DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharif, M., E-mail: msharif.math@pu.edu.pk; Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk; Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782

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-freemore » 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.« less

Kinematic space for conical defects

NASA Astrophysics Data System (ADS)

Cresswell, Jesse C.; Peet, Amanda W.

2017-11-01

Kinematic space can be used as an intermediate step in the AdS/CFT dictionary and lends itself naturally to the description of diffeomorphism invariant quantities. From the bulk it has been defined as the space of boundary anchored geodesics, and from the boundary as the space of pairs of CFT points. When the bulk is not globally AdS3 the appearance of non-minimal geodesics leads to ambiguities in these definitions. In this work conical defect spacetimes are considered as an example where non-minimal geodesics are common. From the bulk it is found that the conical defect kinematic space can be obtained from the AdS3 kinematic space by the same quotient under which one obtains the defect from AdS3. The resulting kinematic space is one of many equivalent fundamental regions. From the boundary the conical defect kinematic space can be determined by breaking up OPE blocks into contributions from individual bulk geodesics. A duality is established between partial OPE blocks and bulk fields integrated over individual geodesics, minimal or non-minimal.

Spacetime completeness of non-singular black holes in conformal gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new typesmore » of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.« less

de Sitter geodesics

NASA Astrophysics Data System (ADS)

Cotăescu, Ion I.

2017-12-01

The geodesics on the (1 + 3)-dimensional de Sitter (dS) spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lemaître-Robertson-Walker, de Sitter-Painlevé and static local charts with Cartesian space coordinates. Moreover, it is shown that there exists a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.

Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

NASA Astrophysics Data System (ADS)

Seriu, Masafumi

2015-10-01

We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

Kinematic space and wormholes

NASA Astrophysics Data System (ADS)

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.

The inherent dynamics of a molecular liquid: geodesic pathways through the potential energy landscape of a liquid of linear molecules.

PubMed

Jacobson, Daniel; Stratt, Richard M

2014-05-07

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation-molecules largely thread their way through narrow channels available in the potential energy landscape.

The inherent dynamics of a molecular liquid: Geodesic pathways through the potential energy landscape of a liquid of linear molecules

NASA Astrophysics Data System (ADS)

Jacobson, Daniel; Stratt, Richard M.

2014-05-01

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.

Space–time and spatial geodesic orbits in Schwarzschild geometry

NASA Astrophysics Data System (ADS)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

NASA Astrophysics Data System (ADS)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

Geodesic curve-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi

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 asmore » a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.« less

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution.

PubMed

Gangadharan, R; Prasanna, G; Bhat, M R; Murthy, C R L; Gopalakrishnan, S

2009-11-01

Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

Self-consistent geodesic equation and quantum tunneling from charged AdS black holes

NASA Astrophysics Data System (ADS)

Deng, Gao-Ming

2017-12-01

Some urgent shortcomings in previous derivations of geodesic equations are remedied in this paper. In contrast to the unnatural and awkward treatment in previous works, here we derive the geodesic equations of massive and massless particles in a unified and self- consistent manner. Furthermore, we extend to investigate the Hawking radiation via tunneling from charged black holes in the context of AdS spacetime. Of special interest, the application of the first law of black hole thermodynamics in tunneling integration manifestly simplifies the calculation.

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

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.

Superintegrability of geodesic motion on the sausage model

NASA Astrophysics Data System (ADS)

Arutyunov, Gleb; Heinze, Martin; Medina-Rincon, Daniel

2017-06-01

Reduction of the η-deformed sigma model on AdS_5× S5 to the two-dimensional squashed sphere (S^2)η can be viewed as a special case of the Fateev sausage model where the coupling constant ν is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model. This paper is a tribute to the memory of Prof Petr Kulish.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.

PubMed

Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang

2013-04-01

An accurate creeping ray-tracing algorithm is presented in this paper to determine the tracks of creeping waves (or creeping rays) on arbitrarily shaped free-form parametric surfaces [nonuniform rational B-splines (NURBS) surfaces]. The main challenge in calculating the surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping rays propagate. On one single parametric surface patch, the geodesic paths need to be computed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of the parameter between the patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Thus, a creeping ray-tracing algorithm is presented in this paper to compute the geodesic paths of creeping rays on the complex objects that are modeled as the combination of several NURBS surface patches. In the algorithm, the creeping ray tracing on each surface patch is performed by solving the geodesic equations with a Runge-Kutta method. When the creeping ray propagates from one patch to another, a transition method is developed to handle the transition of the creeping ray tracing across the border between the patches. This creeping ray-tracing algorithm can meet practical requirements because it can be applied to the objects with complex shapes. The algorithm can also extend the applicability of NURBS for electromagnetic and optical applications. The validity and usefulness of the algorithm can be verified from the numerical results.

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

NASA Technical Reports Server (NTRS)

Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.

1996-01-01

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

NASA Astrophysics Data System (ADS)

Heydari-Fard, M.; Hasani, S. N.

We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kagramanova, Valeria; Kunz, Jutta; Hackmann, Eva

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic functions. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the 'Misner string' in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub [C. W. Misner and A. H. Taub, Sov. Phys. JETP 28, 122 (1969) [Zh. Eksp. Teor. Fiz. 55, 233 (1968)

Winding trajectories of noncircular composite shells

NASA Astrophysics Data System (ADS)

Nikityuk, V. A.; Fedorov, V. V.

1995-07-01

An approach has been proposed for determination of the trajectory parameters of a layer formed by winding of continuous ribbons on a complicated surface. An algorithm has been developed for determining the geodesic trajectories of the reinforcement fiber arrangement, reinforcement angles, and geodesic deviation angles. Conditions have been formulated for positional stability of the ribbons on the surface and avoidance of gaps and overlapping between the ribbons along with restrictions to the surface form. Results are given for a calculation of the geodesic turn parameters on a fuselage surface, which is not a surface of revolution, of a light airplane.

Geodesic motion around traversable wormholes supported by a massless conformally coupled scalar field

NASA Astrophysics Data System (ADS)

Willenborg, Felix; Grunau, Saskia; Kleihaus, Burkhard; Kunz, Jutta

2018-06-01

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the Janis-Newman-Winicour-Wyman spacetime. We study the geodesic motion of timelike and spacelike particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for timelike geodesics only in one of the two worlds. Moreover, under no conditions there exist timelike two world bound orbits.

Impact of energetic-particle-driven geodesic acoustic modes on turbulence.

PubMed

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

2013-03-22

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.

Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

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.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

Thermal Hawking radiation of black hole with supertranslation field

NASA Astrophysics Data System (ADS)

Iofa, Mikhail Z.

2018-01-01

Using the analytical solution for the Schwarzschild metric containing supertranslation field, we consider two main ingredients of calculation of the thermal Hawking black hole radiation: solution for eigenmodes of the d'Alambertian and solution of the geodesic equations for null geodesics. For calculation of Hawking radiation it is essential to determine the behavior of both the eigenmodes and geodesics in the vicinity of horizon. The equation for the eigenmodes is solved, first, perturbatively in the ratio O( C) /M of the supertranslation field to the mass of black hole, and, next, non-perturbatively in the near- horizon region. It is shown that in any order of perturbation theory solution for the eigenmodes in the metric containing supertranslation field differs from solution in the pure Schwarzschild metric by terms of order L 1/2 = (1 - 2 M/r)1/2. In the non-perturbative approach, solution for the eigenmodes differs from solution in the Schwarzschild metric by terms of order L 1/2 which vanish on horizon. Using the simplified form of geodesic equations in vicinity of horizon, it is shown that in vicinity of horizon the null geodesics have the same behavior as in the Schwarzschild metric. As a result, the density matrices of thermal radiation in both cases are the same.

Geodesic congruences in warped spacetimes

NASA Astrophysics Data System (ADS)

Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan

2011-04-01

In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. 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 backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Charbulák, Daniel; Schee, Jan

2018-03-01

We construct the light escape cones of isotropic spot sources of radiation residing in special classes of reference frames in the Kerr-de Sitter (KdS) black hole spacetimes, namely in the fundamental class of `non-geodesic' locally non-rotating reference frames (LNRFs), and two classes of `geodesic' frames, the radial geodesic frames (RGFs), both falling and escaping, and the frames related to the circular geodesic orbits (CGFs). We compare the cones constructed in a given position for the LNRFs, RGFs, and CGFs. We have shown that the photons locally counter-rotating relative to LNRFs with positive impact parameter and negative covariant energy are confined to the ergosphere region. Finally, we demonstrate that the light escaping cones govern the shadows of black holes located in front of a radiating screen, as seen by the observers in the considered frames. For shadows related to distant static observers the LNRFs are relevant.

A Computational Model of Multidimensional Shape

PubMed Central

Liu, Xiuwen; Shi, Yonggang; Dinov, Ivo

2010-01-01

We develop a computational model of shape that extends existing Riemannian models of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. The model employs a representation of shape based on the discrete exterior derivative of parametrizations over a finite simplicial complex. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a formulation that accounts for regional differences and integrates them into a global measure of dissimilarity. The Riemannian shape spaces provide a common framework to treat numerous problems such as the statistical modeling of shapes, the comparison of shapes associated with different individuals or groups, and modeling and simulation of shape dynamics. We give multiple examples of geodesic interpolations and illustrations of the use of the models in brain mapping, particularly, the analysis of anatomical variation based on neuroimaging data. PMID:21057668

Complete integrability of geodesic motion in Sasaki-Einstein toric Yp,q spaces

NASA Astrophysics Data System (ADS)

Babalic, Elena Mirela; Visinescu, Mihai

2015-09-01

We construct explicitly the constants of motion for geodesics in the five-dimensional Sasaki-Einstein spaces Yp,q. To carry out this task, we use the knowledge of the complete set of Killing vectors and Killing-Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on Yp,q spaces. In the particular case of the homogeneous Sasaki-Einstein manifold T1,1 the integrals of motion have simpler forms and the relations between them are described in detail.

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

NASA Astrophysics Data System (ADS)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

On the n-body problem on surfaces of revolution

NASA Astrophysics Data System (ADS)

Stoica, Cristina

2018-05-01

We explore the n-body problem, n ≥ 3, on a surface of revolution with a general interaction depending on the pairwise geodesic distance. Using the geometric methods of classical mechanics we determine a large set of properties. In particular, we show that Saari's conjecture fails on surfaces of revolution admitting a geodesic circle. We define homographic motions and, using the discrete symmetries, prove that when the masses are equal, they form an invariant manifold. On this manifold the dynamics are reducible to a one-degree of freedom system. We also find that for attractive interactions, regular n-gon shaped relative equilibria with trajectories located on geodesic circles typically experience a pitchfork bifurcation. Some applications are included.

Approximate geodesic distances reveal biologically relevant structures in microarray data.

PubMed

Nilsson, Jens; Fioretos, Thoas; Höglund, Mattias; Fontes, Magnus

2004-04-12

Genome-wide gene expression measurements, as currently determined by the microarray technology, can be represented mathematically as points in a high-dimensional gene expression space. Genes interact with each other in regulatory networks, restricting the cellular gene expression profiles to a certain manifold, or surface, in gene expression space. To obtain knowledge about this manifold, various dimensionality reduction methods and distance metrics are used. For data points distributed on curved manifolds, a sensible distance measure would be the geodesic distance along the manifold. In this work, we examine whether an approximate geodesic distance measure captures biological similarities better than the traditionally used Euclidean distance. We computed approximate geodesic distances, determined by the Isomap algorithm, for one set of lymphoma and one set of lung cancer microarray samples. Compared with the ordinary Euclidean distance metric, this distance measure produced more instructive, biologically relevant, visualizations when applying multidimensional scaling. This suggests the Isomap algorithm as a promising tool for the interpretation of microarray data. Furthermore, the results demonstrate the benefit and importance of taking nonlinearities in gene expression data into account.

Which Way Is Jerusalem? Navigating on a Spheroid

ERIC Educational Resources Information Center

Schechter, Murray

2007-01-01

Given two points on a spheroidal planet, what is the direction from the first to the second? The answer depends, of course, on what path you take. This paper compares two paths which suggest themselves, namely, the loxodrome, which is the path in which the direction stays constant, and the geodesic, which is the shortest path. The geodesic does…

Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves

PubMed Central

Joshi, Shantanu H.; Klassen, Eric; Srivastava, Anuj; Jermyn, Ian

2011-01-01

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves. PMID:21738385

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

NASA Astrophysics Data System (ADS)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

Evolution of geodesic congruences in a gravitationally collapsing scalar field background

NASA Astrophysics Data System (ADS)

Shaikh, Rajibul; Kar, Sayan; DasGupta, Anirvan

2014-12-01

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation, and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity) in shaping the overall behavior of geodesic congruences.

Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.

2013-08-01

In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S2 is constructed.

Conformal geodesics in spherically symmetric vacuum spacetimes with cosmological constant

NASA Astrophysics Data System (ADS)

García-Parrado Gómez-Lobo, A.; Gasperín, E.; Valiente Kroon, J. A.

2018-02-01

An analysis of conformal geodesics in the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that the congruence of conformal geodesics arising from this data cover the whole maximal extension of canonical conformal representations of the spacetimes without forming caustic points. For the Schwarzschild–de Sitter family, the resulting congruence can be used to obtain global conformal Gaussian systems of coordinates of the conformal representation. In the case of the Schwarzschild–anti-de Sitter family, the natural parameter of the curves only covers a restricted time span so that these global conformal Gaussian systems do not exist.

Newtonian potential and geodesic completeness in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Edholm, James; Conroy, Aindriú

2017-08-01

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

Geodesic detection of Agulhas rings

NASA Astrophysics Data System (ADS)

Beron-Vera, F. J.; Wang, Y.; Olascoaga, M. J.; Goni, G. J.; Haller, G.

2012-12-01

Mesoscale oceanic eddies are routinely detected from instantaneous velocities. While simple to implement, this Eulerian approach gives frame-dependent results and often hides true material transport by eddies. Building on the recent geodesic theory of transport barriers, we develop an objective (i.e., frame-independent) method for accurately locating coherent Lagrangian eddies. These eddies act as compact water bodies, with boundaries showing no leakage or filamentation over long periods of time. Applying the algorithm to altimetry-derived velocities in the South Atlantic, we detect, for the first time, Agulhas rings that preserve their material coherence for several months, while eddy candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that current Eulerian estimates of the Agulhas leakage need significant revision.Temporal evolution of fluid patches identified as eddies by different methods. First column: eddies extracted using geodesic eddy identification [1,2]. Second column: eddies identified from sea surface height (SSH) using the methodology of Chelton et al. [2] with U/c > 1. Third column: eddies identified as elliptic regions by the Okubo-Weiss (OW) criterion [e.g., 3]. Fourth column: eddies identified as mesoelliptic (ME) regions by Mezic et al.'s [4] criterion. References: [1] Beron-Vera et al. (2012). Geodesic eddy detection suggests reassessment of Agulhas leakage. Proc. Nat. Acad. Sci. USA, submitted. [2] Haller & Beron-Vera (2012). Geodesic theory of transport barriers in two-dimensional flows. Physica D, in press. [2] Chelton et al. (2011). Prog. Oceanog. 91, 167. [3] Chelton et al. (2007). Geophys. Res. Lett. 34, L5606. [4] Mezic et al. (2010). Science 330, 486.

Strong Magnetic Field Fluctuations within Filamentary Auroral Density Cavities Interpreted as VLF Saucer Sources

NASA Technical Reports Server (NTRS)

Knudsen, D. L.; Kabirzadeh, R.; Burchill, J. K.; Pfaff, Robert F.; Wallis, D. D.; Bounds, S. R.; Clemmons, J. H.; Pincon, J.-L.

2012-01-01

The Geoelectrodynamics and Electro-Optical Detection of Electron and SuprathermalIon Currents (GEODESIC) sounding rocket encountered more than 100 filamentary densitycavities associated with enhanced plasma waves at ELF (3 kHz) and VLF (310 kHz)frequencies and at altitudes of 800990 km during an auroral substorm. These cavities weresimilar in size (20 m diameter in most cases) to so-called lower-hybrid cavities (LHCs)observed by previous sounding rockets and satellites; however, in contrast, many of theGEODESIC cavities exhibited up to tenfold enhancements in magnetic wave powerthroughout the VLF band. GEODESIC also observed enhancements of ELF and VLFelectric fields both parallel and perpendicular to the geomagnetic field B0 within cavities,though the VLF E field increases were often not as large proportionally as seen in themagnetic fields. This behavior is opposite to that predicted by previously published theoriesof LHCs based on passive scattering of externally incident auroral hiss. We argue thatthe GEODESIC cavities are active wave generation sites capable of radiating VLF wavesinto the surrounding plasma and producing VLF saucers, with energy supplied by cold,upward flowing electron beams composing the auroral return current. This interpretation issupported by the observation that the most intense waves, both inside and outside cavities,occurred in regions where energetic electron precipitation was largely inhibited orabsent altogether. We suggest that the wave-enhanced cavities encountered by GEODESICwere qualitatively different from those observed by earlier spacecraft because of thefortuitous timing of the GEODESIC launch, which placed the payload at apogee within asubstorm-related return current during its most intense phase, lasting only a few minutes.

