-5.5). We observe significantly lower absolute average mean curvature and shallower sulcal depth in AD subjects, where the group difference becomes more significant if we measure the quantities along the sulcal lines rather than over the entire sulcal area. The most remarkable difference in the AD patients was the average sulcal depth (control: 11.70 and AD: 11.34).
Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
Adamo, T M
2009-01-01
In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the complex gravitational dipole (mass dipole plus 'i' angular momentum) (via an asymptotic tetrad trasnformation) to a frame where the complex dipole vanishes. We apply this procedure to such space-times which are asymptotically stationary or static, and observe that the calculations can be performed exactly, without any use of the approximation schemes which must be employed in general. In particular, we are able to exactly calculate complex center of mass and charge world-lines for such space-times, and - as a special case - when these two complex world-lines coincide, we recover the Dirac value of the gyromagnetic ratio...
Equatorial geodesics in ergoregion of dirty black holes and zero energy observers
Zaslavskii, O. B.
2016-10-01
We consider equatorial motion of particles in the ergoregion of generic axially symmetric rotating black holes. We introduce the notion of zero energy observers (ZEOs) as counterparts to known zero angular observers (ZAMOs). It is shown that the trajectory of a ZEO has precisely one turning point that lies on the boundary of the ergoregion for photons and inside the ergoregion for massive particles. As a consequence, such trajectories enter the ergosphere from the white hole region under horizon and leave it crossing the horizon again (entering the black hole region). The angular velocity of ZEO does not depend on the angular momentum. For particles with E>0 this velocity is bigger than for a ZEO, for Eblack hole can lead to the unbound energy in the centre of mass thus giving a special version of the Bañados-Silk-West effect.
On the Link between Umbilic Geodesics and Soliton Solutions of Nonlinear PDEs
1995-01-01
In this paper we describe a new class of soliton solutions, called umbilic solitons, for certain nonlinear integrable PDES. These umbilic solitons have the property that as the space variable x tends to infinity, the solution tends to a periodic wave, and as x tends to minus infinity, it tends to a phase shifted wave of the same shape. The equations admitting solutions in this new class include the Dym equation and equations in its hierarchy. The methods used to find and analyse these solutio...
DEFF Research Database (Denmark)
Momeni, Arash; Venkov, Alexei
In the paper as a new application of the Jacquet-Langlands correspondence we connect the transfer operators for different cofinite Fuchsian groups by comparing the corresponding Selberg zeta functions....
Drag-free Spacecraft Technologies: criticalities in the initialization of geodesic motion
Zanoni, Carlo
2016-01-01
Present and future space missions rely on systems of increasingly demanding performance for being successful. Drag-free technology is one of the technologies that is fundamental for LISA-Pathfinder, an ESA mission whose launch is planned for the end of September 2015. A purely drag-free object is defined by the absence of all external forces other than gravity. This is not a natural condition and thus requires a proper design of a spacecraft, whose core is an object in free-fall, called test mass (TM). The purity of the drag-free orbit depends on the spacecraft capability of protecting the TM from disturbances, which indeed has limitations. According to a NASA study, such a concept provides substantial economies for LEO satellites. At the same time, a drag-free motion is required in many missions of fundamental physics. eLISA is an ESA concept mission aimed at opening a new window to the universe, black holes, and massive binary systems by means of gravitational waves. LISA-Pathfinder is in charge of proving ...
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
Energy Technology Data Exchange (ETDEWEB)
Weis, Stephan [Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig (Germany)
2015-01-13
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.
LeFloch, Philippe G
2014-01-01
We investigate the late-time asymptotics of future expanding, polarized vacuum Einstein spacetimes with T2-symmetry on T3, which, by definition, admit two spacelike Killing fields. Our main result is the existence of a stable asymptotic regime within this class, that is, we provide here a full description of the late-time asymptotics of the solutions to the Einstein equations when the initial data set is close to the asymptotic regime. Our proof is based on several energy functionals with lower order corrections (as is standard for such problems) and the derivation of a simplified model which we exhibit here. Roughly speaking, the Einstein equations in the symmetry class under consideration consists of a system of wave equations coupled to constraint equations plus a system of ordinary differential equations. The unknowns involved in the system of ordinary equations are blowing up in the future timelike directions. One of our main contributions is the derivation of novel effective equations for suitably renor...
Unique Two-Way Field Probe Concept Utilizing a Geodesic Sphere and Quad-Rotor
2015-03-26
express my sincere appreciation to my faculty advisor, Dr. Peter Collins, for his tremendous patience, guidance and support throughout the course of...determination of a proper predictive and modeling tool for future RCS analysis of icosahedrons spheres. During the course of this research several...the results in Table 9 would be applied to the NRTF radar range model. Using trigonometry ( ), a change in position of 0.5 m in any
Ant foraging and geodesic paths in labyrinths: analytical and computational results.
Vela-Pérez, M; Fontelos, M A; Velázquez, J J L
2013-03-07
In this paper we propose a mechanism for the formation of paths of minimal length between two points (trails) by a collection of individuals undergoing reinforced random walks. This is the case, for instance, of ant colonies in search for food and the development of ant trails connecting nest and food source. Our mechanism involves two main ingredients: (1) the reinforcement due to the gradients in the concentration of some substance (pheromones in the case of ants) and (2) the persistence understood as the tendency to preferably follow straight directions in the absence of any external effect. Our study involves the formulation and analysis of suitable Markov chains for the motion in simple labyrinths, that will be understood as graphs, and numerical computations in more complex graphs reproducing experiments performed in the past with ants. Copyright © 2012 Elsevier Ltd. All rights reserved.
Geodesic dynamo chaotic flows and non-Anosov maps in twisted magnetic flux tubes
de Andrade, Garcia
2008-01-01
Recently Tang and Boozer [{\\textbf{Phys. Plasmas (2000)}}], have investigated the anisotropies in magnetic field dynamo evolution, from local Lyapunov exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux tubes (MFTs). Thiffeault and Boozer [\\textbf{Chaos}(2001)] have investigated the how the vanishing of Riemann curvature constrained the Lyapunov exponential stretching of chaotic flows. In this paper, Tang-Boozer-Thiffeault differential geometric framework is used to investigate effects of twisted magnetic flux tube filled with helical chaotic flows on the Riemann curvature tensor. When Frenet torsion is positive, the Riemann curvature is unstable, while the negative torsion induces an stability when time $t\\to{\\infty}$. This enhances the dynamo action inside the MFTs. The Riemann metric, depends on the radial random flows along the poloidal and toroidal directions. The Anosov flows has been applied by Arnold, Zeldovich, Ruzmaikin and Sokoloff [\\textbf{JETP (1982)}] to build a unifo...
Equatorial geodesics in ergoregion of dirty black holes and zero energy observers
Zaslavskii, O B
2016-01-01
We consider equatorial motion of particles in the ergoregion of generic axially symmetric rotating black holes. We introduce the notion of zero energy observers (ZEOs) as counterparts to known zero angular observers (ZAMOs). It is shown that the trajectory of a ZEO has precisely one turning point that lies on the boundary for photons and inside the ergoregion for massive particles. As a consequence, such trajectories enter the ergosphere from the region under horizon and leave it crossing the horizon again. The angular velocity of ZEO does not depend on the angular momentum. For particles with $E>0$ this velocity is bigger than for a ZEO, for $E<0$ it is smaller. General limitations on the angular momentum are found depending on whether the trajectory lies entirely inside the ergoregion, bounces back from the boundary or intersects it. These results generalize the recent observations made in A. A. Grib, Yu. V. Pavlov, arXiv:1601.02592 for the Kerr metric. We also show that collision between a ZEO and a par...
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
Weis, Stephan
2015-01-01
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.
Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves
Vesely, K
2000-01-01
A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Henon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.
Murari, A.; Boutot, P.; Vega, J.; Gelfusa, M.; Moreno, R.; Verdoolaege, G.; de Vries, P. C.
2013-01-01
Over the last few years progress has been made on the front of disruption prediction in tokamaks. The less forgiving character of the new metallic walls at JET emphasized the importance of disruption prediction and mitigation. Being able not only to predict but also classify the type of disruption w
Lightlike sets with applications to the rigidity of null geodesic incompleteness
Silva, I P Costa e
2014-01-01
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified concusions may arise, showing that those conclusions will fail only in special cases, at least some of which may be described. These are the so-called rigidity theorems, and have many important examples in the especialized literature. In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of maximal compact surfaces. Motivated by some general properties appearing in these proofs, we develop the theory of lightlike sets, entities similar to achronal sets, but more appropriate to deal with low-regularity null submanifolds.
News from the Geodesic Acoustic Mode: Magnetic Shear-, q-, and Geometry Effect
Hallatschek, Klaus
2006-04-01
The generation of GAMs has been studied in greater depth by three-dimensional turbulence simulations. A change of the magnetic shear, in particular, a switch to negative shear profoundly affects the amplification mechanics of the GAMs. Essentially, negative shear flips the symmetry of the turbulence modes with respect to the shear flows, altering the sign of the Stringer-Winsor forces. The phenomenon readily suggests an experimental test, which would quantify the role of the Stringer-Winsor effect in comparison to the Reynolds stress in exciting the GAMs. The safety factor q controls the coupling of the GAMs to the parallel velocity, i.e., sound waves. Lowering q increases this coupling. Since the parallel sound waves in turn are heavily damped by the turbulence, they act as a loss channel. Thus sufficiently low q leads to a quench of the GAM activity, as has been found in recent experiments, too. Finally, the shape of the flux surfaces has great influence on the frequency of the modes and the relative strength of the Stringer-Winsor force. Again, the results suggest a relatively straightforward comparison with experiments. In all these cases one has to carefully differentiate between changes of the turbulence brought about by the parameters, and changed properties of the GAMs and their interaction with the turbulence.
On Geo desic E-quasiconvex Functions and Geo desic E-epigraphs
Institute of Scientific and Technical Information of China (English)
LIN Qing-ying; HUANG Long-guang
2015-01-01
The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic E-convex functions and geodesic E-almostconvex functions are studied. Furthermore, the no-tion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.
2005-01-18
equations are: 0212 2 = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ ∂ + z c d dz x c d dx t c d dt d dt cd td λλλλλ... td , (37) 0 2 2 2 =⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + dx dt z cc dx zd...calculation the sound-speed profile ( )CzKCzc /cosh)( 0= produces a space of constant positive curvature 0KK = . The deviation vector can be solved
Estakhr, Ahmad Reza
2016-10-01
DJ̲μ/Dτ =J̲ν ∂νU̲μ + ∂νT̲μν +Γαβμ J̲αU̲β ︷ Steady Component + ∂νRμν +Γαβμ Rαβ ︷ Perturbations EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows. The EAMG equations are used to describe Relativistic Jet.
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-; ?????, ?. ?.
2006-01-01
???????????? ???????????? ?????????? ?????????? ?????, ??? ?????????? ??? ???????? ???????, ?????????? ??????? ??????? ? ????????????, ?????????? ??????????? ? ?????????????? ????? ? ?????????-??????????? ??????? ? ????????????? ???????? ????????. Universal electronic geodesic marca intended for fixing of stvoriv, determination of angular displacements and where centring? Fixing of line of temple and horizontal line in engineering?geodesic works with the use of laser devices.
基于测地线的超像素谱聚类彩色图像分割%Color image segmentation of spectral clustering based on super pixel geodesic
Institute of Scientific and Technical Information of China (English)
陈莹兰; 陈秀宏
2015-01-01
在图像分割中谱聚类算法得到了广泛的应用,但传统谱聚类算法易受到彩色图像大小和相似性测度的影响,导致计算量大和分割精度低的问题.为了解决这两个问题,提出一种新的基于超像素集测地线特征的谱聚类分割算法.该方法通过对彩色图像进行预分割得到超像素集,并以超像素集为基础构造加权图,利用测地线距离特征和颜色特征构造权值矩阵,最后应用NJW(Ng-Jordan-Weiss)算法得到最终的分割结果.对比实验结果表明该算法在分割精度和计算复杂度上都有较大改善.