Feature Extraction of High-Dimensional Structures for Exploratory Analytics

DTIC Science & Technology

2013-04-01

Comparison of Euclidean vs. geodesic distance. LDRs use metric based on the Euclidean distance between two points, while the NLDRs are based on...geodesic distance. An NLDR successfully unrolls the curved manifold, whereas an LDR fails. ...........................3 1 1. Introduction An...and classical metric multidimensional scaling, are a linear DR ( LDR ). An LDR is based on a linear combination of

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akers, Chris; Bousso, Raphael; Halpern, Illan F.

We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

Adaptive geodesic transform for segmentation of vertebrae on CT images

NASA Astrophysics Data System (ADS)

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.

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface.

PubMed

Ingebrigtsen, Trond S; Toxvaerd, Søren; Heilmann, Ole J; Schrøder, Thomas B; Dyre, Jeppe C

2011-09-14

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 precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced 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 algorithm have identical radial distribution functions for the Lennard-Jones liquid. © 2011 American Institute of Physics

Upper limit on NUT charge from the observed terrestrial Sagnac effect

NASA Astrophysics Data System (ADS)

Kulbakova, A.; Karimov, R. Kh; Izmailov, R. N.; Nandi, K. K.

2018-06-01

The exact Sagnac delay in the Kerr–Taub–NUT (Newman–Unti–Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin , the delay does not vanish. This fact is similar to the non-vanishing of Lense–Thirring precession under even though the two effects originate from different premises. Assuming a reasonable input that the Kerr–Taub–NUT corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge n. It is found that the upper limits on n are far larger than the Earth’s gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain n to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known ‘twin paradox’ of special relativity.

Past incompleteness of a bouncing multiverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vilenkin, Alexander; Zhang, Jun, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu

2014-06-01

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 consistsmore » of a patchwork of FRW regions. The conclusion is that the spacetime is still past-incomplete, even in the presence of AdS bounces.« less

Null geodesics and wave front singularities in the Gödel space-time

NASA Astrophysics Data System (ADS)

Kling, Thomas P.; Roebuck, Kevin; Grotzke, Eric

2018-01-01

We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.

Injection of a Body into a Geodesic: Lessons Learnt from the LISA Pathfinder Case

NASA Technical Reports Server (NTRS)

Bortoluzzi, Daniele; Armano, M.; Audley, H.; Auger, G.; Baird, J.; Binetruy, P.; Born, M.; Bortoluzzi, D.; Brandt, N.; Bursi, A.;

A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation

NASA Astrophysics Data System (ADS)

Ahmed, Faizuddin

2017-12-01

We present a topologically trivial, non-vacuum solution of the Einstein’s field equations in four dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve, which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid p=ω ρ . The metric admits a twisting, shearfree, nonexapnding timelike geodesic congruence. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.

Axisymmetric electrostatic magnetohydrodynamic oscillations in tokamaks with general cross-sections and toroidal flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chu, M. S.; Guo, Wenfeng

2016-06-15

The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the “electrostatic continua.” Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solvedmore » analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic displacements. Based on the general notion that the geodesic component of the GAM is more effective in tearing up the eddies in the electrostatic turbulence, it is important to preferentially excite the GAMs that are non-sound-wave like to maximize the efficiency on turbulence suppression through external means. Finally, approximate formulae for the frequencies of the EMF, ZF, SW, and the GAM for a large aspect ratio circular tokamak rotating at low Mach numbers are also provided.« less

Calculating the Sachs-Wolfe Effect from Solutions of Null Geodesics in Perturbed FRW Spacetime

NASA Astrophysics Data System (ADS)

Arroyo-Cárdenas, C. A.; Muñoz-Cuartas, J. C.

2017-07-01

In the upcoming precision era in cosmology, fine grained effects will be measured accurately. In particular, the late integrated Sachs-Wolfe (ISW) effect measurements will be improved to levels of unprecedented precision. The ISW consists on temperature fluctuations in the CMB due to gravitational redshift induced by the evolving potential well of large scale structure in the Universe. Currently there is large controversy related to the actual observability of the ISW effect. In principle, it is expected that, as an effect of the late accelerated expansion of the universe motivated by the current amount of dark energy, large scale structures may evolve rapidly, inducing an observable signature in the CMB photons in the way of a ISW anisotropy in the CMB. Tension arises since using galaxy redshift surveys some works report a temperature fluctuations with amplitude smaller than predicted by the Lambda-CDM. We argue that these discrepancies may be originated in the approximation that one has to make to get the classic Sachs-Wolfe effect. In this work, we compare the classic Sachs-Wolfe approximation with an exact solution to the propagation of photons in a dynamical background. We solve numerically the null geodesics on a perturbed FRW spacetime in the Newtonian gauge. From null geodesics, temperature fluctuations in the CMB due to the evolving potential has been calculated. Since solving geodesics accounts for more terms than solving the Sachs-Wolfe (approximated) integral, our results are more accurate. We have been able to substract the background cosmological redshift with the information provided by null geodesics, which allows to get an estimate of the integrated Sachs-Wolfe effect contribution to the temperature of the CMB.

Metric Properties of Relativistic Rotating Frames with Axial Symmetry

NASA Astrophysics Data System (ADS)

Torres, S. A.; Arenas, J. R.

2017-07-01

This abstract summarizes our poster contribution to the conference. We study the properties of an axially symmetric stationary gravitational field, by considering the spacetime properties of an uniformly rotating frame and the Einstein's Equivalence Principle (EEP). To undertake this, the weak field and slow-rotation limit of the kerr metric are determined, by making a first-order perturbation to the metric of a rotating frame. Also, we show a local connection between the effects of centrifugal and Coriolis forces with the effects of an axially symmetric stationary weak gravitational field, by calculating the geodesic equations of a free particle. It is observed that these geodesic, applying the (EEP), are locally equivalent to the geodesic equations of a free particle on a rotating frame. Furthermore, some aditional properties as the Lense-Thirring effect, the Sagnac effect, among others are studied.

Tensor networks from kinematic space

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2016-07-20

We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space — the geometry of CFT intervals. In holographic theories kinematic space becomes identified with the space of bulk geodesics studied in integral geometry. We argue that in these settings MERA is best viewed as a discretization of the space of bulk geodesics rather than of the bulk geometry itself. As a test of this kinematic proposal, we compare the MERA representation of the thermofield-double state with the space of geodesics in the two-sided BTZ geometry,more » obtaining a detailed agreement which includes the entwinement sector. In conclusion, we discuss how the kinematic proposal can be extended to excited states by generalizing MERA to a broader class of compression networks.« less

Geodesic least squares regression for scaling studies in magnetic confinement fusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, Geert

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 ofmore » 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.« less

Snyder-like modified gravity in Newton's spacetime

NASA Astrophysics Data System (ADS)

Leiva, Carlos

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

Boundary of the future of a surface

DOE PAGES

Akers, Chris; Bousso, Raphael; Halpern, Illan F.; ...

2018-01-12

We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

Measurement of momentum transfer due to adhesive forces: on-ground testing of in-space body injection into geodesic motion.

PubMed

Bortoluzzi, D; Benedetti, M; Baglivo, L; De Cecco, M; Vitale, S

2011-12-01

In the frame of many scientific space missions, a massive free-falling object is required to mark a geodesic trajectory, i.e., to follow inside a spacecraft an orbit that is determined only by the planetary gravity field. The achievement of high-purity geodesic trajectories sets tight design constraints on the reference sensor that hosts and controls the reference body. Among these, a mechanism may be required to cage the reference body during the spacecraft launch and to inject it into the geodesic trajectory once on-orbit. The separation of the body from the injection mechanism must be realized against the action of adhesion forces, and in the worst case this is performed dynamically, relying on the body's inertia through a quick retraction of the holding finger(s). Unfortunately, this manoeuvre may not avoid transferring some momentum to the body, which may affect or even jeopardize the subsequent spacecraft control if the residual velocity is too large. The transferred momentum measurement facility (TMMF) was developed to reproduce representative conditions of the in-flight dynamic injection and to measure the transferred momentum to the released test mass. In this paper, we describe the design and development of the TMMF together with the achieved measurement performance.

On static solutions of the Einstein-Scalar Field equations

NASA Astrophysics Data System (ADS)

Reiris, Martín

2017-03-01

In this article we study self-gravitating static solutions of the Einstein-Scalar Field system in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential V(φ ), and provide full global geometric estimates when the solutions exist. The most complete results are obtained for the physically important Klein-Gordon field and are summarised as follows. When V(φ )=m2|φ |2, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is φ is constant and equal to zero if m≠ 0). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When V(φ )=m2|φ |2+2Λ , that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when Λ >0, whereas when Λ <0 it is proved that no non-vacuum geodesically complete solution exists unless m2<-2Λ /(n-1), ( n is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on novel techniques in comparison geometry á la Bakry-Émery that have their own interest.

On six-dimensional pseudo-Riemannian almost g.o. spaces

NASA Astrophysics Data System (ADS)

Dušek, Zdeněk; Kowalski, Oldřich

2007-09-01

We modify the "Kaplan example" (a six-dimensional nilpotent Lie group which is a Riemannian g.o. space) and we obtain two pseudo-Riemannian homogeneous spaces with noncompact isotropy group. These examples have the property that all geodesics are homogeneous up to a set of measure zero. We also show that the (incomplete) geodesic graphs are strongly discontinuous at the boundary, i.e., the limits along certain curves are always infinite.

Using Riemannian geometry to obtain new results on Dikin and Karmarkar methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira, P.; Joao, X.; Piaui, T.

1994-12-31

We are motivated by a 1990 Karmarkar paper on Riemannian geometry and Interior Point Methods. In this talk we show 3 results. (1) Karmarkar direction can be derived from the Dikin one. This is obtained by constructing a certain Z(x) representation of the null space of the unitary simplex (e, x) = 1; then the projective direction is the image under Z(x) of the affine-scaling one, when it is restricted to that simplex. (2) Second order information on Dikin and Karmarkar methods. We establish computable Hessians for each of the metrics corresponding to both directions, thus permitting the generation ofmore » {open_quotes}second order{close_quotes} methods. (3) Dikin and Karmarkar geodesic descent methods. For those directions, we make computable the theoretical Luenberger geodesic descent method, since we are able to explicit very accurate expressions of the corresponding geodesics. Convergence results are given.« less

Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. E.

2018-02-01

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

Exact moduli space metrics for hyperbolic vortex polygons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krusch, S.; Speight, J. M.

2010-02-15

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as {sigma}{sub n,m}, are spaces of C{sub n}-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of {sigma}{sub n,m} are investigated, and it is found that {sigma}{sub n,n-1} is isometric to the hyperbolic plane of curvature -(3{pi}n){sup -1}. The geodesic flow on {sigma}{sub n,m} and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys.more » Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.« less

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.

Average geodesic distance of skeleton networks of Sierpinski tetrahedron

NASA Astrophysics Data System (ADS)

Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao

2018-04-01

The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.

Strolling along gauge theory vacua

NASA Astrophysics Data System (ADS)

Seraj, Ali; Van den Bleeken, Dieter

2017-08-01

We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.

Geodesic denoising for optical coherence tomography images

NASA Astrophysics Data System (ADS)

Shahrian Varnousfaderani, Ehsan; Vogl, Wolf-Dieter; Wu, Jing; Gerendas, Bianca S.; Simader, Christian; Langs, Georg; Waldstein, Sebastian M.; Schmidt-Erfurth, Ursula

2016-03-01

Optical coherence tomography (OCT) is an optical signal acquisition method capturing micrometer resolution, cross-sectional three-dimensional images. OCT images are used widely in ophthalmology to diagnose and monitor retinal diseases such as age-related macular degeneration (AMD) and Glaucoma. While OCT allows the visualization of retinal structures such as vessels and retinal layers, image quality and contrast is reduced by speckle noise, obfuscating small, low intensity structures and structural boundaries. Existing denoising methods for OCT images may remove clinically significant image features such as texture and boundaries of anomalies. In this paper, we propose a novel patch based denoising method, Geodesic Denoising. The method reduces noise in OCT images while preserving clinically significant, although small, pathological structures, such as fluid-filled cysts in diseased retinas. Our method selects optimal image patch distribution representations based on geodesic patch similarity to noisy samples. Patch distributions are then randomly sampled to build a set of best matching candidates for every noisy sample, and the denoised value is computed based on a geodesic weighted average of the best candidate samples. Our method is evaluated qualitatively on real pathological OCT scans and quantitatively on a proposed set of ground truth, noise free synthetic OCT scans with artificially added noise and pathologies. Experimental results show that performance of our method is comparable with state of the art denoising methods while outperforming them in preserving the critical clinically relevant structures.

Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows

NASA Astrophysics Data System (ADS)

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.

New perspectives for high accuracy SLR with second generation geodesic satellites

NASA Technical Reports Server (NTRS)

Lund, Glenn

1993-01-01

This paper reports on the accuracy limitations imposed by geodesic satellite signatures, and on the potential for achieving millimetric performances by means of alternative satellite concepts and an optimized 2-color system tradeoff. Long distance laser ranging, when performed between a ground (emitter/receiver) station and a distant geodesic satellite, is now reputed to enable short arc trajectory determinations to be achieved with an accuracy of 1 to 2 centimeters. This state-of-the-art accuracy is limited principally by the uncertainties inherent to single-color atmospheric path length correction. Motivated by the study of phenomena such as postglacial rebound, and the detailed analysis of small-scale volcanic and strain deformations, the drive towards millimetric accuracies will inevitably be felt. With the advent of short pulse (less than 50 ps) dual wavelength ranging, combined with adequate detection equipment (such as a fast-scanning streak camera or ultra-fast solid-state detectors) the atmospheric uncertainty could potentially be reduced to the level of a few millimeters, thus, exposing other less significant error contributions, of which by far the most significant will then be the morphology of the retroreflector satellites themselves. Existing geodesic satellites are simply dense spheres, several 10's of cm in diameter, encrusted with a large number (426 in the case of LAGEOS) of small cube-corner reflectors. A single incident pulse, thus, results in a significant number of randomly phased, quasi-simultaneous return pulses. These combine coherently at the receiver to produce a convolved interference waveform which cannot, on a shot to shot basis, be accurately and unambiguously correlated to the satellite center of mass. This paper proposes alternative geodesic satellite concepts, based on the use of a very small number of cube-corner retroreflectors, in which the above difficulties are eliminated while ensuring, for a given emitted pulse, the return of a single clean pulse with an adequate cross-section.

Towards timelike singularity via AdS dual

NASA Astrophysics Data System (ADS)

Bhowmick, Samrat; Chatterjee, Soumyabrata

2017-07-01

It is well known that Kasner geometry with spacelike singularity can be extended to bulk AdS-like geometry, furthermore, one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including spacelike geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

Vortex pairs on surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koiller, Jair; Boatto, Stefanella

2009-05-06

A pair of infinitesimally close opposite vortices moving on a curved surface moves along a geodesic, according to a conjecture by Kimura. We outline a proof. Numerical simulations are presented for a pair of opposite vortices at a close but nonzero distance on a surface of revolution, the catenoid. We conjecture that the vortex pair system on a triaxial ellipsoid is a KAM perturbation of Jacobi's geodesic problem. We outline some preliminary calculations required for this study. Finding the surfaces for which the vortex pair system is integrable is in order.

Lagrangian averaging with geodesic mean

NASA Astrophysics Data System (ADS)

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Lagrangian averaging with geodesic mean.

PubMed

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

On geodesics of the rotation group SO(3)

NASA Astrophysics Data System (ADS)

Novelia, Alyssa; O'Reilly, Oliver M.

2015-11-01

Geodesics on SO(3) are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in optometry and the latter features in the interpolation of rotations in computer graphics. The simplicity of these two disparate interpretations belies the complexity of the corresponding rotations. Using a quaternion representation for a rotation, we present a simple proof of the equivalence of the aforementioned characterizations and a straightforward method to establish features of the corresponding rotations.

Energetic-particle-induced geodesic acoustic mode.

PubMed

Fu, G Y

2008-10-31

A new energetic particle-induced geodesic acoustic mode (EGAM) is shown to exist. The mode frequency and mode structure are determined nonperturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam-driven n=0 mode in DIII-D.

Differential invariants and exact solutions of the Einstein equations

NASA Astrophysics Data System (ADS)

Lychagin, Valentin; Yumaguzhin, Valeriy

2017-06-01

In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.