Unknotting tunnels in hyperbolic 3-manifolds
Adams, Colin
2012-01-01
An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel.
Sokołowski, Leszek M
2014-01-01
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain...
Violation of cosmic censorship in the gravitational collapse of a dust cloud in five dimensions
Mizuno, Ryosuke; Ohashi, Seij; Shiromizu, Tetsuya
2016-10-01
We analyze the null geodesic equations in five-dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equations emanating from the central singularity for smooth initial distribution of dust. Moreover, we also show that the null geodesics can extend to null infinity in a certain case, which implies violation of the cosmic censorship conjecture.
Violation of cosmic censorship in the gravitational collapse of a dust cloud in five dimension
Mizuno, Ryosuke; Shiromizu, Tetsuya
2016-01-01
We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation emanating from central singularity for smooth initial distribution of dust. Moreover, we also show that the null geodesics can extend to null infinity in a certain case, which imply the violation of cosmic censorship conjecture.
Classification of cosmological milestones
Fernández-Jambrina, L
2006-01-01
In this paper causal geodesic completeness of FLRW cosmological models is analysed in terms of generalised power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Krolak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally alllowed models which have been proposed recently are lightlike geodesically complete.
How Does Naked Singularity Look?
Nakao, Ken-ichi; Kobayashi, Naoki; Ishihara, Hideki
2002-01-01
There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust fluid, we study these singular null geodesics in detail. We see the time evolution of the angular diameter of the central naked singularity and show that it might be bounded above by the value corresponding to the circular null geodesic in the Schwarzschild spa...
Equations of motion with respect to the (1 + 1 + 3) threading of a 5D universe
Energy Technology Data Exchange (ETDEWEB)
Bejancu, Aurel [Kuwait University, Department of Mathematics, Safat (Kuwait)
2016-01-15
We continue our research work started in Bejancu (Eur Phys J C 75:346, 2015), and obtain in a covariant form the equations of motion with respect to the (1+1+3) threading of a 5D universe (anti M, anti g). The natural splitting of the tangent bundle of anti M leads to the study of three categories of geodesics: spatial geodesics, temporal geodesics, and vertical geodesics. As an application of the general theory, we introduce and study what we call the 5D Robertson-Walker universe. (orig.)
Chaotic motion of particles in the accelerating and rotating black holes spacetime
Chen, Songbai; Jing, Jiliang
2016-01-01
We have investigated the motion of timelike particles along geodesic in the background of accelerating and rotating black hole spacetime. We confirmed that the chaos exists in the geodesic motion of the particles by Poincar\\'e sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram. Moreover, we probe the effects of the acceleration and rotation parameters on the chaotic behavior of a timelike geodesic particle in the black hole spacetime. Our results show that the acceleration brings richer physics for the geodesic motion of particles.
NVU dynamics. II. Comparing to four other dynamics
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Toxværd, Søren; Schrøder, Thomas;
2011-01-01
In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, “NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface,” J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potenti...
Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
Directory of Open Access Journals (Sweden)
Dmitry Chernyavsky
2016-10-01
Full Text Available The group theoretic construction is applied to construct a novel dynamical realization of the l-conformal Galilei group in terms of geodesic equations on the coset space. A peculiar feature of the geodesics is that all their integrals of motion, including the accelerations, are functionally independent. The analysis in the recent work [Chernyavsky and Galajinsky (2016 [35
Cylindrically bounded constant mean curvature surfaces in $\\mathbb{H}^2\\times\\mathbb{R}$
Mazet, Laurent
2012-01-01
In this paper we prove that a properly embedded constant mean curvature surface in $\\mathbb{H}^2\\times\\mathbb{R}$ which has finite topology and stays at a finite distance from a vertical geodesic line is invariant by rotation around a vertical geodesic line.
2010-07-01
... Pacific Ocean and the Dixon Entrance, except where this line intersects geodesics connecting the following... follows: (1) Beginning at a point 58° 11-44 N, 136° 39-25 W , thence southeasterly along a line three... portion of each such geodesic in paragraph (1) of this definition situated beyond 3 nautical miles from...
The Dynamics of Pendulums on Surfaces of Constant Curvature
Energy Technology Data Exchange (ETDEWEB)
Coulton, P. [Eastern Illinois University, Mathematics Department (United States)], E-mail: prcoulton@eiu.edu; Foote, R. [Wabash College (United States)], E-mail: footer@wabash.edu; Galperin, G. [Eastern Illinois University, Mathematics Department (United States)], E-mail: ggalperin@eiu.edu
2009-05-15
We define the notion of a pendulum on a surface of constant curvature and study the motion of a mass at a fixed distance from a pivot. We consider some special cases: first a pivot that moves with constant speed along a geodesic, and then a pivot that undergoes acceleration along a fixed geodesic.
Approximate Noether gauge symmetries of the Bardeen model
Energy Technology Data Exchange (ETDEWEB)
Camci, U. [Akdeniz University, Department of Physics, Faculty of Science, Antalya (Turkey)
2014-12-01
We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis of the spacetime of the Bardeen model up to third-order approximate Noether gauge symmetries is presented. (orig.)
Chaos in Kundt Type-Ⅲ Spacetimes
Institute of Scientific and Technical Information of China (English)
I. Sakalli; M. Halilsoy
2011-01-01
We consider geodesic motion in a particular Kundt type-Ⅲ spacetime in which the Einstein-Yang-Mills equations admit the solutions. On a particular surface as constraint,we project the geodesics into the (x,y) plane and treat the problem as a two-dimensional one.Our numerical study shows that chaotic behavior emerges under reasonable conditions.
Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
Chernyavsky, Dmitry
2016-10-01
The group theoretic construction is applied to construct a novel dynamical realization of the l-conformal Galilei group in terms of geodesic equations on the coset space. A peculiar feature of the geodesics is that all their integrals of motion, including the accelerations, are functionally independent. The analysis in the recent work [Chernyavsky and Galajinsky (2016) [35
A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space
Garcia-Prada, Oscar
2010-01-01
We prove a Milnor-Wood inequality for representations of the fundamental group of a compact complex hyperbolic manifold in the group of isometries of quaternionic hyperbolic space. Of special interest is the case of equality, and its application to rigidity. We show that equality can only be achieved for totally geodesic representations, thereby establishing a global rigidity theorem for totally geodesic representations.
The quantum unique ergodicity conjecture for thin sets
Young, Matthew P
2013-01-01
We consider some analogs of the quantum unique ergodicity conjecture for geodesics, horocycles, or ``shrinking'' families of sets. In particular, we prove the analog of the QUE conjecture for Eisenstein series restricted to the infinite geodesic connecting 0 and infinity inside the modular surface.
Open Problem: Kernel methods on manifolds and metric spaces
DEFF Research Database (Denmark)
Feragen, Aasa; Hauberg, Søren
2016-01-01
Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong...
Principal normal indicatrices of closed space curves
DEFF Research Database (Denmark)
Røgen, Peter
1999-01-01
A theorem due to J. Weiner, which is also proven by B. Solomon, implies that a principal normal indicatrix of a closed space curve with nonvanishing curvature has integrated geodesic curvature zero and contains no subarc with integrated geodesic curvature pi. We prove that the inverse problem alw...
Pressurizable structures comprising different surface sections
Koussios, S.; Bergsma, O.K.; Beukers, A.
2004-01-01
The invention relates to composite pressurizable structures which are overwound with fibres or are braided. The pressurizable structures comprise axial sections which in turn comprise both concave and convex surfaces. The shape characteristics are related to geodesic as well as non-geodesic trajecto
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 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 optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...... 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...
On the twin paradox in static spacetimes: I. Schwarzschild metric
Sokolowski, Leszek M
2012-01-01
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.
Probing crunching AdS cosmologies
Kumar, S Prem
2015-01-01
Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch singularities. Using a specific analytically tractable solution within a particular single scalar truncation of N=8 supergravity on AdS_4, we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factor a_{max} . Radial geodesics connecting antipodal points necessarily have de Sitter energy E \\leq a_{max}, while geodesics with E > a_{max} terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved "outw...
Probing crunching AdS cosmologies
Kumar, S. Prem; Vaganov, Vladislav
2016-02-01
Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch singularities. Using a specific analytically tractable solution within a particular single scalar truncation of {N}=8 supergravity on AdS4, we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factor ã max. Radial geodesics connecting antipodal points necessarily have de Sitter energy Ɛ ≲ ã max, while geodesics with Ɛ > ã max terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved "outward" in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green's function has a branch point determined by ã max which corresponds to the lowest quasinormal frequency.
Rehabilitating space-times with NUTs
Energy Technology Data Exchange (ETDEWEB)
Clément, Gérard, E-mail: gerard.clement@lapth.cnrs.fr [LAPTh, Université Savoie Mont Blanc, CNRS, 9 chemin de Bellevue, BP 110, F-74941, Annecy-le-Vieux cedex (France); Gal' tsov, Dmitri, E-mail: galtsov@phys.msu.ru [Department of Theoretical Physics, Faculty of Physics, Moscow State University, 119899, Moscow (Russian Federation); Guenouche, Mourad, E-mail: guenouche_mourad@umc.edu.dz [Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université de Constantine 1 (Algeria); Department of Physics, Faculty of Sciences, Hassiba Benbouali University of Chlef (Algeria)
2015-11-12
We revisit the Taub–NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub–NUT solution as physically relevant are removed.
What is the meaning of non-uniqueness of FRW metric in cosmology?
Verozub, Leonid V
2011-01-01
FRW metric in cosmology is a good example to make sure that space-time metric does not determine the gravitational field unequivocally. Due to invariance of the equations of geodesic lines under a continuous group of transformations of the coefficients of affine connection, there is a wide class of transformations of standard objects of Riemannian space-time which leaves invariant the equations of motion of test particles. Therefore, any theory of gravitation, based on the hypothesis of the geodesic motion of test particles must be invariant under geodesic mappings of the used space-time.
The Real Meaning of Complex Minkowski-Space World-Lines
Adamo, T M
2009-01-01
In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.
Rehabilitating space-times with NUTs
Clément, Gérard; Guenouche, Mourad
2015-01-01
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal {\\em geodesics}. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.
Rehabilitating space-times with NUTs
Directory of Open Access Journals (Sweden)
Gérard Clément
2015-11-01
Full Text Available We revisit the Taub–NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub–NUT solution as physically relevant are removed.
Singularity-free Bianchi spaces with nonlinear electrodynamics
García-Salcedo, R; Garcia-Salcedo, Ricardo; Breton, Nora
2004-01-01
In this paper we present the analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G$_3$. We study analytical extensions as well as geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete, like G$_3$II and G$_3$VIII; however Bianchi G$_3$IX presents the phenomenon of geodesics that are imprisoned. In contrast, diagonal Bianchi spaces like G$_3$I, G$_3$III and Kantowski-Sachs have a finite time existence ending in a scalar polynomial curvature singularity.
Hawking Radiation of the Charged Particle via Tunneling from the Kaluza-Klein Black Hole
Pu, Jin; Han, Yan
2016-12-01
In this paper, by applying the Lagrangian analysis on the action, we first redefine the geodesic equation of the charged massive particle. Then, basing on the new definition of the geodesic equation, we revisit the Hawking radiation of the charged massive particle via tunneling from the event horizon of the Kaluza-Klein black hole. In our treatment, the geodesic equation of the charged massive particle is defined uniformly with that of the massless particle, which overcomes the shortcomings of its previous definition, and is more suitable for the tunneling mechanism. The highlight of our work is a new and important development for the Parikh-Wilczek's tunneling method.