2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds

NASA Astrophysics Data System (ADS)

Araya Quezada, Ignacio Jesus

In this thesis, we discuss two different contexts where the idea of gauge symmetry and duality is used to solve the dynamics of physical systems. The first of such contexts is 2T-physics in the worldline in d+2 dimensions, where the principle of Sp(2,R) gauge symmetry in phase space is used to relate different 1T systems in (d -- 1) + 1 dimensions, such as a free relativistic particle, and a relativistic particle in an arbitrary V(x2) potential. Because each 1T shadow system corresponds to a particular gauge of the underlying symmetry, there is a web of dualities relating them. The dualities between said systems amount to canonical transformations including time and energy, which allows the different systems to be described by different Hamiltonians, and consequently, to correspond to different dynamics in the (d -- 1)+1 phase space. The second context, corresponds to a Weyl invariant scalar-tensor theory of gravity, obtained as a direct prediction of 2T gravity, where the Weyl symmetry is used to obtain geodesically complete dynamics both in the context of cosmology and black hole (BH) backgrounds. The geodesic incompleteness of usual Einstein gravity, in the presence of singularities in spacetime, is related to the definition of the Einstein gauge, which fixes the sign and magnitude of the gravitational constant GN, and therefore misses the existence of antigravity patches, which are expected to arise generically just beyond gravitational singularities. The definition of the Einstein gauge can be generalized by incorporating a sign flip of the gravitational constant GN at the transitions between gravity and antigravity. This sign is a key aspect that allows us to define geodesically complete dynamics in cosmology and in BH backgrounds, particularly, in the case of the 4D Schwarzschild BH and the 2D stringy BH. The complete nature of particle geodesics in these BH backgrounds is exhibited explicitly at the classical level, and the extension of these results to the behavior of fields, interpreted as the first quantized particle wavefunctions in the backgrounds is discussed for the 2D stringy BH case. It is shown that the geodesic completion also carries through at the quantum level, by examining the effective potential of the corresponding Schwarzschild problem. Also, in the case of the 2D stringy BH, it is explicitly shown that the spacetime has a multi-sheeted structure, which resolves possible issues like the presence of closed timelike curves. This multi-sheeted structure is conjectured to exist also for the 4D Schwarzschild BH (and perhaps for all BH backgrounds). The main new results of this thesis are the extended network of dualities, in the form of canonical transformations including time and energy, between the 1T dynamical systems, presented in Chapter 2 and the construction of the geodesically complete 4D Schwarzschild and 2D stringy black hole backgrounds, presented in Chapter 3.

Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity

NASA Astrophysics Data System (ADS)

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.

Optimal design of geodesically stiffened composite cylindrical shells

NASA Technical Reports Server (NTRS)

Gendron, G.; Guerdal, Z.

1992-01-01

An optimization system based on the finite element code Computations Structural Mechanics (CSM) Testbed and the optimization program, Automated Design Synthesis (ADS), is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thickness, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stingers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example.

FAST TRACK COMMUNICATION: Shear coordinate description of the quantized versal unfolding of a D4 singularity

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2010-11-01

In this communication, by using Teichmüller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingof-Ginzburg Poisson bracket on the affine D4 cubic. We prove that this bracket is the image under the Riemann-Hilbert map of the Poisson-Lie bracket on \\oplus _{1}^3\\mathfrak {sl}^\\ast (2,{{\\bb C}}) . We realize the action of the mapping class group by the action of the braid group on the geodesic functions. This action coincides with the procedure of analytic continuation of solutions of the sixth Painlevé equation. Finally, we produce the explicit quantization of the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere and of the braid group action.

Spacetime encodings. II. Pictures of integrability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brink, Jeandrew

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a 2 degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion, and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation ismore » designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about 2 degree of freedom systems. Evidence is given, in the form of an orbit-crossing structure, that geodesics in SAV spacetimes might admit a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic)« less

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

Boundary singularities produced by the motion of soap films.

PubMed

Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

2014-06-10

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

Newton's absolute time and space in general relativity

NASA Astrophysics Data System (ADS)

Gautreau, Ronald

2000-04-01

I describe a reference system in a spherically symmetric gravitational field that is built around times recorded by radially moving geodesic clocks. The geodesic time coordinate t and the curvature spatial radial coordinate R result in spacetime descriptions of the motion of the geodesic clocks that are exactly identical with equations following from Newton's absolute time and space used with his inverse square law. I show how to use the resulting Newtonian/general-relativistic equations for geodesic clocks to generate exact relativistic metric forms in terms of the coordinates (R,t). Newtonian theory does not describe light. However, the motion of light can be determined from the (R,t) general-relativistic metric forms obtained from Newtonian theory by setting ds2(R,t)=0. In this sense, a theory of light can be related to absolute time and space of Newtonian gravitational theory. I illustrate the (R,t) methodology by first solving the equations that result from a Newtonian picture and then examining the exact metric forms for the general-relativistic problems of the Schwarzschild field, gravitational collapse and expansion of a zero-pressure perfect fluid, and zero-pressure big-bang cosmology. I also briefly describe other applications of the Newtonian/general-relativistic formulation to: embedding a Schwarzschild mass into cosmology; continuously following an expanding universe from radiation to matter domination; Dirac's Large Numbers hypothesis; the incompleteness of Kruskal-Szekeres spacetime; double valuedness in cosmology; and the de Sitter universe.

Geodesic acoustic modes in noncircular cross section tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com; Lakhin, V. P.; Konovaltseva, L. V.

2017-03-15

The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.

MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I.

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.

Observed angles and geodesic light-cone coordinates

NASA Astrophysics Data System (ADS)

Mitsou, Ermis; Scaccabarozzi, Fulvio; Fanizza, Giuseppe

2018-05-01

We discuss the interpretation of the angles in the geodesic light-cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always possible in principle, one cannot implement it in the usual gauge-fixing way, i.e. through a set of conditions on the GLC metric. Rather, one needs to invoke a tetrad at the observer and a Cartesian-like coordinate system in order to obtain the desired map globally on the observed sky.

Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Wang, Bin

2018-02-01

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2).

PubMed

Duits, R; Boscain, U; Rossi, F; Sachkov, Y

To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem P curve of minimizing [Formula: see text] for a planar curve having fixed initial and final positions and directions. Here κ ( s ) is the curvature of the curve with free total length ℓ . This problem comes from a model of geometry of vision due to Petitot (in J. Physiol. Paris 97:265-309, 2003; Math. Inf. Sci. Humaines 145:5-101, 1999), and Citti & Sarti (in J. Math. Imaging Vis. 24(3):307-326, 2006). In previous work we proved that the range [Formula: see text] of the exponential map of the underlying geometric problem formulated on SE(2) consists of precisely those end-conditions ( x fin , y fin , θ fin ) that can be connected by a globally minimizing geodesic starting at the origin ( x in , y in , θ in )=(0,0,0). From the applied imaging point of view it is relevant to analyze the sub-Riemannian geodesics and [Formula: see text] in detail. In this article we show that [Formula: see text] is contained in half space x ≥0 and (0, y fin )≠(0,0) is reached with angle π ,show that the boundary [Formula: see text] consists of endpoints of minimizers either starting or ending in a cusp,analyze and plot the cones of reachable angles θ fin per spatial endpoint ( x fin , y fin ),relate the endings of association fields to [Formula: see text] and compute the length towards a cusp,analyze the exponential map both with the common arc-length parametrization t in the sub-Riemannian manifold [Formula: see text] and with spatial arc-length parametrization s in the plane [Formula: see text]. Surprisingly, s -parametrization simplifies the exponential map, the curvature formulas, the cusp-surface, and the boundary value problem,present a novel efficient algorithm solving the boundary value problem,show that sub-Riemannian geodesics solve Petitot's circle bundle model (cf. Petitot in J. Physiol. Paris 97:265-309, [2003]),show a clear similarity with association field lines and sub-Riemannian geodesics.

Boundary singularities produced by the motion of soap films

PubMed Central

Goldstein, Raymond E.; McTavish, James; Moffatt, H. Keith; Pesci, Adriana I.

2014-01-01

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a “neck-pinching” boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck’s geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures. PMID:24843162

Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

NASA Astrophysics Data System (ADS)

Barack, Leor

The question of motion in a gravitationally bound two-body system is a longstanding open problem of General Relativity. When the mass ratio eta; is small, the problem lends itself to a perturbative treatment, wherein corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in η, using the language of an effective gravitational self-force. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will give a brief survey of this activity and its achievements so far, and will identify the challenges that lie ahead. As concrete examples, I will discuss recent calculations of certain conservative post-geodesic effects of the self-force, including the O(η ) correction to the precession rate of the periastron. I will highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alani, Ivo; Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar

In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruencemore » emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.« less

Pulmonary parenchyma segmentation in thin CT image sequences with spectral clustering and geodesic active contour model based on similarity

NASA Astrophysics Data System (ADS)

He, Nana; Zhang, Xiaolong; Zhao, Juanjuan; Zhao, Huilan; Qiang, Yan

2017-07-01

While the popular thin layer scanning technology of spiral CT has helped to improve diagnoses of lung diseases, the large volumes of scanning images produced by the technology also dramatically increase the load of physicians in lesion detection. Computer-aided diagnosis techniques like lesions segmentation in thin CT sequences have been developed to address this issue, but it remains a challenge to achieve high segmentation efficiency and accuracy without much involvement of human manual intervention. In this paper, we present our research on automated segmentation of lung parenchyma with an improved geodesic active contour model that is geodesic active contour model based on similarity (GACBS). Combining spectral clustering algorithm based on Nystrom (SCN) with GACBS, this algorithm first extracts key image slices, then uses these slices to generate an initial contour of pulmonary parenchyma of un-segmented slices with an interpolation algorithm, and finally segments lung parenchyma of un-segmented slices. Experimental results show that the segmentation results generated by our method are close to what manual segmentation can produce, with an average volume overlap ratio of 91.48%.

Tidal stresses and energy gaps in microstate geometries

NASA Astrophysics Data System (ADS)

Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.

2018-02-01

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

NASA Astrophysics Data System (ADS)

Sadiq, Jam; Zlochower, Yosef; Nakano, Hiroyuki

2018-04-01

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.

Complete integrability of geodesics in toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-01-01

We describe a method for constructing Killing-Yano tensors on toric Sasaki- Einstein manifolds using their geometrical properties. We take advantage of the fact that the metric cones of these spaces are Calabi-Yau manifolds. The complete list of special Killing forms can be extracted making use of the description of the Calabi-Yau manifolds in terms of toric data. This general procedure for toric Sasaki-Einstein manifolds is exemplified in the case of the 5-dimensional spaces Yp,q and T1,1. Finally we discuss the integrability of geodesic motion in these spaces.

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

Arcmancer: Geodesics and polarized radiative transfer library

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.

2018-05-01

Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.

From GLC to double-null coordinates and illustration with static black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nugier, Fabien, E-mail: fnugier@ntu.edu.tw

We present a system of coordinates deriving directly from the so-called Geodesic Light-Cone (GLC) coordinates and made of two null scalars intersecting on a 2-dimensional sphere parameterized by two constant angles along geodesics. These coordinates are shown to be equivalent to the well-known double-null coordinates. As GLC, they present interesting properties for cosmology and astrophysics. We discuss this latter topic for static black holes, showing simple descriptions for the metric or particles and photons trajectories. We also briefly comment on the time of flight of ultra-relativistic particles.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X. Q.; Xiong, Z.; Nevins, W. M.

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon} scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Gao, Z.; Nevins, W. M.; McKee, G. R.

2008-05-01

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio γ scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Analytical collisionless damping rate of geodesic acoustic mode

NASA Astrophysics Data System (ADS)

Ren, H.; Xu, X. Q.

2016-10-01

Collisionless damping of geodesic acoustic mode (GAM) is analytically investigated by considering the finite-orbit-width (FOW) resonance effect to the 3rd order in the gyro-kinetic equations. A concise and transparent expression for the damping rate is presented for the first time. Good agreement is found between the analytical damping rate and the previous TEMPEST simulation result (Xu 2008 et al Phys. Rev. Lett. 100 215001) for systematic q scans. Our result also shows that it is of sufficient accuracy and has to take into account the FOW effect to the 3rd order.

TEMPEST simulations of collisionless damping of the geodesic-acoustic mode in edge-plasma pedestals.

PubMed

Xu, X Q; Xiong, Z; Gao, Z; Nevins, W M; McKee, G R

2008-05-30

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes

NASA Astrophysics Data System (ADS)

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.

Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan

2017-06-01

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure pc to the central energy density ρc, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N in (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number l > 50, while for smaller values of l the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N >= 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10-3 of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linearmore » perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.« less

Deployable geodesic truss structure

NASA Technical Reports Server (NTRS)

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.

OPTOELECTRONICS, FIBER OPTICS, AND OTHER ASPECTS OF QUANTUM ELECTRONICS: Integrated-optical spectrum analyzer based on Ti:LiNbO3 with an optimized system of interdigital transducers and spherical geodesic lenses

NASA Astrophysics Data System (ADS)

Golovanova, T. M.; Gryaznov, Yu M.; Dianov, Evgenii M.; Dobryakova, N. G.; Kiselev, A. V.; Prokhorov, A. M.; Shcherbakov, E. A.

1989-08-01

An investigation was made of the parameters of an integrated-optical spectrum analyzer consisting of a Ti:LiNbO3 crystal and a semiconductor laser with a built-in microobjective, spherical geodesic lenses, and an optimized system of interdigital (opposed-comb) transducers. The characteristics of this spectrum analyzer were as follows: the band of operating frequencies was 181 MHz (at the 3 dB level); the resolution was 2.8 MHz; the signal/noise ratio (under a control voltage of 4 V) was 20 dB.

TEMPEST Simulations of Collisionless Damping of Geodesic-Acoustic Mode in Edge Plasma Pedestal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X; Xiong, Z; Nevins, W

The fully nonlinear 4D TEMPEST gyrokinetic continuum code produces frequency, collisionless damping of geodesic-acoustic mode (GAM) and zonal flow with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon}-scan and the tokamak safety factor q-scan in homogeneous plasmas. The TEMPEST simulation shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude.

Investigation of energetic particle induced geodesic acoustic mode

NASA Astrophysics Data System (ADS)

Schneller, Mirjam; Fu, Guoyong; Chavdarovski, Ilija; Wang, Weixing; Lauber, Philipp; Lu, Zhixin

2017-10-01

Energetic particles are ubiquitous in present and future tokamaks due to heating systems and fusion reactions. Anisotropy in the distribution function of the energetic particle population is able to excite oscillations from the continuous spectrum of geodesic acoustic modes (GAMs), which cannot be driven by plasma pressure gradients due to their toroidally and nearly poloidally symmetric structures. These oscillations are known as energetic particle-induced geodesic acoustic modes (EGAMs) [G.Y. Fu'08] and have been observed in recent experiments [R. Nazikian'08]. EGAMs are particularly attractive in the framework of turbulence regulation, since they lead to an oscillatory radial electric shear which can potentially saturate the turbulence. For the presented work, the nonlinear gyrokinetic, electrostatic, particle-in-cell code GTS [W.X. Wang'06] has been extended to include an energetic particle population following either bump-on-tail Maxwellian or slowing-down [Stix'76] distribution function. With this new tool, we study growth rate, frequency and mode structure of the EGAM in an ASDEX Upgrade-like scenario. A detailed understanding of EGAM excitation reveals essential for future studies of EGAM interaction with micro-turbulence. Funded by the Max Planck Princeton Research Center. Computational resources of MPCDF and NERSC are greatefully acknowledged.

On the transformations of the dynamical equations

NASA Astrophysics Data System (ADS)

Levi-Civita, T.

2009-08-01

In this issue we bring to the reader’s attention a translation of Levi-Civita’s work “Sulle trasformazioni delle equazioni dinamiche”. This paper, written by Levi-Civita at the onset of his career, is remarkable in many respects. Both the main result and the method developed in the paper brought the author in line with the greatest mathematicians of his day and seriously influenced the further progress of geometry and the theory of integrable systems. Speaking modern language the main result of his paper is the deduction of the general geodesic equivalence equation in invariant form and local classification of geodesically equivalent Riemannian metrics in the case of arbitrary dimension, i.e., metrics having the same geodesics considered as unparameterized curves (this classification problem was formulated by Beltrami in 1865). Levi-Civita’s work produced a great impact on further development of the theory of geodesically equivalent metrics and geodesic mappings, and still remains one of the most important tools in this area of differential geometry. In this paper the author uses a new method based on the concept of Riemannian connection, which later has been also referred to as the Levi-Civita connection. This paper is truly a pioneering work in the sense that the real power of covariant differentiation techniques in solving a concrete and highly nontrivial problem from the theory of dynamical systems was demonstrated. The author skillfully operates and weaves together many of the most advanced (for that times) algebraic, geometric and analytic methods. Moreover, an attentive reader can also notice several forerunning ideas of the method of moving frames, which was developed a few decades later by E. Cartan. We hope that the reader will appreciate the style of exposition as well. This work, focused on the essence of the problem and free of manipulation with abstract mathematical terms, is a good example of a classical text of the late 19th century. Owing to this, the paper is easy to read and understand in spite of some different notation and terminology. The Editorial Board is very grateful to Professor Sergio Benenti for the translation of the original Italian text and valuable comments (see marginal notes at the end of the text, p. 612).

Quantum Computational Geodesics

DTIC Science & Technology

2010-01-01

dtU (t)†  unvec κt   t ∫ 0 drκ−1r vec C(r...U(t). (209) If J(T ) = 0 in equation 209, then d dt J(0) = j−1T   T ∫ 0 dtU (t)†  unvec κt   t ∫ 0 drκ−1r vec C(r)    U(t)   . (210...equation 211, one obtains the so-called geodesic derivative (1) d dq Hq(0) = j −1 T   T ∫ 0 dtU (t)†unvec   κt   t ∫ 0 drκ−1r vec C(r)   

VizieR Online Data Catalog: ynogkm: code for calculating time-like geodesics (Yang+, 2014)

NASA Astrophysics Data System (ADS)

Yang, X.-L.; Wang, J.-C.

2013-11-01

Here we present the source file for a new public code named ynogkm, aim on calculating the time-like geodesics in a Kerr-Newmann spacetime fast. In the code the four Boyer-Lindquis coordinates and proper time are expressed as functions of a parameter p semi-analytically, i.e., r(p), μ(p), φ(p), t(p), and σ(p), by using the Weiers- trass' and Jacobi's elliptic functions and integrals. All of the ellip- tic integrals are computed by Carlson's elliptic integral method, which guarantees the fast speed of the code.The source Fortran file ynogkm.f90 contains three modules: constants, rootfind, ellfunction, and blcoordinates. (3 data files).

Influence of a weak gravitational wave on a bound system of two point-masses. [of binary stars

NASA Technical Reports Server (NTRS)

Turner, M. S.

1979-01-01

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Pragmatic approach to gravitational radiation reaction in binary black holes

PubMed

Lousto

2000-06-05

We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into l multipoles to show that all l-metric coefficients are C0 at the location of the particle. Summing over l, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's zeta-function regularization scheme and numerically compute the first-order geodesics.

Witten diagrams revisited: the AdS geometry of conformal blocks

DOE PAGES

Hijano, Eliot; Kraus, Per; Perlmutter, Eric; ...

2016-01-25

Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram", which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we also consider the case of four-point functions of scalar operators, and show how to easily reproduce existingmore » results for the relevant conformal blocks in arbitrary dimension.« less

A type N radiation field solution with Λ <0 in a curved space-time and closed time-like curves

NASA Astrophysics Data System (ADS)

Ahmed, Faizuddin

2018-05-01

An anti-de Sitter background four-dimensional type N solution of the Einstein's field equations, is presented. The matter-energy content pure radiation field satisfies the null energy condition (NEC), and the metric is free-from curvature divergence. In addition, the metric admits a non-expanding, non-twisting and shear-free geodesic null congruence which is not covariantly constant. The space-time admits closed time-like curves which appear after a certain instant of time in a causally well-behaved manner. Finally, the physical interpretation of the solution, based on the study of the equation of the geodesics deviation, is analyzed.

Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-06-01

We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.

Active motion on curved surfaces

NASA Astrophysics Data System (ADS)

Castro-Villarreal, Pavel; Sevilla, Francisco J.

2018-05-01

A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the telegrapher equation. Such a generalized equation is explicitly derived as the polar approximation of the hierarchy of equations obtained from the corresponding Fokker-Planck equation of active particles diffusing on curved surfaces. The general solution to the generalized telegrapher equation is given for a pulse with vanishing current as initial data. Expressions for the probability density and the mean squared geodesic displacement are given in the limit of weak curvature. As an explicit example of the formulated theory, the case of active motion on the sphere is presented, where oscillations observed in the mean squared geodesic displacement are explained.

Geodesic least squares regression on information manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be

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 thismore » to scaling laws in magnetic confinement fusion.« less

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

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 standardmore » least squares.« less

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

Quantum healing of spacetime singularities: A review

NASA Astrophysics Data System (ADS)

Konkowski, D. A.; Helliwell, T. M.

2018-02-01

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karch, Andreas; Sato, Yoshiki

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams whichmore » exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.« less

Optimum design of Geodesic dome’s jointing system

NASA Astrophysics Data System (ADS)

Tran, Huy. T.

2018-04-01

This study attempts to create a new design for joint connector of Geodesic dome. A new type of joint connector design is proposed for flexible rotating connection; comparing it to another, this design is cheaper and workable. After calculating the bearing capacity of the sample according to EC3 and Vietnam standard TCVN 5575-2012, FEM model of the design sample is carried out in many specific situation to consider the stress distribution, the deformation, the local destruction… in the connector. The analytical results and the FE data are consistent. The FE analysis also points out the behavior of some details that simple calculation cannot show. Hence, we can choose the optimum design of joint connector.

Fractal spectral triples on Kellendonk's C∗-algebra of a substitution tiling

NASA Astrophysics Data System (ADS)

Mampusti, Michael; Whittaker, Michael F.

2017-02-01

We introduce a new class of noncommutative spectral triples on Kellendonk's C∗-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is θ-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.

Rapid geodesic mapping of brain functional connectivity: implementation of a dedicated co-processor in a field-programmable gate array (FPGA) and application to resting state functional MRI.

PubMed

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. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

Planning maximally smooth hand movements constrained to nonplanar workspaces.

PubMed

Liebermann, Dario G; Krasovsky, Tal; Berman, Sigal

2008-11-01

The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.

Design and evaluation of a foam-filled hat-stiffened panel concept for aircraft primary structural applications

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.

1993-01-01

Geodesically stiffened structures are very efficient in carrying combined bending, torsion, and pressure loading that is typical of primary aircraft structures. They are also very damage tolerant since there are multiple load paths available to redistribute loads compared to prismatically stiffened structures. Geodesically stiffened structures utilize continuous filament composite materials which make them amenable to automated manufacturing processes to reduce cost. The current practice for geodesically stiffened structures is to use a solid blade construction for the stiffener. This stiffener configuration is not an efficient concept and there is a need to identify other stiffener configurations that are more efficient but utilize the same manufacturing process as the solid blade. This paper describes a foam-filled stiffener cross section that is more efficient than a solid-blade stiffener in the load range corresponding to primary aircraft structures. A prismatic hat-stiffener panel design is then selected for structural evaluation in uni-axial compression with and without impact damage. Experimental results for both single stiffener specimens and multi-stiffener panel specimens are presented. Finite element analysis results are presented that predict the buckling and postbuckling response of the test specimens. Analytical results for both the element and panel specimens are compared with experimental results.

Evaluation of five diffeomorphic image registration algorithms for mouse brain magnetic resonance microscopy.

PubMed

Fu, Zhenrong; Lin, Lan; Tian, Miao; Wang, Jingxuan; Zhang, Baiwen; Chu, Pingping; Li, Shaowu; Pathan, Muhammad Mohsin; Deng, Yulin; Wu, Shuicai

2017-11-01

The development of genetically engineered mouse models for neuronal diseases and behavioural disorders have generated a growing need for small animal imaging. High-resolution magnetic resonance microscopy (MRM) provides powerful capabilities for noninvasive studies of mouse brains, while avoiding some limits associated with the histological procedures. Quantitative comparison of structural images is a critical step in brain imaging analysis, which highly relies on the performance of image registration techniques. Nowadays, there is a mushrooming growth of human brain registration algorithms, while fine-tuning of those algorithms for mouse brain MRMs is rarely addressed. Because of their topology preservation property and outstanding performance in human studies, diffeomorphic transformations have become popular in computational anatomy. In this study, we specially tuned five diffeomorphic image registration algorithms [DARTEL, geodesic shooting, diffeo-demons, SyN (Greedy-SyN and geodesic-SyN)] for mouse brain MRMs and evaluated their performance using three measures [volume overlap percentage (VOP), residual intensity error (RIE) and surface concordance ratio (SCR)]. Geodesic-SyN performed significantly better than the other methods according to all three different measures. These findings are important for the studies on structural brain changes that may occur in wild-type and transgenic mouse brains. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

YNOGK: A New Public Code for Calculating Null Geodesics in the Kerr Spacetime

NASA Astrophysics Data System (ADS)

Yang, Xiaolin; Wang, Jiancheng

2013-07-01

Following the work of Dexter & Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter & Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham & Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/~yangxl/yxl.html.

Micromirror arrays using KOH:H[sub 2]O micromachining of silicon for lens templates, geodesic lenses, and other applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kendall, D.L.; Eaton, W.P.; Manginell, R.

Micromirrors having diameters from a few micrometers to several millimeters have been produced on (100) silicon by wet-chemical etching in KOH:H[sub 2]O. The f/[number sign]'s range from about 2.5 to at least 10. The microroughness of an etched mirror with diameter 550 [mu]m and 9.6-[mu]m sagitta is less than 5 nm and its surface figure is within 0.5 [mu]m of a perfect sphere. Data over a wide range of diameters are presented and a semiempirical model is developed to explain the behavior. The concordance of the normalized etched profiles for all diameter mirrors demonstrates that the etching is dominated bymore » surface reaction rather than diffusion limitation. Design and fabrication schemes are presented for making a wide range of mirror diameters and focal lengths, for both single micromirrors and arrays. The etched depressions can be used as templates for microlenses and as substrates for geodesic waveguide lenses and arrays. Chem-mechanical polishing on the etched structures reduces the edge curvature and produces oblate spheroidal surfaces, both of which should improve geodesic lens behavior. The etched structures can also be used as variable crystal orientation substrates for epitaxial nucleation and various surface analysis studies.« less

Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications

NASA Astrophysics Data System (ADS)

Kendall, Don L.; Eaton, William P.; Manginell, Ronald P.; Digges, Thomas G.

1994-11-01

Micromirrors having diameters from a few micrometers to several millimeters have been produced on (100) silicon by wet-chemical etching in KOH:H2O. The f/#'s range from about 2.5 to at least 10. The microroughness of an etched mirror with diameter 550 micrometers and 9.6-micrometers sagitta is less than 5 nm and its surface figure is within 0.5 micrometers of a perfect sphere. Data over a wide range of diameters are presented and a semiempirical model is developed to explain the behavior. The concordance of the normalized etched profiles for all diameter mirrors demonstrates that the etching is dominated by surface reaction rather than diffusion limitation. Design and fabrication schemes are presented for making a wide range of mirror diameters and focal lengths, for both single micromirrors and arrays. The etched depressions can be used as templates for microlenses and as substrates for geodesic waveguide lenses and arrays. Chem-mechanical polishing on the etched structures reduces the edge curvature and produces oblate spheroidal surfaces, both of which should improve geodesic lens behavior. The etched structures can also be used as variable crystal orientation substrates for epitaxial nucleation and various surface analysis studies.

Structure of the effective potential for a spherical wormhole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Montelongo Garcia, N.; Zannias, T.

2008-09-15

The structure of the effective potential V describing causal geodesics near the throat of an arbitrary spherical wormhole is analyzed. Einstein's equations relative to a set of regular coordinates covering a vicinity of the throat imply that any spherical wormhole can be constructed from solutions of an effective initial value problem with the throat serving as an initial value surface. The initial data involve matter variables, the area A(0) of the throat, and the gradient {lambda}(0) of the redshift factor on the throat. Whenever {lambda}(0)=0, the effective potential V has a critical point on the throat. Conditions upon the datamore » are derived ensuring that the critical point is a local minimum (respectively maximum). For particular families of quasi-Schwarzschild wormholes, V exhibits a local minimum on the throat independently upon the energy E and angular momentum L{sup 2} of the test particles and thus such wormholes admit stable circular timelike and null geodesics on the throat. For families of Chaplygin wormholes, we show that such geodesics are unstable. Based on a suitable power series representation of the metric, properties of V away from the throat are obtained that are useful for the analysis of accretion disks and radiation processes near the throat of any spherical wormhole.« less

Shaping of arm configuration space by prescription of non-Euclidean metrics with applications to human motor control

NASA Astrophysics Data System (ADS)

Biess, Armin

2013-01-01

The study of the kinematic and dynamic features of human arm movements provides insights into the computational strategies underlying human motor control. In this paper a differential geometric approach to movement control is taken by endowing arm configuration space with different non-Euclidean metric structures to study the predictions of the generalized minimum-jerk (MJ) model in the resulting Riemannian manifold for different types of human arm movements. For each metric space the solution of the generalized MJ model is given by reparametrized geodesic paths. This geodesic model is applied to a variety of motor tasks ranging from three-dimensional unconstrained movements of a four degree of freedom arm between pointlike targets to constrained movements where the hand location is confined to a surface (e.g., a sphere) or a curve (e.g., an ellipse). For the latter speed-curvature relations are derived depending on the boundary conditions imposed (periodic or nonperiodic) and the compatibility with the empirical one-third power law is shown. Based on these theoretical studies and recent experimental findings, I argue that geodesics may be an emergent property of the motor system and that the sensorimotor system may shape arm configuration space by learning metric structures through sensorimotor feedback.

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

PubMed

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, spectral integral-iteration algorithms and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases, Schnetter's "pretracking" algorithm can greatly improve an elliptic-PDE algorithm's robustness. Flow algorithms are generally quite slow but can be very robust in their convergence. Minimization methods are slow and relatively inaccurate in the context of a finite differencing simulation, but in a spectral code they can be relatively faster and more robust.

F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

NASA Astrophysics Data System (ADS)

Karney, C. F. F.; Deakin, R. E.

2010-08-01

Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3 cm over distances in excess of 1000 km (and the method remains accurate for geodesics that encircle the Earth). Despite the use of logarithms, Bessel's numerical methods are surprisingly up-to-date: he writes out his series in a form that allows them to be extended to any order and he carries out a rather detailed analysis of the numerical errors. Bessel's derivation and tables were extensively used throughout the nineteenth century and many twentieth century works continued to refer to ``Bessel's method''. However, over time, the attributions to Bessel have become diluted as authors cite more recent works. This trend accelerated with the introduction of electronic calculators when Bessel's algorithms were thought to be too complex and simpler less accurate ones were substituted (these approximate algorithms are still in widespread use). However, now that floating-point hardware is fast and accurate, it is these later algorithms that often seem outdated, while Bessel's are easily adapted for implementation on modern computers.

Positive-entropy Hamiltonian systems on Nilmanifolds via scattering

NASA Astrophysics Data System (ADS)

Butler, Leo T.

2014-10-01

Let Σ be a compact quotient of T4, the Lie group of 4 × 4 upper triangular matrices with unity along the diagonal. The Lie algebra {\\mathfrak t}4 of T4 has the standard basis {Xij} of matrices with 0 everywhere but in the (i, j) entry, which is unity. Let g be the Carnot metric, a sub-Riemannian metric, on T4 for which Xi, i+1, (i = 1, 2, 3), is an orthonormal basis. Montgomery, Shapiro and Stolin showed that the geodesic flow of g is algebraically non-integrable. This paper proves that the geodesic flow of that Carnot metric on TΣ has positive topological entropy and its Euler field is real-analytically non-integrable. It extends earlier work by Butler and Gelfreich.

Boundary holographic Witten diagrams

DOE PAGES

Karch, Andreas; Sato, Yoshiki

2017-09-25

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams whichmore » exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.« less

Methods of Information Geometry to model complex shapes

NASA Astrophysics Data System (ADS)

De Sanctis, A.; Gattone, S. A.

2016-09-01

In this paper, a new statistical method to model patterns emerging in complex systems is proposed. A framework for shape analysis of 2- dimensional landmark data is introduced, in which each landmark is represented by a bivariate Gaussian distribution. From Information Geometry we know that Fisher-Rao metric endows the statistical manifold of parameters of a family of probability distributions with a Riemannian metric. Thus this approach allows to reconstruct the intermediate steps in the evolution between observed shapes by computing the geodesic, with respect to the Fisher-Rao metric, between the corresponding distributions. Furthermore, the geodesic path can be used for shape predictions. As application, we study the evolution of the rat skull shape. A future application in Ophthalmology is introduced.

Rational first integrals of geodesic equations and generalised hidden symmetries

NASA Astrophysics Data System (ADS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-10-01

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.

On the heteroclinic connection problem for multi-well gradient systems

NASA Astrophysics Data System (ADS)

Zuniga, Andres; Sternberg, Peter

2016-10-01

We revisit the existence problem of heteroclinic connections in RN associated with Hamiltonian systems involving potentials W :RN → R having several global minima. Under very mild assumptions on W we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor √{ W}. Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise to a heteroclinic connection between the two wells. This work improves upon the approach of [22] and represents a more geometric alternative to the approaches of e.g. [5,10,14,17] for finding such connections.

Quantum frictionless trajectories versus geodesics

NASA Astrophysics Data System (ADS)

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.

Geodesic-light-cone coordinates and the Bianchi I spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe, E-mail: pierre.fleury@uct.ac.za, E-mail: fnugier@ntu.edu.tw, E-mail: giuseppe.fanizza@ba.infn.it

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;more » and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.« less

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

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.

Vacuum solutions admitting a geodesic null congruence with shear proportional to expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kupeli, A.H.

Algebraically general, nontwisting solutions for the vacuum to vacuum generalized Kerr--Schild (GKS) transformation are obtained. These solutions admit a geodesic null congruence with shear proportional to expansion. In the Newman--Penrose formalism, if l/sup ..mu../ is chosen to be the null vector of the GKS transformation, this property is stated as sigma = arho and Da = 0. It is assumed that a is a constant, and the background is chosen as a pp-wave solution. For generic values of a, the GKS metrics consist of the Kasner solutions. For a = +- (1 +- (2)/sup 1/2/), there are solutions with lessmore » symmetries including special cases of the Kota--Perjes and Lukacs solutions.« less

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Accelerated observers and the notion of singular spacetime

NASA Astrophysics Data System (ADS)

Olmo, Gonzalo J.; Rubiera-Garcia, Diego; Sanchez-Puente, Antonio

2018-03-01

Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from in nity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at in nity with non-zero initial inward velocity; Gautreau-Ho mann (GH) time coordinates are adapted to observers dropped from rest from a nite distance from the black hole horizon. We construct from these an LMP family and a propertime 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 Lema^tre coordinates as well.