Hawking Radiation of the Charged Particle via Tunneling from the Kaluza-Klein Black Hole
Pu, Jin; Han, Yan
2016-08-01
In this paper, by applying the Lagrangian analysis on the action, we first redefine the geodesic equation of the charged massive particle. Then, basing on the new definition of the geodesic equation, we revisit the Hawking radiation of the charged massive particle via tunneling from the event horizon of the Kaluza-Klein black hole. In our treatment, the geodesic equation of the charged massive particle is defined uniformly with that of the massless particle, which overcomes the shortcomings of its previous definition, and is more suitable for the tunneling mechanism. The highlight of our work is a new and important development for the Parikh-Wilczek's tunneling method.
Immersed surfaces in the modular orbifold
Calegari, Danny
2010-01-01
A hyperbolic conjugacy class in the modular group PSL(2,Z) corresponds to a closed geodesic in the modular orbifold. Some of these geodesics virtually bound immersed surfaces, and some do not; the distinction is related to the polyhedral structure in the unit ball of the stable commutator length norm. We prove the following stability theorem: for every hyperbolic element of the modular group, the product of this element with a sufficiently large power of a parabolic element is represented by a geodesic that virtually bounds an immersed surface.
Rehabilitating space-times with NUTs
Clément, Gérard; Gal'tsov, Dmitri; Guenouche, Mourad
2015-11-01
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.
Photon emission of extremal Kerr-Newman black holes
Wei, Shao-Wen; Wang, Yong-Qiang; Liu, Yu-Xiao
2016-01-01
In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound. For the case that the polar angles of the two endpoints of the geodesic coincide, the relation between the radial values of the two endpoints is found, and the shifts in the azimuthal angle and time are also obtained.
Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.
Miller, Michael I; Trouvé, Alain; Younes, Laurent
2015-01-01
The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.
Einstein's equivalence principle in cosmology
Kopeikin, Sergei M
2013-01-01
We study physical consequences of the Einstein equivalence principle (EEP) for a Hubble observer in FLRW universe. We introduce the local inertial coordinates with the help of a special conformal transformation. The local inertial metric is Minkowski flat and materialized by a congruence of time-like geodesics of static observers. The static observers are equipped with the ideal clocks measuring the proper time that is synchronized with the clocks of the Hubble observer. The local inertial metric is used for physical measurements of spacetime intervals with the ideal clocks and rulers. The special conformal transformation preserves null geodesics but does not keep invariant time-like geodesics. Moreover, it makes the rate of the local time coordinate dependent on velocity of the particle which makes impossible to rich the uniform parameterization of the world lines of static observers and light geodesics with a single parameter - they differ by the conformal factor of FLRW metric. The most convenient way to s...
Quasinormal Modes of the Draining Bathtub
Oliveira, Leandro A.; Crispino, Luís C. B.; Dolan, Sam R.
2015-01-01
We present an investigation of the quasinormal modes of the draining bathtub using three different methods, namely: finite difference, continued fraction and geodesic expansion. We compare the results obtained with these different approaches.
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
ISCOs in Extremal Gibbons-Maeda-Garfinkle-Horowitz-Strominger Blackholes
Pradhan, Partha Pratim
2012-01-01
We examine the geodesic motion of neutral test particles for equatorial timelike circular geodesics and null circular geodesics, both extremal and non-extremal case of charged blackholes in string theory. We show that at the extremal limit ($Q^{2}=2M^{2}e^{2\\phi_{0}}$) for Gibbons-Maeda-Garfinkle-Horowitz-Strominger(GMGHS) blackholes, the radius of ISCO(Innermost Stable Circular Orbit)$(r_{ISCO})$, photon orbit$(r_{ph})$ and marginally bound circular orbit $(r_{mb})$ coincides with the event horizon$(r_{hor})$ i.e. $r_{ISCO}=r_{ph}=r_{mb}=r_{hor}=2M $. Since the proper radial distances on a constant time slice both in Schwarzschild and Painlev\\'{e}-Gullstrand coordinates becomes zero, therefore these three orbits indeed coincident with the null geodesic generators of the event horizon.
Geometric Structures and Field Equations of Dirac-Lu Space
Institute of Scientific and Technical Information of China (English)
REN Xin-An; ZHANG Li-You
2008-01-01
In this paper, a -invariant Lorentz metric on the Dirac-Lu space is given, and then the geodesic equation is investigated. Finally, we discuss the field equations and find their solutions by the method of separating variables.
Matsyuk, Roman
2015-01-01
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.
Boucher, W
2011-01-01
We elucidate the mechanism where by gravitational fluctuations are frozen in during a period of inflation but nevertheless within the past horizon of any geodesic observer the spacetime settles down exponentially fast to the de-Sitter metric.
Coverings and integrability of the Gauss-Mainardi-Codazzi equations
Krasilchchik, I; Krasil'shchik, Joseph; Marvan, Michal
1998-01-01
Using covering theory approach (zero-curvature representations with the gauge group SL2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic coordinates. For each choice, four integrable systems are obtained.
Aero-Acoustic Propulsion Lab (AAPL)
Federal Laboratory Consortium — This facility is an acoustically treated geodesic dome. The 130-ft-diameter dome is 65-ft high and acts as a noise barrier, protecting adjacent Glenn buildings and...
Holographic Dual to Conical Defects III: Improved Image Method
Aref'eva, I Ya; Tikhanovskaya, M D
2016-01-01
The geodesics prescription in holographic approach in Lorentzian signature is valid only for geodesics which connect spacelike-separated points at the boundary, since there is no timelike geodesics which reach the boundary. There is also no straightforward analytic Euclidean continuation for a general background, such as e. g. moving particle in AdS. We propose an improved geodesic image method for two-point Lorentzian correlators which is valid for arbitrary time intervals in case of the bulk spacetime deformed by point particles. We illustrate that our prescription is consistent with the case when the analytic continuation exists and with the quasigeodesics prescription used in previous work. We also discuss some other applications of the improved image method, such as holographic entanglement entropy and multiple particles in AdS3.