Light-cone observables and gauge-invariance in the geodesic light-cone formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and itmore » complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.« less

Structural Analysis of Helios Filament-Wound Tanks Subjected to Internal Pressure and Cooling

NASA Technical Reports Server (NTRS)

Ko, William L

2005-01-01

A finite-element stress analysis is performed on Helios filament-wound hydrogen tanks to examine the stress field and effect of end dome geometry on the stress field. Each tank is composed of a central circular cylindrical section with either geodesic or hemispherical end domes, which have metallic polar bosses. The tanks are subjected to combined and separate internal pressure and temperature loading conditions, and the stress contributions of each loading component are examined. The tank-wall-polar-boss interfacial meridional tensile stress in the hemispherical dome is found to be approximately 27 percent lower than that in the geodesic dome. The effects of both material anisotropy and the aluminum lining on the intensities of tensile meridional stress at the tank-wall-polar-boss bonding interface are examined.

Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haas, Roland

2007-06-15

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a samplemore » of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.« less

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baleanu, Dumitru; Institute of Space Sciences, P.O. Box MG-6, Magurele-Bucharest

The geodesic motion of pseudo-classical spinning particles in extended Euclidean Taub-NUT space was analyzed. The non-generic symmetries of Taub-NUT was investigated. We found new non-generic symmetries in the presence of electromagnetic field like a monopole.

Calculating observables in inhomogeneous cosmologies. Part I: general framework

NASA Astrophysics Data System (ADS)

Hellaby, Charles; Walters, Anthony

2018-02-01

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

Geodesic Distance Algorithm for Extracting the Ascending Aorta from 3D CT Images

PubMed Central

Jang, Yeonggul; Jung, Ho Yub; Hong, Youngtaek; Cho, Iksung; Shim, Hackjoon; Chang, Hyuk-Jae

2016-01-01

This paper presents a method for the automatic 3D segmentation of the ascending aorta from coronary computed tomography angiography (CCTA). The segmentation is performed in three steps. First, the initial seed points are selected by minimizing a newly proposed energy function across the Hough circles. Second, the ascending aorta is segmented by geodesic distance transformation. Third, the seed points are effectively transferred through the next axial slice by a novel transfer function. Experiments are performed using a database composed of 10 patients' CCTA images. For the experiment, the ground truths are annotated manually on the axial image slices by a medical expert. A comparative evaluation with state-of-the-art commercial aorta segmentation algorithms shows that our approach is computationally more efficient and accurate under the DSC (Dice Similarity Coefficient) measurements. PMID:26904151

Projective flatness in the quantisation of bosons and fermions

NASA Astrophysics Data System (ADS)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Geodesics In A Spinning String Spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Culetu, Hristu

2006-11-28

The geodesics equations for a rotating observer in a spinning string geometry are investigated using the Euler - Lagrange equations. For test particles with vanishing angular momentum, the radial equation of motion does not depend on the angular velocity {omega} but on the angular momentum of the string. A massless particle moves tachyonic but iteed tends asymptotically to unit velocity after a time of the order of few Planck time b. The spacetime has a horizon at r = 0, irrespective of the value of {omega} but its angular velocity is given by {omega} - 1/b. The Sagnac time delaymore » is computed proving to depend both on {omega} and the radius of the circular orbit. The velocity of an ingoing massive test particle approaches zero very close to the spinning string, as if it were rejected by it.« less

Global two-fluid simulations of geodesic acoustic modes in strongly shaped tight aspect ratio tokamak plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robinson, J. R.; Hnat, B.; Thyagaraja, A.

2013-05-15

Following recent observations suggesting the presence of the geodesic acoustic mode (GAM) in ohmically heated discharges in the Mega Amp Spherical Tokamak (MAST) [J. R. Robinson et al., Plasma Phys. Controlled Fusion 54, 105007 (2012)], the behaviour of the GAM is studied numerically using the two fluid, global code CENTORI [P. J. Knight et al. Comput. Phys. Commun. 183, 2346 (2012)]. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation, and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matchedmore » to those of MAST. Increasing aspect ratio yields good agreement between the GAM frequency found in the simulations and an analytical result obtained for elongated large aspect ratio plasmas.« less

CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

PubMed Central

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. PMID:21941525

On the Penrose inequality along null hypersurfaces

NASA Astrophysics Data System (ADS)

Mars, Marc; Soria, Alberto

2016-06-01

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a functional on surfaces and studying its properties along a null hypersurface Ω extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawking energy along a specific class of geodesic foliations called Geodesic Asymptotically Bondi (GAB), which are shown to always exist. Whenever this foliation approaches large spheres, this inequality becomes the null Penrose inequality and we recover the results of Ludvigsen-Vickers (1983 J. Phys. A: Math. Gen. 16 3349-53) and Bergqvist (1997 Class. Quantum Grav. 14 2577-83). By exploiting further properties of the functional along general geodesic foliations, we introduce an approach to the null Penrose inequality called the Renormalized Area Method and find a set of two conditions which imply the validity of the null Penrose inequality. One of the conditions involves a limit at infinity and the other a restriction on the spacetime curvature along the flow. We investigate their range of applicability in two particular but interesting cases, namely the shear-free and vacuum case, where the null Penrose inequality is known to hold from the results by Sauter (2008 PhD Thesis Zürich ETH), and the case of null shells propagating in the Minkowski spacetime. Finally, a general inequality bounding the area of the quasi-local black hole in terms of an asymptotic quantity intrinsic of Ω is derived.

Critical phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case

NASA Astrophysics Data System (ADS)

Gundlach, Carsten; Akcay, Sarp; Barack, Leor; Nagar, Alessandro

2012-10-01

In numerical simulations of black hole binaries, Pretorius and Khurana [Classical Quantum Gravity 24, S83 (2007)CQGRDG0264-938110.1088/0264-9381/24/12/S07] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n≃-γln⁡|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent γ. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n∞≃0.41/η, where η is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.

Computing Diffeomorphic Paths for Large Motion Interpolation.

PubMed

Seo, Dohyung; Jeffrey, Ho; Vemuri, Baba C

2013-06-01

In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff (Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff (Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map of Diff (Ω) to the quotient space Diff ( M )/ Diff ( M ) μ obtained by quotienting out the subgroup of volume-preserving diffeomorphisms Diff ( M ) μ . This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).

Cosmic acceleration from matter-curvature coupling

NASA Astrophysics Data System (ADS)

Zaregonbadi, Raziyeh; Farhoudi, Mehrdad

2016-10-01

We consider f( {R,T} ) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory, the coupling energy-momentum tensor is not conserved. However, we mainly focus on a particular model that matter is minimally coupled to the geometry in the metric formalism and wherein, its coupling energy-momentum tensor is also conserved. We obtain the corresponding Raychaudhuri dynamical equation that presents the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can lead to an acceleration phase after the matter dominated phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the motion of the free test particles on their geodesics, and derive the geodesic deviation equation in this modified theory to study the accelerating universe within the spatially flat FLRW background. Actually, this equation gives the relative accelerations of adjacent particles as a measurable physical quantity, and provides an elegant tool to investigate the timelike and the null structures of spacetime geometries. Then, through the null deviation vector, we find the observer area-distance as a function of the redshift for the chosen model, and compare the results with the corresponding results obtained in the literature.

Contraction coefficients for noisy quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hiai, Fumio, E-mail: hiai.fumio@gmail.com; Ruskai, Mary Beth, E-mail: ruskai@member.ams.org

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.

Testing for a cosmological influence on local physics using atomic and gravitational clocks

NASA Technical Reports Server (NTRS)

Adams, P. J.; Hellings, R. W.; Canuto, V. M.; Goldman, I.

1983-01-01

The existence of a possible influence of the large-scale structure of the universe on local physics is discussed. A particular realization of such an influence is discussed in terms of the behavior in time of atomic and gravitational clocks. Two natural categories of metric theories embodying a cosmic infuence exist. The first category has geodesic equations of motion in atomic units, while the second category has geodesic equations of motion in gravitational units. Equations of motion for test bodies are derived for both categories of theories in the appropriate parametrized post-Newtonian limit and are applied to the Solar System. Ranging data to the Viking lander on Mars are of sufficient precision to reveal (1) if such a cosmological influence exists at the level of Hubble's constant, and (2) which category of theories is appropriate for a descripton of the phenomenon.

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Minimal conditions for the existence of a Hawking-like flux

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barcelo, Carlos; Liberati, Stefano; Sonego, Sebastiano

2011-02-15

We investigate the minimal conditions that an asymptotically flat general relativistic spacetime must satisfy in order for a Hawking-like Planckian flux of particles to arrive at future null infinity. We demonstrate that there is no requirement that any sort of horizon form anywhere in the spacetime. We find that the irreducible core requirement is encoded in an approximately exponential 'peeling' relationship between affine coordinates on past and future null infinity. As long as a suitable adiabaticity condition holds, then a Planck-distributed Hawking-like flux will arrive at future null infinity with temperature determined by the e-folding properties of the outgoing nullmore » geodesics. The temperature of the Hawking-like flux can slowly evolve as a function of time. We also show that the notion of peeling of null geodesics is distinct from the usual notion of 'inaffinity' used in Hawking's definition of surface gravity.« less

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

NASA Astrophysics Data System (ADS)

Pu, Jin; Han, Yan

2017-08-01

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek's semiclassical tunneling method.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment

NASA Astrophysics Data System (ADS)

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-01

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

NASA Astrophysics Data System (ADS)

Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

2018-05-01

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment.

PubMed

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-27

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Comprehensive comparisons of geodesic acoustic mode characteristics and dynamics between Tore Supra experiments and gyrokinetic simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.

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 timemore » 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.« less

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Low-Dimensional Statistics of Anatomical Variability via Compact Representation of Image Deformations.

PubMed

Zhang, Miaomiao; Wells, William M; Golland, Polina

2016-10-01

Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

A Time-Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

NASA Astrophysics Data System (ADS)

Vo Van, Thuan

2017-12-01

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time-space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space-time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space-time-matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

Fullerene-like chemistry at the interior carbon atoms of an alkene-centered C26H12 geodesic polyarene.

PubMed

Bronstein, Hindy E; Scott, Lawrence T

2008-01-04

The title compound (1) undergoes 1,2-addition reactions of both electrophilic and nucleophilic reagents preferentially at the "interior" carbon atoms of the central 6:6-bond to give fullerene-type adducts 2, 3, 4, and 5. Such fullerene-like chemistry is unprecedented for a topologically 2-dimensional polycyclic aromatic hydrocarbon and qualifies this geodesic polyarene as a "bridge" between the old flat world of polycyclic aromatic hydrocarbons (PAHs) and the new round world of fullerenes. The relief of pyramidalization strain, as in the addition reactions of fullerenes, presumably contributes to the atypical mode of reactivity seen in 1. Molecular orbital calculations, however, reveal features of the nonalternant pi system in 1 that may also play an important role. Thus, the fullerene-like chemistry of 1 may be driven by two or more factors, the relative importances of which are difficult to discern.

A Review of Depth and Normal Fusion Algorithms

PubMed Central

Štolc, Svorad; Pock, Thomas

2018-01-01

Geometric surface information such as depth maps and surface normals can be acquired by various methods such as stereo light fields, shape from shading and photometric stereo techniques. We compare several algorithms which deal with the combination of depth with surface normal information in order to reconstruct a refined depth map. The reasons for performance differences are examined from the perspective of alternative formulations of surface normals for depth reconstruction. We review and analyze methods in a systematic way. Based on our findings, we introduce a new generalized fusion method, which is formulated as a least squares problem and outperforms previous methods in the depth error domain by introducing a novel normal weighting that performs closer to the geodesic distance measure. Furthermore, a novel method is introduced based on Total Generalized Variation (TGV) which further outperforms previous approaches in terms of the geodesic normal distance error and maintains comparable quality in the depth error domain. PMID:29389903

Holographic definition of points and distances

NASA Astrophysics Data System (ADS)

Czech, Bartłomiej; Lamprou, Lampros

2014-11-01

We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 —the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of nonminimal geodesics.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

NASA Astrophysics Data System (ADS)

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).

Site-selective covalent functionalization at interior carbon atoms and on the rim of circumtrindene, a C36H12 open geodesic polyarene

PubMed Central

Cho, Hee Yeon; Ansems, Ronald B M

2014-01-01

Summary Circumtrindene (6, C36H12), one of the largest open geodesic polyarenes ever reported, exhibits fullerene-like reactivity at its interior carbon atoms, whereas its edge carbons react like those of planar polycyclic aromatic hydrocarbons (PAHs). The Bingel–Hirsch and Prato reactions – two traditional methods for fullerene functionalization – afford derivatives of circumtrindene with one of the interior 6:6 C=C bonds modified. On the other hand, functionalization on the rim of circumtrindene can be achieved by normal electrophilic aromatic substitution, the most common reaction of planar PAHs. This peripheral functionalization has been used to extend the π-system of the polyarene by subsequent coupling reactions and to probe the magnetic environment of the concave/convex space around the hydrocarbon bowl. For both classes of functionalization, computational results are reported to complement the experimental observations. PMID:24991245

Spacetime encodings. IV. The relationship between Weyl curvature and Killing tensors in stationary axisymmetric vacuum spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brink, Jeandrew

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetricmore » noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.« less

Flat monodromies and a Moduli Space Size Conjecture

NASA Astrophysics Data System (ADS)

Hebecker, Arthur; Henkenjohann, Philipp; Witkowski, Lukas T.

2017-12-01

We investigate how super-Planckian axions can arise when type IIB 3-form flux is used to restrict a two-axion field space to a one-dimensional winding trajectory. If one does not attempt to address notoriously complicated issues like Kähler moduli stabilization, SUSY-breaking and inflation, this can be done very explicitly. We show that the presence of flux generates flat monodromies in the moduli space which we therefore call `Monodromic Moduli Space'. While we do indeed find long axionic trajectories, these are non-geodesic. Moreover, the length of geodesics remains highly constrained, in spite of the (finite) monodromy group introduced by the flux. We attempt to formulate this in terms of a `Moduli Space Size Conjecture'. Interesting mathematical structures arise in that the relevant spaces turn out to be fundamental domains of congruence subgroups of the modular group. In addition, new perspectives on inflation in string theory emerge.

Inside out: meet the operators inside the horizon. On bulk reconstruction behind causal horizons

NASA Astrophysics Data System (ADS)

Almheiri, Ahmed; Anous, Tarek; Lewkowycz, Aitor

2018-01-01

Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study the reconstruction of operators behind causal horizons in time dependent geometries obtained by acting with shockwaves on pure states or thermal states. These geometries admit a natural basis of gauge invariant operators, namely those geodesically dressed to the boundary along geodesics which emanate from the bifurcate horizon at constant Rindler time. We outline a procedure for obtaining operators behind the causal horizon but inside the entanglement wedge by exploiting the equality between bulk and boundary time evolution, as well as the freedom to consider the operators evolved by distinct Hamiltonians. This requires we carefully keep track of how the operators are gravitationally dressed and that we address issues regarding background dependence. We compare this procedure to reconstruction using modular flow, and illustrate some formal points in simple cases such as AdS2 and AdS3.

Elementary Development of the Gravitational Self-Force

NASA Astrophysics Data System (ADS)

Detweiler, Steven

The gravitational field of a particle of small mass m moving through curved spacetime, with metric g ab , is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through O(m). One part is an inhomogeneous field h ab S which, near the particle, looks like the Coulomb m / r field with tidal distortion from the local Riemann tensor. This singular field is defined in a neighborhood of the small particle and does not depend upon boundary conditions or upon the behavior of the source in either the past or the future. The other part is a homogeneous field h ab R. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric g ab + h ab R. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

Generalised Eisenhart lift of the Toda chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cariglia, Marco, E-mail: marco@iceb.ufop.br; Gibbons, Gary, E-mail: g.w.gibbons@damtp.cam.ac.uk

The Toda chain of nearest neighbour interacting particles on a line can be described both in terms of geodesic motion on a manifold with one extra dimension, the Eisenhart lift, or in terms of geodesic motion in a symmetric space with several extra dimensions. We examine the relationship between these two realisations and discover that the symmetric space is a generalised, multi-particle Eisenhart lift of the original problem that reduces to the standard Eisenhart lift. Such generalised Eisenhart lift acts as an inverse Kaluza-Klein reduction, promoting coupling constants to momenta in higher dimension. In particular, isometries of the generalised liftmore » metric correspond to energy preserving transformations that mix coordinates and coupling constants. A by-product of the analysis is that the lift of the Toda Lax pair can be used to construct higher rank Killing tensors for both the standard and generalised lift metrics.« less

Clustering of the human skeletal muscle fibers using linear programming and angular Hilbertian metrics.

PubMed

Neji, Radhouène; Besbes, Ahmed; Komodakis, Nikos; Deux, Jean-François; Maatouk, Mezri; Rahmouni, Alain; Bassez, Guillaume; Fleury, Gilles; Paragios, Nikos

2009-01-01

In this paper, we present a manifold clustering method fo the classification of fibers obtained from diffusion tensor images (DTI) of the human skeletal muscle. Using a linear programming formulation of prototype-based clustering, we propose a novel fiber classification algorithm over manifolds that circumvents the necessity to embed the data in low dimensional spaces and determines automatically the number of clusters. Furthermore, we propose the use of angular Hilbertian metrics between multivariate normal distributions to define a family of distances between tensors that we generalize to fibers. These metrics are used to approximate the geodesic distances over the fiber manifold. We also discuss the case where only geodesic distances to a reduced set of landmark fibers are available. The experimental validation of the method is done using a manually annotated significant dataset of DTI of the calf muscle for healthy and diseased subjects.

Unsupervised Classification of PolSAR Data Using a Scattering Similarity Measure Derived From a Geodesic Distance

NASA Astrophysics Data System (ADS)

Ratha, Debanshu; Bhattacharya, Avik; Frery, Alejandro C.

2018-01-01

In this letter, we propose a novel technique for obtaining scattering components from Polarimetric Synthetic Aperture Radar (PolSAR) data using the geodesic distance on the unit sphere. This geodesic distance is obtained between an elementary target and the observed Kennaugh matrix, and it is further utilized to compute a similarity measure between scattering mechanisms. The normalized similarity measure for each elementary target is then modulated with the total scattering power (Span). This measure is used to categorize pixels into three categories i.e. odd-bounce, double-bounce and volume, depending on which of the above scattering mechanisms dominate. Then the maximum likelihood classifier of [J.-S. Lee, M. R. Grunes, E. Pottier, and L. Ferro-Famil, Unsupervised terrain classification preserving polarimetric scattering characteristics, IEEE Trans. Geos. Rem. Sens., vol. 42, no. 4, pp. 722731, April 2004.] based on the complex Wishart distribution is iteratively used for each category. Dominant scattering mechanisms are thus preserved in this classification scheme. We show results for L-band AIRSAR and ALOS-2 datasets acquired over San Francisco and Mumbai, respectively. The scattering mechanisms are better preserved using the proposed methodology than the unsupervised classification results using the Freeman-Durden scattering powers on an orientation angle (OA) corrected PolSAR image. Furthermore, (1) the scattering similarity is a completely non-negative quantity unlike the negative powers that might occur in double- bounce and odd-bounce scattering component under Freeman Durden decomposition (FDD), and (2) the methodology can be extended to more canonical targets as well as for bistatic scattering.

Recruitment and Recommendation of College Students: North Korea.

DTIC Science & Technology

1960-09-14

Journalism, Chinese Literat- ure, Library Science , Russian Language and Literature, Geology, Geodesic Chart Science (Ch’ukchi Chldohak), Planning...History, Philosophy, Library Science , Politi- cal Economy, and Meteorological ^um.unhak/. (f) The Preparatory School for Honor Soldiers. 2. Kim

High-resolution observations of core and suprathermal ions in the auroral ionosphere: Techniques and results from the GEODESIC sounding rocket

NASA Astrophysics Data System (ADS)

Burchill, Johnathan Kerr

Low-energy (Ek ˜ 10-1--10 1 eV) ions comprise the bulk of Earth's ionosphere, and represent the initial stages of ion heating and outflow from Earth's auroral regions. The suprathermal ion imager (SII) is a fast (˜93 images/sec), compact, two-dimensional ion energy (0 < Ek < 20 eV) and direction-of-arrival analyzer designed to observe the energy distributions of these ions in detail, with emphasis on exploring small-scale (˜10--100 m) structure in the ionosphere. The SII was flown into an auroral substorm on the GEODESIC sounding rocket from Poker Flat, Alaska, on 26 February 2000. The technical element of this thesis deals with the development of a computer model of the SII, and techniques for extracting and interpreting physical quantities from the SII observations. Laboratory and in-flight calibrations demonstrate that the analyzer imaging capability departs from the ideal model. Nevertheless, the SII represents a technological step forward, and has yielded new scientific results. The scientific element of this thesis focuses on simultaneous observations of ion energy distributions and low-frequency plasma waves in the topside (500--1000 km) auroral ionosphere. GEODESIC encountered three types of plasma wave which have previously been associated with ion heating. However, heated ions were only observed in association with localized density depletions and wave enhancements known as lower-hybrid solitary structures (LHSS). Approximately 90% of the LHSS ion number density is comprised of the ambient isotropic sub-eV core population. The remaining 10% corresponds to transverse acceleration of ions (TAI) to within 5° transverse to the geomagnetic field and to mean energies up to 5--10 eV, consistent with previous findings. Contrary to previously published observations, the GEODESIC TAI is consistent with localized bulk heating of some of the ambient core. Ion heating was not observed in association with large-scale (>1 km) broadband extremely low frequency (BB ELF) wave enhancements. Similarly, no ion heating was detected in the presence of large amplitude, short perpendicular wavelength Alfven waves. Differences between low-frequency ion flow fluctuations and convection drift fluctuations can be explained only partially by ion polarization drift physics.

Map Projection Induced Variations in Locations of Polygon Geofence Edges

NASA Technical Reports Server (NTRS)

Neeley, Paula; Narkawicz, Anthony

2017-01-01

This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.

Motion4D-library extended

NASA Astrophysics Data System (ADS)

Müller, Thomas

2011-06-01

The new version of the Motion4D-library now also includes the integration of a Sachs basis and the Jacobi equation to determine gravitational lensing of pointlike sources for arbitrary spacetimes.New version program summaryProgram title: Motion4D-libraryCatalogue identifier: AEEX_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 219 441No. of bytes in distributed program, including test data, etc.: 6 968 223Distribution format: tar.gzProgramming language: C++Computer: All platforms with a C++ compilerOperating system: Linux, WindowsRAM: 61 MbytesClassification: 1.5External routines: Gnu Scientic Library (GSL) (http://www.gnu.org/software/gsl/)Catalogue identifier of previous version: AEEX_v2_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 703Does the new version supersede the previous version?: YesNature of problem: Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes. Determine gravitational lensing by integration of Jacobi equation and parallel transport of Sachs basis.Solution method: Integration of ordinary differential equations.Reasons for new version: The main novelty of the current version is the extension to integrate the Jacobi equation and the parallel transport of the Sachs basis along null geodesics. In combination, the change of the cross section of a light bundle and thus the gravitational lensing effect of a spacetime can be determined. Furthermore, we have implemented several new metrics.Summary of revisions: The main novelty of the current version is the integration of the Jacobi equation and the parallel transport of the Sachs basis along null geodesics. The corresponding set of equations readd2xμdλ2=-Γρσμdxρdλdxσdλ, ds1,2μdλ=-Γρσμdxρdλs1,2σ, d2Y1,2μdλ2=-2ΓρσμdxρdλdY1,2σdλ-Γρσ,νμdxρdλdxσdλYν, where (1) is the geodesic equation, (2) represents the parallel transport of the two Sachs basis vectors s, and (3) is the Jacobi equation for the two Jacobi fields Y.The initial directions of the Sachs basis vectors s=(0,s)=s1,2μ∂ are defined perpendicular to the initial direction υ→ of the light ray, see also Fig. 1,s=(-, s=(-. Display OmittedA congruence of null geodesics with central null geodesic γ which starts at the observer O with an infinitesimal circular cross section is defined by the above mentioned two Jacobi fields with initial conditions Y1,2μ|=0 and (dY1,2μ/dλ)|=s1,2μ. The cross section of this congruence along γ is described by the Jacobian J(λ)=gYiμsjν|. However, to determine the gravitational lensing of a pointlike source S that is connected to the observer via γ, we need the reverse Jacobian JS. Fortunately, the reverse Jacobian is just the negative transpose of the original Jacobian JO,J:=JS=-(J)T. The Jacobian J transforms the circular shape of the congruence into an ellipse whose shape parameters (M: major/minor axis, ψ: angle of major axis, ɛ: ellipticity) readM=2αsinζcosζ-βsin2ζ+J112+J212, ψ=arctan2(Jcosζ+Jsinζ,Jcosζ+Jsinζ), ɛ=‖M-M‖‖M+M‖ withζ=12arctan2αβ,ζ=ζ+π2, and the parameters α=JJ+JJ, β=J112-J122+J212-J222. The magnification factor is given byμ=λ2MM. These shape parameters can be easily visualized in the new version of the GeodesicViewer, see Ref. [1]. A detailed discussion of gravitational lensing can be found, for example, in Schneider et al. [2].In the following, a list of newly implemented metrics is given:BertottiKasner: see Rindler [3].BesselGravWaveCart: gravitational Bessel wave from Kramer [4].DeSitterUniv, DeSitterUnivConf: de Sitter universe in Cartesian and conformal coordinates.Ernst: Black hole in a magnetic universe by Ernst [5].ExtremeReissnerNordstromDihole: see Chandrasekhar [6].HalilsoyWave: see Ref. [7].JaNeWi: Janis-Newman-Winicour metric, see Ref. [8].MinkowskiConformal: Minkowski metric in conformally rescaled coordinates.PTD_AI, PTD_AII, PTD_AIII, PTD_BI, PTD_BII, PTD_BIII, PTD_C Petrov-Type D - Levi-Civita spacetimes, see Ref. [7].PainleveGullstrand: Schwarzschild metric in Painlevé-Gullstrand coordinates, see Ref. [9].PlaneGravWave: Plane gravitational wave, see Ref. [10].SchwarzschildIsotropic: Schwarzschild metric in isotropic coordinates, see Ref. [11].SchwarzschildTortoise: Schwarzschild metric in tortoise coordinates, see Ref. [11].Sultana-Dyer: A black hole in the Einstein-de Sitter universe by Sultana and Dyer [12].TaubNUT: see Ref. [13]. The Christoffel symbols and the natural local tetrads of these new metrics are given in the Catalogue of Spacetimes, Ref. [14].To study the behavior of geodesics, it is often useful to determine an effective potential like in classical mechanics. For several metrics, we followed the Euler-Lagrangian approach as described by Rindler [10] and implemented an effective potential for a specific situation. As an example, consider the Lagrangian L=-αt˙+α-1r˙+r2φ˙ for timelike geodesics in the ϑ=π/2 hypersurface in the Schwarzschild spacetime with α=1-2m/r. The Euler-Lagrangian equations lead to the energy balance equation r˙+V(r)=k2 with the effective potential V(r)=(r-2m)(r2+h2)/r3 and the constants of motion k=αt˙ and h=r2φ˙. The constants of motion for a timelike geodesic that starts at (r=10m,φ=0) with initial direction ξ=π/4 with respect to the black hole direction and with initial velocity β=0.7 read k≈1.252 and h≈6.931. Then, from the energy balance equation we immediately obtain the radius of closest approach r≈5.927.Beside a standard Runge-Kutta fourth-order integrator and the integrators of the Gnu Scientific Library (GSL), we also implemented a standard Bulirsch-Stoer integrator.Running time: The test runs provided with the distribution require only a few seconds to run.References:T. Müller, New version announcement to the GeodesicViewer, http://cpc.cs.qub.ac.uk/summaries/AEFP_v2_0.html.P. Schneider, J. Ehlers, E. E. Falco, Gravitational Lenses, Springer, 1992.W. Rindler, Phys. Lett. A 245 (1998) 363.D. Kramer, Ann. Phys. 9 (2000) 331.F.J. Ernst, J. Math. Phys. 17 (1976) 54.S. Chandrasekhar, Proc. R. Soc. Lond. A 421 (1989) 227.H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of the Einstein Field Equations, Cambridge University Press, 2009.A.I. Janis, E.T. Newman, J. Winicour, Phys. Rev. Lett. 20 (1968) 878.K. Martel, E. Poisson, Am. J. Phys. 69 (2001) 476.W. Rindler, Relativity - Special, General, and Cosmology, Oxford University Press, Oxford, 2007.C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, W.H. Freeman, 1973.J. Sultana, C.C. Dyer, Gen. Relativ. Gravit. 37 (2005) 1349.D. Bini, C. Cherubini, Robert T. Jantzen, Class. Quantum Grav. 19 (2002) 5481.T. Muller, F. Grave, arXiv:0904.4184 [gr-qc].

Project COLD.

ERIC Educational Resources Information Center

Kazanjian, Wendy C.

1982-01-01

Describes Project COLD (Climate, Ocean, Land, Discovery) a scientific study of the Polar Regions, a collection of 35 modules used within the framework of existing subjects: oceanography, biology, geology, meterology, geography, social science. Includes a partial list of topics and one activity (geodesic dome) from a module. (Author/SK)

Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group

NASA Astrophysics Data System (ADS)

Ardentov, Andrei A.; Sachkov, Yuri L.

2017-12-01

We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

NASA Astrophysics Data System (ADS)

Urbanec, M.; Török, G.; Šrámková, E.; Čech, P.; Stuchlík, Z.; Bakala, P.

2010-11-01

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius RNS is larger than the related radius of the marginally stable circular orbit rms for nuclear matter equations of state and spin frequencies up to 800 Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius is RNS ˜ rms. The “Paczyński modulation” mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below 1 M⊙, and spin frequencies above 800 Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.

Point Picking and Distributing on the Disc and Sphere

DTIC Science & Technology

2015-07-01

interesting application of geodesic subdivision is the design of domes, buildings, and structures (e.g., Spaceship Earth14 at Epcot, Walt Disney World; the...Computational Geometry in C. Cambridge (United Kingdom): Cambridge University Press; 1993. 41 14. Spaceship Earth. Walt Disney World; [accessed 2014

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Progress in Mathematical Programming.

DTIC Science & Technology

1987-03-04

Philip Gill, Neal Glassman, Donald Goldfarb, Clovis Gonzaga, Harvey Greenberg , Peter Gritzmann, James K. Ho, Alan Hoffman, T. C. Hu, Hiroshi Imai...polar polytope P’ if 0 E P. The image trajectories are geodesics of a projectively invariant geometry on P 0 , Hilbert geometry. This work relates

Canonical Formulation of Supermechanics

NASA Astrophysics Data System (ADS)

Matsumoto, S.

1990-07-01

The canonical formulation of a theory of dynamical systems with both Grassmann even and odd variables is investigated. The sufficient condition for the system being analytically solvable is given. The geodesic motion of a particle in the super Poincaré upper half plane is solved as an example.

Metrisability of Painlevé equations

NASA Astrophysics Data System (ADS)

Contatto, Felipe; Dunajski, Maciej

2018-02-01

We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ordinary differential equations with the Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.

Segmented strings in AdS 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Callebaut, Nele; Gubser, Steven S.; Samberg, Andreas

We study segmented strings in flat space and in AdS 3. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In AdS 3, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an AdS 2 subspace of AdS 3. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We studymore » several examples of closed segmented strings in AdS 3 and find an unexpected quasi-periodic behavior. Here, we also work out a WKB analysis of quantum states of yo-yo strings in AdS 5 and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.« less

Segmented strings in AdS 3

DOE PAGES

Callebaut, Nele; Gubser, Steven S.; Samberg, Andreas; ...

2015-11-17

We study segmented strings in flat space and in AdS 3. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In AdS 3, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an AdS 2 subspace of AdS 3. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We studymore » several examples of closed segmented strings in AdS 3 and find an unexpected quasi-periodic behavior. Here, we also work out a WKB analysis of quantum states of yo-yo strings in AdS 5 and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.« less

A Global Covariance Descriptor for Nuclear Atypia Scoring in Breast Histopathology Images.

PubMed

Khan, Adnan Mujahid; Sirinukunwattana, Korsuk; Rajpoot, Nasir

2015-09-01

Nuclear atypia scoring is a diagnostic measure commonly used to assess tumor grade of various cancers, including breast cancer. It provides a quantitative measure of deviation in visual appearance of cell nuclei from those in normal epithelial cells. In this paper, we present a novel image-level descriptor for nuclear atypia scoring in breast cancer histopathology images. The method is based on the region covariance descriptor that has recently become a popular method in various computer vision applications. The descriptor in its original form is not suitable for classification of histopathology images as cancerous histopathology images tend to possess diversely heterogeneous regions in a single field of view. Our proposed image-level descriptor, which we term as the geodesic mean of region covariance descriptors, possesses all the attractive properties of covariance descriptors lending itself to tractable geodesic-distance-based k-nearest neighbor classification using efficient kernels. The experimental results suggest that the proposed image descriptor yields high classification accuracy compared to a variety of widely used image-level descriptors.

Geometrical structure of Neural Networks: Geodesics, Jeffrey's Prior and Hyper-ribbons

NASA Astrophysics Data System (ADS)

Hayden, Lorien; Alemi, Alex; Sethna, James

2014-03-01

Neural networks are learning algorithms which are employed in a host of Machine Learning problems including speech recognition, object classification and data mining. In practice, neural networks learn a low dimensional representation of high dimensional data and define a model manifold which is an embedding of this low dimensional structure in the higher dimensional space. In this work, we explore the geometrical structure of a neural network model manifold. A Stacked Denoising Autoencoder and a Deep Belief Network are trained on handwritten digits from the MNIST database. Construction of geodesics along the surface and of slices taken from the high dimensional manifolds reveal a hierarchy of widths corresponding to a hyper-ribbon structure. This property indicates that neural networks fall into the class of sloppy models, in which certain parameter combinations dominate the behavior. Employing this information could prove valuable in designing both neural network architectures and training algorithms. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No . DGE-1144153.

On Ramachandran angles, closed strings and knots in protein structure

NASA Astrophysics Data System (ADS)

Chen, Si; Niemi, Antti J.