Surface-preserving robust watermarking of 3-D shapes.
Luo, Ming; Bors, Adrian G
2011-10-01
This paper describes a new statistical approach for watermarking mesh representations of 3-D graphical objects. A robust digital watermarking method has to mitigate among the requirements of watermark invisibility, robustness, embedding capacity and key security. The proposed method employs a mesh propagation distance metric procedure called the fast marching method (FMM), which defines regions of equal geodesic distance width calculated with respect to a reference location on the mesh. Each of these regions is used for embedding a single bit. The embedding is performed by changing the normalized distribution of local geodesic distances from within each region. Two different embedding methods are used by changing the mean or the variance of geodesic distance distributions. Geodesic distances are slightly modified statistically by displacing the vertices in their existing triangle planes. The vertex displacements, performed according to the FMM, ensure a minimal surface distortion while embedding the watermark code. Robustness to a variety of attacks is shown according to experimental results.
Conjugate Points on a Type of K(a)hler Manifolds
Institute of Scientific and Technical Information of China (English)
Wei Ming LIU; Fu Sheng DENG
2013-01-01
We study conjugate points on a type of K(a)hler manifolds,which are submanifolds of Grassmannian manifolds.And then we give the applications to the study of the index of geodesics and homotopy groups.
Contraction coefficients for noisy quantum channels
Energy Technology Data Exchange (ETDEWEB)
Hiai, Fumio, E-mail: hiai.fumio@gmail.com [Tohoku University, Hakusan 3-8-16-303, Abiko 270-1154 (Japan); Ruskai, Mary Beth, E-mail: ruskai@member.ams.org [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2016-01-15
Generalized relative entropy, monotone Riemannian metrics, geodesic distance, and trace distance are all known to decrease under the action of quantum channels. We give some new bounds on, and relationships between, the maximal contraction for these quantities.
Bounds on Gromov Hyperbolicity Constant in Graphs
Indian Academy of Sciences (India)
José M Rodríguez; José M Sigarreta
2012-02-01
If is a geodesic metric space and 1,2,3 $\\in$ , a geodesic triangle ={1,2,3} is the union of the three geodesics [1,2], [2,3] and [31] in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e. ()=$inf{$≥ 0$ : is -hyperbolic}. In this paper we relate the hyperbolicity constant of a graph with some known parameters of the graph, as its independence number, its maximum and minimum degree and its domination number. Furthermore, we compute explicitly the hyperbolicity constant of some class of product graphs.
Hyperbolicity in Median Graphs
Indian Academy of Sciences (India)
José M Sigarreta
2013-11-01
If is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1 x_2],[x_2 x_3]$ and $[x_3 x_1]$ in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e.,$(X)=\\inf\\{≥ 0: X \\quad\\text{is}\\quad -\\text{hyperbolic}\\}$. In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its bigons are thin.
Dryuma, V S
1998-01-01
The law of transformation of affine connection for n-dimensional manifolds as the system of nonlinear equations on local coordinates of manifold is considered. The extension of the Darboux-Lame system of equations to the spaces of constant negative curvature is demonstrated. Geodesic deviation equation as well as the equations of geodesics are presented in the form of the matrix Darboux-Lame system of equations.
Pancharatnam geometric phase originating from successive partial projections
Indian Academy of Sciences (India)
Sohrab Abbas; Apoorva G Wagh
2008-11-01
The spin of a polarized neutron beam subjected to a partial projection in another direction, traces a geodesic arc in the 2-sphere ray space. We delineate the geometric phase resulting from two successive partial projections on a general quantal state and derive the direction and strength of the third partial projection that would close the geodesic triangle. The constraint for the three successive partial projections to be identically equivalent to a net spin rotation regardless of the initial state, is derived.
2D Dubins Path in Environments with Obstacle
Directory of Open Access Journals (Sweden)
Dongxiao Yang
2013-01-01
Full Text Available We recapitulate the achievement about the Dubins path as well as some precise proofs which are important but omitted by Dubins. Then we prove that the shortest path (R*-geodesic in environments with an obstacle consists of no more than five segments, each of which is either an arc or a straight line. To obtain such R*-geodesic, an effective algorithm is presented followed by a numerical simulation as verification.
The geometry of a vorticity model equation
Escher, Joachim; Wunsch, Marcus
2010-01-01
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\\ge 2$.
On electric field in anti-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Cheong, Lee Yen, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Yan, Chew Xiao, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Ching, Dennis Ling Chuan, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my [Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Bandar Seri Iskandar, Tronoh 31750, Perak (Malaysia)
2014-10-24
In this paper we calculate the electromagnetic field produced using retarded Green's function in Anti-de Sitter spacetime (AdS). Since this spacetime is non-globally hyperbolic and has no Cauchy surface, we only consider the field originated from a charge moving along its geodesic in the region consists of points covered by future null geodesic of the charge.
Paliathanasis, A.; Krishnakumar, K.; Leach, P. G. L.
2016-04-01
We discuss the relationship between the Noether point symmetries of the geodesic Lagrangian, in a (pseudo)Riemannian manifold, with the elements of the Homothetic algebra of the space. We observe that the classification problem of the Noether symmetries for the geodesic Lagrangian is equivalent with the classification of the Homothetic algebra of the space, which in the case of a Friedmann-Lemaître-Robertson-Walker spacetime is a well-known result in the literature.
Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping
2013-01-01
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic ...
Horwitz, L P; Horwitz, Lawrence P.; Oron, Ori
2004-01-01
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic motion can be put into correspondence with general relativity. One obtains in this way a quantum theory on a flat spacetime, obeying the rules of the standard quantum theory in Lorentz covariant form, with a spacetime dependent Lorentz tensor $g_{\\mu\
Physical Interpretation of Antigravity
2015-01-01
Geodesic incompleteness is a problem in both general relativity and string theory. The Weyl invariant Standard Model coupled to General Relativity (SM+GR), and a similar treatment of string theory, are improved theories that are geodesically complete. A notable prediction of this approach is that there must be antigravity regions of spacetime connected to gravity regions through gravitational singularities such as those that occur in black holes and cosmological bang/crunch. Antigravity regio...
Zhang, Y.; Dioos, B.; Hu, Z.; Vrancken, L.; Wang, X.
2016-10-01
In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kähler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3.
New mathematical framework for spherical gravitational collapse
Giambo, R; Magli, G; Piccione, P; Giambo', Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2003-01-01
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed.
New mathematical framework for spherical gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Giambo, Roberto [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy); Giannoni, Fabio [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy); Magli, Giulio [Dipartimento di Matematica, Politecnico di Milano (Italy); Piccione, Paolo [Dipartimento di Matematica e Informatica, Universita di Camerino (Italy)
2003-03-21
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)
Photon emission of extremal Kerr-Newman black holes
Energy Technology Data Exchange (ETDEWEB)
Wei, Shao-Wen; Gu, Bao-Min; Wang, Yong-Qiang; Liu, Yu-Xiao [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China)
2017-02-15
In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained. (orig.)
Wenninger, Magnus J
2012-01-01
Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. Discusses tessellation, or tiling, and how to make spherical models of the semiregular solids and concludes with a discussion of the relationship of polyhedra to geodesic domes and directions for building models of domes. "". . . very pleasant reading."" - Science. 1979 edition.
Generalized Mattig's relation in Brans-Dicke-Rastall gravity
Salako, Ines G; Jawad, Abdul
2016-01-01
The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $\\eta(z)$ and observer area distance $r_0(z)$ and compare the results with $\\Lambda$CDM model.
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.
Light cones in relativity: Real, complex and virtual, with applications
Adamo, T M
2011-01-01
We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity acts as a "holographic screen," interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex world-line; a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we ...
Circular Orbits in the Taub-NUT and mass-less Taub-NUT Space-time
Pradhan, Parthapratim
2016-01-01
In this work we study the equatorial causal geodesics of the Taub-NUT(TN) space-time in comparison with \\emph{mass-less} TN space-time. We emphasized both on the null circular geodesics and time-like circular geodesics. From the effective potential diagram of null and time-like geodesics, we differentiate the geodesics structure between TN spacetime and mass-less TN space-time. It has been shown that there is a key role of the NUT parameter to changes the shape of pattern of the potential well in the NUT spacetime in comparison with mass-less NUT space-time. We compared the ISCO (innermost stable circular orbit), MBCO (marginally bound circular orbit) and CPO (circular photon orbit) of the said space-time with graphically in comparison with mass-less cases. Moreover, we compute the radius of ISCO, MBCO and CPO for \\emph{extreme} TN black hole. Interestingly, we show that these \\emph{three radii} coincides with the Killing horizon i.e. the null geodesic generators of the horizon. Finally in Appendix, we comput...
Probing crunching AdS cosmologies
Energy Technology Data Exchange (ETDEWEB)
Kumar, S. Prem; Vaganov, Vladislav [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom)
2016-02-03
Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch singularities. Using a specific analytically tractable solution within a particular single scalar truncation of N=8 supergravity on AdS{sub 4}, we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factor ã{sub max}. Radial geodesics connecting antipodal points necessarily have de Sitter energy E≲ã{sub max}, while geodesics with E>ã{sub max} terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved “outward” in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green’s function has a branch point determined by ã{sub max} which corresponds to the lowest quasinormal frequency.
Zhang, Jian-dong; Chen, Bin
2017-01-01
The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincaré disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincaré disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the SL(2,R) leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore, we discuss the fundamental regions in the kinematic space for the BTZ blackhole and multi-boundary wormholes.
Shear-free axial model in massive Brans-Dicke gravity
Sharif, M.; Manzoor, Rubab
2017-01-01
This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans-Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-free condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.
Zhang, Jian-dong
2016-01-01
The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincar\\'e disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincar\\'e disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the $SL(2,\\mathbb{R})$ leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore...
Shear-free axial model in massive Brans–Dicke gravity
Energy Technology Data Exchange (ETDEWEB)
Sharif, M., E-mail: msharif.math@pu.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782 (Pakistan)
2017-01-15
This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans–Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-free condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.
Clément, Gérard; Gal'tsov, Dmitri; Guenouche, Mourad
2016-01-01
We show that supercritically charged black holes with a Newman-Unti-Tamburino (NUT) parameter provide a new setting for traversable wormholes. This does not require exotic matter, but there is a price—the Misner string singularities. Without assuming time periodicity to make Misner strings unobservable, we show that, contrary to expectations, geodesics do not stop there. Moreover, since there is no central singularity, the spacetime turns out to be geodesically complete. Another unpleasant feature of spacetimes with NUTs is the presence of regions where the azimuthal angle φ becomes timelike, signalling the appearance of closed timelike curves (CTCs). We show that among them there are no closed timelike or null geodesics, so the freely falling observers should not encounter causality violations. Considering worldlines of charged particles, we find that, although these can become closed in the vicinity of the wormhole throat for large enough charge-to-mass ratio, the noncausal orbits are still disconnected from the distant zones. Integrating the geodesic equations completely, we demonstrate the existence of timelike and null geodesics connecting two asymptotic regions of the wormhole, such that the tidal forces in the throat are reasonably small. We also discuss bounds on the NUT charge which follow from the Schwinger pair creation and ionization thresholds.
The left invariant metric in the general linear group
Andruchow, Esteban; Recht, Lazaro; Varela, Alejandro
2011-01-01
Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimizing paths in the group are shown to have a velocity with constant singular values and multiplicity. In several special cases, these geodesic paths are computed explicitly. In particular the Riemannian geodesics, corresponding to the case p=2, are characterized as the product of two one-parameter groups. It is also shown that geodesics are one-parameter groups if and only if the initial velocity is a normal matrix. These results are further extended to the context of compact operators with p-summable spectrum, where a differential equation for the spectral projections of the velocity vector of an extremal path is obtained.
Weyl Anomaly and Initial Singularity Crossing
Awad, Adel
2015-01-01
We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in mat...
Tipler, F. J.
1985-05-01
A number of recent theorems by Krolak (1983) and Newman (1983) purport to prove cosmic censorship by showing that strong-curvature singularities must be hidden behind horizons. It is shown that the 'null strong-curvature' condition which Newman imposes on certain classes of null geodesics to restrict curvature growth in the space-time does not hold in many physically realistic space-times: it is not satisfied by any null geodesic in the relevant class in any open Friedmann cosmological model, nor does it hold for any null geodesic in the relevant class in maximal Schwarzschild space. More generally it is argued that the singularity predicted by the Penrose singularity theorem is unlikely to be of the type eliminated by Newman. Thus the Newman theorems are probably without physical significance. The Krolak theorems, although based on a physically significant definition of strong curvature singularity, are mathematically invalid, and this approach cannot be used to obtain a cosmic-censorship theorem.
Metric Measure Space as a Framework for Gravitation
Rahmanpour, Nafiseh
2016-01-01
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in bo...
Noether gauge symmetry classes for pp-wave spacetimes
Camci, U
2016-01-01
The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three Noether gauge symmetry, and furthermore the number of Noether gauge symmetries turn out to be four, five, six, seven and eight. We found that all conformally flat plane wave spacetimes admit the maximal, i.e. ten, Noether gauge symmetry. Also it is found that if the pp-wave spacetime is non-conformally flat plane wave, then the number of Noether gauge symmetry is nine or ten. By means of the obtained Noether constants the search of the exact solutions of the geodesic equations for the pp-wave spacetimes is considered and we found new exact solutions of the geodesic equations in some special Noether gauge symmetry classes.
High energy particle collisions near black holes
Directory of Open Access Journals (Sweden)
Zaslavskii O. B.
2016-01-01
Full Text Available If two geodesic particles collide near a rotating black hole, their energy in the centre of mass frame Ec.m. can become unbound under certain conditions (the so-called BSW effect. The special role is played here by so-called critical geodesics when one of particles has fine-tuned energy and angular momentum. The nature of geodesics reveals itself also in fate of the debris after collisions. One of particles moving to a remote observer is necessarily near-critical. We discuss, when such a collision can give rise not only unboud Ec.m. but also unbound Killing energy E (so-called super-Penrose process.
Smearing of chaos in sandwich pp-waves
Podolsky, J
1999-01-01
Recent results demonstrating the chaotic behavior of geodesics in non-homogeneous vacuum pp-wave solutions are generalized. Here we concentrate on motion in non-homogeneous sandwich pp-waves and show that chaos smears as the duration of these gravitational waves is reduced. As the number of radial bounces of any geodesic decreases, the outcome channels to infinity become fuzzy, and thus the fractal structure of the initial conditions characterizing chaos is cut at lower and lower levels. In the limit of impulsive waves, the motion is fully non-chaotic. This is proved by presenting the geodesics in a simple explicit form which permits a physical interpretation, and demonstrates the focusing effect. It is shown that a circle of test particles is deformed by the impulse into a family of closed hypotrochoidal curves in the transversal plane. These are deformed in the longitudinal direction in such a way that a specific closed caustic surface is formed.
Past incompleteness of a bouncing multiverse
Vilenkin, Alexander
2014-01-01
According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate this issue in a simple multiverse model, where the spacetime consists of a patchwork of FRW regions. The conclusion is that the spacetime is still past-incomplete, even in the presence of AdS bounces.
A Remark on Contact Hypersurfaces of a Complex Hyperbolic Space
Institute of Scientific and Technical Information of China (English)
许志才
1993-01-01
A differentiable manifold is said to be contact if it admits a linear functional f on the tangent bundle satisfying f∧ (df)n-1≠0.This remark obtain the following the classification:Let M be a complete connected contact hyper-surface of CH2(-4),then M is congruent to one of the following:(i) A tube of redius r>0 around a totally geodesic,totally real hyperbolic space form H2(-1);(ii)A tube of radius r>0 around a totally geodesic complex hyperbolic space form CH1(-4);(iii)A geodesic hypersphere of radius r>0,or(iv)A horosphere.
Genetic selection of neutron star structure matching the X-ray observations
Stuchlik, Zdenek; Torok, Gabriel; Urbanec, Martin; Bakala, Pavel
2008-01-01
Assuming a resonant origin of the quasiperiodic oscillations observed in the X-ray neutron star binary systems, we apply a genetic algorithm method for selection of neutron star models. It was suggested that pairs of kilo-Hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. In several specific models, the two modes are related to physically plausible combinations of Keplerian, vertical and radial frequencies of geodesic orbital motion. We investigate this concept for a specific neutron star source, a fixed pair of modes and various neutron star equations of state. Each neutron star model is characterized by the equation of state (EOS), rotation frequency ($\\Omega$) and central energy density ($\\rho_\\mathrm c$). These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. When the parameters of n...
A pseudo-Newtonian limit for test motion in arbitrary space-times
Witzany, Vojtech
2016-01-01
We present a particular low-energy limit of the Hamiltonian of free test particle motion in arbitrary relativistic space-times. As it turns out, this limit gives insight into the general Newtonian limit by providing an intermediate, "pseudo-Newtonian" step, which encompasses some pseudo-Newtonian formulas already present in the literature. If the metric is expressed so as to be diagonal in the coordinate-time components, we are able to derive a description exactly reproducing the spatial shapes of geodesics. In fully general space-times where dragging ("time non-diagonal") terms appear in the metric, the limit at least yields a previously unknown Hamiltonian reproducing exact shapes of null geodesics. Furthermore, if the space-time is stationary, the exact shapes of null geodesics can be also correctly parametrized by coordinate-time, the limit thus provides an alternative Hamiltonian for computations in gravitational lensing. Relevant astrophysical superpositions of gravitating sources, the addition of elect...