2016-08-01

The Ramachandran angles (φ,\\psi ) of a protein backbone form the vertices of a piecewise geodesic curve on the surface of a torus. When the ends of the curve are connected to each other similarly, by a geodesic, the result is a closed string that in general wraps around the torus a number of times both in the meridional and the longitudinal directions. The two wrapping numbers are global characteristics of the protein structure. A statistical analysis of the wrapping numbers in terms of crystallographic x-ray structures in the protein data bank (PDB) reveals that proteins have no net chirality in the ϕ direction but in the ψ direction, proteins prefer to display chirality. A comparison between the wrapping numbers and the concept of folding index discloses a non-linearity in their relationship. Thus these three integer valued invariants can be used in tandem, to scrutinize and classify the global loop structure of individual PDB proteins, in terms of the overall fold topology.

Lensing in the geodesic light-cone coordinates and its (exact) illustration to an off-center observer in Lemaȋtre-Tolman-Bondi models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fanizza, G.; Nugier, F., E-mail: giuseppe.fanizza@ba.infn.it, E-mail: fabienjean.nugier@unibo.it

We present in this paper a new application of the geodesic light-cone (GLC) gauge for weak lensing calculations. Using interesting properties of this gauge, we derive an exact expression of the amplification matrix—involving convergence, magnification and shear—and of the deformation matrix—involving the optical scalars. These expressions are simple and non-perturbative as long as no caustics are created on the past light-cone and are, by construction, free from the thin lens approximation. We apply these general expressions on the example of an Lemaȋtre-Tolman-Bondi (LTB) model with an off-center observer and obtain explicit forms for the lensing quantities as a direct consequencemore » of the non-perturbative transformation between GLC and LTB coordinates. We show their evolution in redshift after a numerical integration, for underdense and overdense LTB models, and interpret their respective variations in the simple non-curvature case.« less

Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity

NASA Astrophysics Data System (ADS)

Tsuchida, T.; Watanabe, K.

1999-01-01

We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.

Probabilistic modeling of anatomical variability using a low dimensional parameterization of diffeomorphisms.

PubMed

Zhang, Miaomiao; Wells, William M; Golland, Polina

2017-10-01

We present an efficient probabilistic model of anatomical variability in a linear space of initial velocities of diffeomorphic transformations and demonstrate its benefits in clinical studies of brain anatomy. To overcome the computational challenges of the high dimensional deformation-based descriptors, we develop a latent variable model for principal geodesic analysis (PGA) based on a low dimensional shape descriptor that effectively captures the intrinsic variability in a population. We define a novel shape prior that explicitly represents principal modes as a multivariate complex Gaussian distribution on the initial velocities in a bandlimited space. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than the state-of-the-art method such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA) that operate in the high dimensional image space. Copyright © 2017 Elsevier B.V. All rights reserved.

Spatio-temporal dynamics of turbulence trapped in geodesic acoustic modes

NASA Astrophysics Data System (ADS)

Sasaki, M.; Kobayashi, T.; Itoh, K.; Kasuya, N.; Kosuga, Y.; Fujisawa, A.; Itoh, S.-I.

2018-01-01

The spatio-temporal dynamics of turbulence with the interaction of geodesic acoustic modes (GAMs) are investigated, focusing on the phase-space structure of turbulence, where the phase-space consists of real-space and wavenumber-space. Based on the wave-kinetic framework, the coupling equation between the GAM and the turbulence is numerically solved. The turbulence trapped by the GAM velocity field is obtained. Due to the trapping effect, the turbulence intensity increases where the second derivative of the GAM velocity (curvature of the GAM) is negative. While, in the positive-curvature region, the turbulence is suppressed. Since the trapped turbulence propagates with the GAMs, this relationship is sustained spatially and temporally. The dynamics of the turbulence in the wavenumber spectrum are converted in the evolution of the frequency spectrum, and the simulation result is compared with the experimental observation in JFT-2M tokamak, where the similar patterns are obtained. The turbulence trapping effect is a key to understand the spatial structure of the turbulence in the presence of sheared flows.

Tunneling of Charged Massive Particles from Taub-NUT-Reissner-Nordström-AdS Black Holes

NASA Astrophysics Data System (ADS)

Ali, M. Hossain; Sultana, Kausari

2014-05-01

We apply the null-geodesic method to investigate tunneling radiation of charged and magnetized massive particles from Taub-NUT-Reissner-Nordström black holes endowed with electric as well as magnetic charges in Anti-de Sitter (AdS) spaces. The geodesics of charged massive particle tunneling from the black hole is not lightlike, but can be determined by the phase velocity. We find that the tunneling rate is related to the difference of Bekenstein-Hawking entropies of the black hole before and after the emission of particles. The entropy differs from just a quarter area at the horizon of black holes with NUT parameter. The emission spectrum is not precisely thermal anymore and the deviation from the precisely thermal spectrum can bring some information out, which can be treated as an explanation to the information loss paradox. The result can also be treated as a quantum-corrected radiation temperature, which is dependent on the black hole background and the radiation particle's energy and charges.

Geodesic acoustic mode driven by energetic particles with bump-on-tail distribution

NASA Astrophysics Data System (ADS)

Ren, Haijun; Wang, Hao

2018-04-01

Energetic-particle-driven geodesic acoustic mode (EGAM) is analytically investigated by adopting the bump-on-tail distribution for energetic particles (EPs), which is created by the fact that the charge exchange time (τcx ) is sufficiently shorter than the slowing down time (τsl ). The dispersion relation is derived in the use of gyro-kinetic equations. Due to the finite ratio of the critical energy and the initial energy of EPs, defined as τc , the dispersion relation is numerically evaluated and the effect of finite τc is examined. Following relative simulation and experimental work, we specifically considered two cases: τsl/τcx = 3.4 and τsl/τcx = 20.4 . The pitch angle is shown to significantly enhance the growth rate and meanwhile, the real frequency is dramatically decreased with increasing pitch angle. The excitation of high-frequency EGAM is found, and this is consistent with both the experiment and the simulation. The number density effect of energetic particles, represented by \

Equilibrium configurations of perfect fluid orbiting Schwarzschild-de Sitter black holes

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Slaný, P.; Hledík, S.

2000-11-01

The hydrodynamical structure of perfect fluid orbiting Schwarzschild-de Sitter black holes is investigated for configurations with uniform distribution of angular momentum density. It is shown that in the black-hole backgrounds admitting the existence of stable circular geodesics, closed equipotential surfaces with a cusp, allowing the existence of toroidal accretion disks, can exist. Two surfaces with a cusp exist for the angular momentum density smaller than the one corresponding to marginally bound circular geodesics; the equipotential surface corresponding to the marginally bound circular orbit has just two cusps. The outer cusp is located nearby the static radius where the gravitational attraction is compensated by the cosmological repulsion. Therefore, due to the presence of a repulsive cosmological constant, the outflow from thick accretion disks can be driven by the same mechanism as the accretion onto the black hole. Moreover, properties of open equipotential surfaces in vicinity of the axis of rotation suggest a strong collimation effects of the repulsive cosmological constant acting on jets produced by the accretion disks.

Tracking Organs Composed of One or Multiple Regions Using Geodesic Active Region Models

NASA Astrophysics Data System (ADS)

Martínez, A.; Jiménez, J. J.

In radiotherapy treatment it is very important to find out the target organs on the medical image sequence in order to determine and apply the proper dose. The techniques to achieve this goal can be classified into extrinsic and intrinsic. Intrinsic techniques only use image processing with medical images associated to the radiotherapy treatment, as we deal in this chapter. To accurately perform this organ tracking it is necessary to find out segmentation and tracking models that were able to be applied to several image modalities involved on a radiotherapy session (CT See Modality , MRI , etc.). The movements of the organs are mainly affected by two factors: breathing and involuntary movements associated with the internal organs or patient positioning. Among the several alternatives to track the organs of interest, a model based on geodesic active regions is proposed. This model has been tested over CT images from the pelvic, cardiac, and thoracic area. A new model for the segmentation of organs composed by more than one region is proposed.

Light propagation in the averaged universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagheri, Samae; Schwarz, Dominik J., E-mail: s_bagheri@physik.uni-bielefeld.de, E-mail: dschwarz@physik.uni-bielefeld.de

Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of themore » null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lemaître (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.« less

Twin Paradox: A Complete Treatment from the Point of View of Each Twin.

ERIC Educational Resources Information Center

Perrin, Robert

1979-01-01

Modifies and expands on the treatment of the twin paradox by solving the gravitational field equations and geodesic equations of motion in the traveling twin's reference frame, thus determining the time elapsed on the Earth during the periods of acceleration. (Author/GA)

Motions in Taub-NUT-de Sitter spinning spacetime

NASA Astrophysics Data System (ADS)

Banu, Akhtara

2012-09-01

We investigate the geodesic motion of pseudo-classical spinning particles in the Taub-NUT-de Sitter spacetime. We obtain the conserved quantities from the solutions of the generalized Killing equations for spinning spaces. Applying the formalism the motion of a pseudo-classical Dirac fermion is analyzed on a cone and plane.

Gardening with Greenhouses

ERIC Educational Resources Information Center

Keeler, Rusty

2010-01-01

Greenhouses come in all shapes, sizes, and price ranges: from simple hand-built plastic-covered frames to dazzling geodesic domes. Some child care centers install greenhouses as a part of their outdoor garden space. Other centers have incorporated a greenhouse into the building itself. Greenhouses provide a great opportunity for children to grow…

An analytical approach to the external force-free motion of pendulums on surfaces of constant curvature

NASA Astrophysics Data System (ADS)

Rubio, Rafael M.; Salamanca, Juan J.

2018-07-01

The dynamics of external force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagrangian of the system. As an application it is possible the study of elastic and quantum pendulums.

Not Your Grandparents' Vocational School

ERIC Educational Resources Information Center

Schachter, Ron

2012-01-01

Manufacturing biodiesel fuel, building a geodesic-domed greenhouse, measuring the environmental impact of abandoned industrial canals--these might well fit the mission of cutting-edge companies specializing in green technologies, or they could be part of the curriculum at an institution of advanced science and engineering such as MIT or Cal Tech.…

The Cheapbook: A Compendium of Inexpensive Exhibit Ideas, 1995 Edition.

ERIC Educational Resources Information Center

Orselli, Paul, Ed.

This guide includes complete installation descriptions of 30 exhibits. They include: the adjustable birthday cake, ball-in-tube, Bernoulli Box, chain wave, collapsible truss bridge, double wave device, eddy currents raceway, full-length mirror, geodesic domes, giant magnetic tangrams, harmonic cantilever, hyperboloid of revolution, lifting lever,…

Killing Forms on the Five-Dimensional Einstein-Sasaki Y(p, q) Spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2012-12-01

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes

NASA Astrophysics Data System (ADS)

Saini, Sahil; Singh, Parampreet

2018-03-01

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations—the connection operator based ‘A’ quantization and the extrinsic curvature based ‘K’ quantization. We show that in the effective spacetime description with arbitrary matter content, it is necessary to include inverse triad corrections to resolve all the strong singularities in the ‘A’ quantization. Whereas in the ‘K’ quantization these results can be obtained without including inverse triad corrections. Under these conditions, the energy density, expansion and shear scalars for both of the quantization prescriptions are bounded. Notably, both the quantizations can result in potentially curvature divergent events if matter content allows divergences in the partial derivatives of the energy density with respect to the triad variables at a finite energy density. Such events are found to be weak curvature singularities beyond which geodesics can be extended in the effective spacetime. Our results show that all potential strong curvature singularities of the classical theory are forbidden in Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never breaks down for such events.

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

NASA Technical Reports Server (NTRS)

Chrzanowski, P. L.; Misner, C. W.

1974-01-01

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Numerical modelling of geodesic acoustic mode relaxation in a tokamak edge

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2013-05-08

Here, the edge of a tokamak in a high confinement (H mode) regime is characterized by steep density gradients and a large radial electric field. Recent analytical studies demonstrated that the presence of a strong radial electric field consistent with a subsonic pedestal equilibrium modifies the conventional results of the neoclassical formalism developed for the core region. In the present work we make use of the recently developed gyrokinetic code COGENT to numerically investigate neoclassical transport in a tokamak edge including the effects of a strong radial electric field. The results of numerical simulations are found to be in goodmore » qualitative agreement with the theoretical predictions and the quantitative discrepancy is discussed. In addition, the present work investigates the effects of a strong radial electric field on the relaxation of geodesic acoustic modes (GAMs) in a tokamak edge. Numerical simulations demonstrate that the presence of a strong radial electric field characteristic of a tokamak pedestal can enhance the GAM decay rate, and heuristic arguments elucidating this finding are provided.« less

Why did the apple fall? A new model to explain Einstein’s gravity

NASA Astrophysics Data System (ADS)

Stannard, Warren; Blair, David; Zadnik, Marjan; Kaur, Tejinder

2017-01-01

Newton described gravity as an attractive force between two masses but Einstein’s General Theory of Relativity provides a very different explanation. Implicit in Einstein’s theory is the idea that gravitational effects are the result of a distortion in the shape of space-time. Despite its elegance, Einstein’s concept of gravity is rarely encountered outside of an advanced physics course as it is often considered to be too complex and too mathematical. This paper describes a new conceptual and quantitative model of gravity based on General Relativity at a level most science students should be able to understand. The model illustrates geodesics using analogies with paths of navigation on the surface of the Earth. This is extended to space and time maps incorporating the time warping effects of General Relativity. Using basic geometry, the geodesic path of a falling object near the surface of the Earth is found. From this the acceleration of an object in free fall is calculated. The model presented in this paper can answer the question, ‘Why do things fall?’ without resorting to Newton’s gravitational force.

Geodesic acoustic mode (GAM) like oscillations and RMP effect in the STOR-M tokamak

NASA Astrophysics Data System (ADS)

Basu, Debjyoti; Nakajima, Masaru; Melnikov, A. V.; McColl, David; Rohollahi, Akbar; Elgriw, Sayf; Xiao, Chijin; Hirose, Akira

2018-02-01

A new kind of quasi-coherent mode was observed in ohmic plasma in the STOR-M tokamak. It is featured with a clear solitary peak around 30-35 kHz in the power spectra of the ion saturation current (I_sat) of Langmuir probe as well as poloidal and toroidal mode numbers (m  =  1,n  =  0) as per the prediction of conventional geodesic acoustic mode (GAM) theory. The dispersion relation of the mode is also similar to GAM and it also shows collisional damping. In contrast to conventional GAM, the floating potential ϕ of the observed GAM-like mode does not show similar symmetric poloidal and toroidal mode numbers (m  =  0,n  =  0), but has (m  =  1,n  =  1). The GAM-like mode has also a pronounced magnetic component with mixed poloidal modes (m=3~and~m=5; n=1 ), as observed by Mirnov coils. This mode is suppressed by the application of resonance magnetic perturbations.

Group invariant solutions of the Ernst equation of general relativity theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pryse, P.V.

The local symmetry group of the Ernst Equation for stationary, axisymmetric, vacuum space-time manifolds is computed by application of the method of Olver. Several implicit solutions of the equation are found by use of this group. Each of these solutions is given in terms of a function defined as a solution of an ordinary differential equation. One of these equations is integrated by quadratures by use of its own local symmetry group, the result being three explicit solutions of the Ernst Equation. For one of these solutions the metric of the space-time manifold is constructed and studied. The solutions hasmore » a ring curvature singularity and it is asymptotically flat in the sense that the curvature invariants approach zero at spatial infinity. The timelike and null geodesics on the symmetry axis and in the plane of the ring singularity are described. The test particles following these geodesics are seen to be repelled by the ring, which suggests the interpretation of this solution as representing the exterior gravitational field of a rotating ring of matter with negative gravitational mass.« less

2D Affine and Projective Shape Analysis.

PubMed

Bryner, Darshan; Klassen, Eric; Huiling Le; Srivastava, Anuj

2014-05-01

Current techniques for shape analysis tend to seek invariance to similarity transformations (rotation, translation, and scale), but certain imaging situations require invariance to larger groups, such as affine or projective groups. Here we present a general Riemannian framework for shape analysis of planar objects where metrics and related quantities are invariant to affine and projective groups. Highlighting two possibilities for representing object boundaries-ordered points (or landmarks) and parameterized curves-we study different combinations of these representations (points and curves) and transformations (affine and projective). Specifically, we provide solutions to three out of four situations and develop algorithms for computing geodesics and intrinsic sample statistics, leading up to Gaussian-type statistical models, and classifying test shapes using such models learned from training data. In the case of parameterized curves, we also achieve the desired goal of invariance to re-parameterizations. The geodesics are constructed by particularizing the path-straightening algorithm to geometries of current manifolds and are used, in turn, to compute shape statistics and Gaussian-type shape models. We demonstrate these ideas using a number of examples from shape and activity recognition.

Gravitational self-force on generic bound geodesics in Kerr spacetime

NASA Astrophysics Data System (ADS)

van de Meent, Maarten

2018-05-01

In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar ψ4 , which in turn is obtained by solving the Teukolsky equation using semianalytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) l -mode regularization. We test our implementation by comparing the large l -behavior against the analytically known regularization parameters. In addition we validate our results by comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon.

Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, Yading, E-mail: yading.yuan@mssm.edu; Chao, Ming; Sheu, Ren-Dih

Purpose: 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. Methods: 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.more » 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. Results: 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{sup 3}, whereas it was 1719 cm{sup 3} for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. Conclusions: 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 borders could significantly reduce contour leakage during active contour evolution.« less

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

NASA Astrophysics Data System (ADS)

Šrámková, E.; Török, G.; Kotrlová, A.; Bakala, P.; Abramowicz, M. A.; Stuchlík, Z.; Goluchová, K.; Kluźniak, W.

2015-06-01

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a ≡ cJ/GM2 ≲ 0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a ≳ 0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a ~ 0.7 to a ~ 0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a ≲ 0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a ~ 1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).

The combined geodetic network adjusted on the reference ellipsoid - a comparison of three functional models for GNSS observations

NASA Astrophysics Data System (ADS)

Kadaj, Roman

2016-12-01

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

SU-F-R-27: Use Local Shape Descriptor Based On Geodesic Distance to Predict Survival in Non-Small Cell Lung Cancer After Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, H; Yan, L; Huang, K

2016-06-15

Purpose: The shape of the Positron Emission Tomography (PET) image represents the heterogeneity of tumor growth in various directions, and thus could be associated with tumor malignancy. We have proposed a median geodesic distance (MGD) to represent the local complexity of the shape and use a normalized MGD (NMGD) to quantify the shape, and found a potential correlation of NMGD to survival in a 20-patient pilot study. This study was to verify the finding in a larger patient cohort. Methods: Geodesic distance of two vertices on a surface is defined as the shortest path on the surface connecting the twomore » vertices. The MGD was calculated for each vertex on the surface to display the local complexity of the shape. The NMGD was determined as: NMGD = 100*standard deviation(MGDs)/mean(MGDs). We applied the NMGD to 40 NSCLC patients who were enrolled in prospective PET image protocols and received radiotherapy. Each patient had a pre-treatment PET scan with the resolution of 4mm*4mm*5mm. Tumors were contoured by a professional radiation oncologist and triangulation meshes were built up based on the contours. Results: The mean and standard deviation of NMGD was 6.4±3.0. The OS was 33.1±16.9 months for low NMGD group, and 15.4±15.6 months for the high NMGD group. The low NMGD group had significant better OS than the high NMGD group (p=0.0013). Conclusion: NMGD could be used as a shape biomarker to predict survival and the MGD could be combined with image texture in future to increase prediction accuracy. This study was supported by Award Number 1R01CA166948 from the NIH and National Cancer Institute.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Logan, B.G.

A recently completed two-year study of a commercial tandem mirror reactor design (Mirror Advanced Reactor Study (MARS)) is briefly reviewed. The end plugs are designed for trapped particle stability, MHD ballooning, balanced geodesic curvature, and small radial electric fields in the central cell. New technologies such as lithium-lead blankets, 24T hybrid coils, gridless direct converters and plasma halo vacuum pumps are highlighted.

No ISCOs in Charged Myers Perry Spacetimes by Measuring Lyapunov Exponent

NASA Astrophysics Data System (ADS)

Pradhan, Parthapratim

2015-01-01

By computing coordinate time Lyapunov exponent, we prove that for more than four spacetime dimensions (N ≥ 3), there are no Innermost Stable Circular Orbit (ISCO) in charged Myers Perry blackhole spacetime.Using it, we show that the instability of equatorial circular geodesics, both massive and massless particles for such types of blackhole space-times.

Minimal measures on surfaces of higher genus

NASA Astrophysics Data System (ADS)

Wang, Fang

We study the minimal measures for positive definite autonomous Lagrangian systems defined on the tangent bundles of compact surfaces with genus greater than one. We present some results on the structure of minimal measures on compact surfaces. Specifically, we give a finer description of the structure of minimal measures with rational rotation vectors for geodesic flows on compact surfaces.

Design of a Lighter Than Air Vehicle That Achieves Positive Buoyancy in Air Using a Vacuum

DTIC Science & Technology

2012-06-01

on 12 Dec 1951 [37]. In his patent, Fuller 46 described a geodesic sphere based on a 20 sided polyhedron called an icosahedron. The icosahedron...shown in Figure 14, is a polyhedron composed of 20 equilateral triangles in which each vertex lies on the surface of an imaginary sphere (shown as

Visual Analytics for Exploration of a High-Dimensional Structure

DTIC Science & Technology

2013-04-01

5 Figure 3. Comparison of Euclidean vs. geodesic distance. LDRs use...manifold, whereas an LDR fails. ...........................6 Figure 4. WEKA GUI for data mining HDD using FRFS-ACO...multidimensional scaling (CMDS)— are a linear DR ( LDR ). An LDR is based on a linear combination of the feature data. LDRs keep similar data points close together

Persistent Target Tracking Using Likelihood Fusion in Wide-Area and Full Motion Video Sequences

DTIC Science & Technology

2012-07-01

624–637, 2010. [33] R. Pelapur, K. Palaniappan, F. Bunyak, and G. Seetharaman, “Vehicle orientation estimation using radon transform-based voting in...pp. 873–880. [37] F. Bunyak, K. Palaniappan, S. K. Nath, and G. Seetharaman, “Flux tensor constrained geodesic active contours with sensor fusion for

Dynamics of test particles in thin-shell wormhole spacetimes

NASA Astrophysics Data System (ADS)

Diemer, Valeria; Smolarek, Elena

2013-09-01

Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.

Asymptotic Behaviour of Solitons with a Double Spectral Parameter for the Bogomolny Equation in (2+1)-Dimensional Anti de Sitter Space

NASA Astrophysics Data System (ADS)

Ji, Xue-Feng; Zhou, Zi-Xiang

2005-07-01

The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)-dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.

The three-body problem and equivariant Riemannian geometry

NASA Astrophysics Data System (ADS)

Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.

2017-08-01

We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.

A Continuum Mechanical Approach to Geodesics in Shape Space

DTIC Science & Technology

2010-01-01

the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a ...investigate the close link between abstract geometry on the infinite -dimen- sional space of shapes and the continuum mechanical view of shapes as boundary...are texture-coded in the bottom row. of multiple components of volumetric objects. The

Unique Two-Way Field Probe Concept Utilizing a Geodesic Sphere and Quad-Rotor

DTIC Science & Technology

2015-03-26

82 Appendix C ...For instance, a 2 GHz frequency has a wavelength of 0.15 meters (λ = c /f = 3 x 108 m/s/2 x 109 s); whereas, a 10 GHz transmitted frequency will...in both polarizations and both poses (hexagon down and pentagon down) The ACR’s experimental results can be found in Appendix C . The

On the shape of things: From holography to elastica

NASA Astrophysics Data System (ADS)

Fonda, Piermarco; Jejjala, Vishnu; Veliz-Osorio, Alvaro

2017-10-01

We explore the question of which shape a manifold is compelled to take when immersed in another one, provided it must be the extremum of some functional. We consider a family of functionals which depend quadratically on the extrinsic curvatures and on projections of the ambient curvatures. These functionals capture a number of physical setups ranging from holography to the study of membranes and elastica. We present a detailed derivation of the equations of motion, known as the shape equations, placing particular emphasis on the issue of gauge freedom in the choice of normal frame. We apply these equations to the particular case of holographic entanglement entropy for higher curvature three dimensional gravity and find new classes of entangling curves. In particular, we discuss the case of New Massive Gravity where we show that non-geodesic entangling curves have always a smaller on-shell value of the entropy functional. Then we apply this formalism to the computation of the entanglement entropy for dual logarithmic CFTs. Nevertheless, the correct value for the entanglement entropy is provided by geodesics. Then, we discuss the importance of these equations in the context of classical elastica and comment on terms that break gauge invariance.

Generic effective source for scalar self-force calculations

NASA Astrophysics Data System (ADS)

Wardell, Barry; Vega, Ian; Thornburg, Jonathan; Diener, Peter

2012-05-01

A leading approach to the modeling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic timelike geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.

A stereoscopic look into the bulk

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2016-07-26

Here, we present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural CFT operators whose duals are simple, diffeomorphism-invariant bulk operators. The CFT operators of interest are the “OPE blocks,” contributions to the OPE from a single conformal family. In holographic theories, we show that the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. One widely studied example of an OPE block is the modular Hamiltonian, which is dual to the fluctuation in the area of a minimalmore » surface. Thus, our operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields. Although the OPE blocks are non-local operators in the CFT, they admit a simple geometric description as fields in kinematic space — the space of pairs of CFT points. We develop the tools for constructing local bulk operators in terms of these non-local objects. The OPE blocks also allow for conceptually clean and technically simple derivations of many results known in the literature, including linearized Einstein’s equations and the relation between conformal blocks and geodesic Witten diagrams.« less

Shape complexes: the intersection of label orderings and star convexity constraints in continuous max-flow medical image segmentation

PubMed Central

Baxter, John S. H.; Inoue, Jiro; Drangova, Maria; Peters, Terry M.

2016-01-01

Abstract. Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of “shape complexes,” which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems. PMID:28018937

Spherical self-organizing map using efficient indexed geodesic data structure.

PubMed

Wu, Yingxin; Takatsuka, Masahiro

2006-01-01

The two-dimensional (2D) Self-Organizing Map (SOM) has a well-known "border effect". Several spherical SOMs which use lattices of the tessellated icosahedron have been proposed to solve this problem. However, existing data structures for such SOMs are either not space efficient or are time consuming when searching the neighborhood. We introduce a 2D rectangular grid data structure to store the icosahedron-based geodesic dome. Vertices relationships are maintained by their positions in the data structure rather than by immediate neighbor pointers or an adjacency list. Increasing the number of neurons can be done efficiently because the overhead caused by pointer updates is reduced. Experiments show that the spherical SOM using our data structure, called a GeoSOM, runs with comparable speed to the conventional 2D SOM. The GeoSOM also reduces data distortion due to removal of the boundaries. Furthermore, we developed an interface to project the GeoSOM onto the 2D plane using a cartographic approach, which gives users a global view of the spherical data map. Users can change the center of the 2D data map interactively. In the end, we compare the GeoSOM to the other spherical SOMs by space complexity and time complexity.

Generation of an Atlas of the Proximal Femur and Its Application to Trabecular Bone Analysis

PubMed Central

Carballido-Gamio, Julio; Folkesson, Jenny; Karampinos, Dimitrios C.; Baum, Thomas; Link, Thomas M.; Majumdar, Sharmila; Krug, Roland

2013-01-01

Automatic placement of anatomically corresponding volumes of interest and comparison of parameters against a standard of reference are essential components in studies of trabecular bone. Only recently, in vivo MR images of the proximal femur, an important fracture site, could be acquired with high-spatial resolution. The purpose of this MRI trabecular bone study was two-fold: (1) to generate an atlas of the proximal femur to automatically place anatomically corresponding volumes of interest in a population study and (2) to demonstrate how mean models of geodesic topological analysis parameters can be generated to be used as potential standard of reference. Ten females were used to generate the atlas and geodesic topological analysis models, and 10 females were used to demonstrate the atlas-based trabecular bone analysis. All alignments were based on three-dimensional (3D) multiresolution affine transformations followed by 3D multiresolution free-form deformations. Mean distances less than 1 mm between aligned femora, and sharp edges in the atlas and in fused gray-level images of registered femora indicated that the anatomical variability was well accommodated and explained by the free-form deformations. PMID:21432904

Cosmological singularities in Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Woolgar, Eric

2014-12-01

We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-Émery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy condition on the Bakry-Émery-Ricci tensor and obtain singularity theorems of a cosmological type, both for zero and for positive cosmological constant. That is, we find conditions under which every timelike geodesic is incomplete. These conditions are given by 'open' inequalities, so we examine the borderline (equality) cases and show that certain singularities are avoided in these cases only if the geometry is rigid; i.e., if it splits as a Lorentzian product or, for a positive cosmological constant, a warped product, and the weight function is constant along the time direction. Then the product case is future timelike geodesically complete while, in the warped product case, worldlines of certain conformally static observers are complete. Our results answer a question posed by J Case. We then apply our results to the cosmology of scalar-tensor gravitation theories. We focus on the Brans-Dicke family of theories in 4 spacetime dimensions, where we obtain 'Jordan frame' singularity theorems for big bang singularities.

ODYSSEY: A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pu, Hung-Yi; Yun, Kiyun; Yoon, Suk-Jin

General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge–Kutta integrationmore » step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey-Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.« less

a Super Voxel-Based Riemannian Graph for Multi Scale Segmentation of LIDAR Point Clouds

NASA Astrophysics Data System (ADS)

Li, Minglei

2018-04-01

Automatically segmenting LiDAR points into respective independent partitions has become a topic of great importance in photogrammetry, remote sensing and computer vision. In this paper, we cast the problem of point cloud segmentation as a graph optimization problem by constructing a Riemannian graph. The scale space of the observed scene is explored by an octree-based over-segmentation with different depths. The over-segmentation produces many super voxels which restrict the structure of the scene and will be used as nodes of the graph. The Kruskal coordinates are used to compute edge weights that are proportional to the geodesic distance between nodes. Then we compute the edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between super voxel nodes on the scene surface. The final segmentation results are generated by clustering similar super voxels and cutting off the weak edges in the graph. The performance of this method was evaluated on LiDAR point clouds for both indoor and outdoor scenes. Additionally, extensive comparisons to state of the art techniques show that our algorithm outperforms on many metrics.

Tracking Organs Composed of One or Multiple Regions Using Geodesic Active Region Models

NASA Astrophysics Data System (ADS)

Martínez, A.; Jiménez, J. J.

In radiotherapy treatment it is very important to find out the target organs on the medical image sequence in order to determine and apply the proper dose. The techniques to achieve this goal can be classified into extrinsic and intrinsic. Intrinsic techniques only use image processing with medical images associated to the radiotherapy Radiotherapy treatment, as we deal in this chapter. To accurately perform this organ tracking it is necessary to find out segmentation and tracking models that were able to be applied to several image modalities involved on a radiotherapy session (CT CT See Modality , MRI Magnetic resoance imaging , etc.). The movements of the organs are mainly affected by two factors: breathing and involuntary movements associated with the internal organs or patient positioning. Among the several alternatives to track the organs of interest, a model based on geodesic active regions is proposed. This model has been tested over CT Computed tomography images from the pelvic, cardiac, and thoracic area. A new model for the segmentation of organs composed by more than one region is proposed.

Investigating social cognition in infants and adults using dense array electroencephalography ((d)EEG).

PubMed

Akano, Adekemi J; Haley, David W; Dudek, Joanna

2011-06-27

Dense array electroencephalography ((d)EEG), which provides a non-invasive window for measuring brain activity and a temporal resolution unsurpassed by any other current brain imaging technology¹, ² is being used increasingly in the study of social cognitive functioning in infants and adults. While (d)EEG is enabling researchers to examine brain activity patterns with unprecedented levels of sensitivity, conventional EEG recording systems continue to face certain limitations, including 1) poor spatial resolution and source localization³,⁴2) the physical discomfort for test subjects of enduring the individual application of numerous electrodes to the surface of the scalp, and 3) the complexity for researchers of learning to use multiple software packages to collect and process data. Here we present an overview of an established methodology that represents a significant improvement on conventional methodologies for studying EEG in infants and adults. Although several analytical software techniques can be used to establish indirect indices of source localization to improve the spatial resolution of (d)EEG, the HydroCel Geodesic Sensor Net (HCGSN) by Electrical Geodesics, Inc. (EGI), a dense sensory array that maintains equal distances among adjacent recording electrodes on all surfaces of the scalp, further enhances spatial resolution⁴,⁵(,)⁶ compared to standard (d)EEG systems. The sponge-based HCGSN can be applied rapidly and without scalp abrasion, making it ideal for use with adults⁷,⁸ children⁹,¹⁰, ¹¹,¹² and infants¹², in both research and clinical ⁴,⁵,⁶,¹³,¹⁴,¹⁵settings. This feature allows for considerable cost and time savings by decreasing the average net application time compared to other (d)EEG systems. Moreover, the HCGSN includes unified, seamless software applications for all phases of data, greatly simplifying the collection, processing, and analysis of (d)EEG data. The HCGSN features a low-profile electrode pedestal, which, when filled with electrolyte solution, creates a sealed microenvironment and an electrode-scalp interface. In all Geodesic (d;)EEG systems, EEG sensors detect changes in voltage originating from the participant's scalp, along with a small amount of electrical noise originating from the room environment. Electrical signals from all sensors of the Geodesic sensor net are received simultaneously by the amplifier, where they are automatically processed, packaged, and sent to the data-acquisition computer (DAC). Once received by the DAC, scalp electrical activity can be isolated from artifacts for analysis using the filtering and artifact detection tools included in the EGI software. Typically, the HCGSN can be used continuously for only up to two hours because the electrolyte solution dries out over time, gradually decreasing the quality of the scalp-electrode interface. In the Parent-Infant Research Lab at the University of Toronto, we are using (d)EEG to study social cognitive processes including memory, emotion, goals, intentionality, anticipation, and executive functioning in both adult and infant participants.

Trajectory Calculations for Spherical Geodesic Grids in Cartesian Space

DTIC Science & Technology

1999-07-01

2 Dtu , t). By applying a rotation transformation as in McDonald and Bates (1989), we get the arrival points in the rotated space l9 5 arctan[cosu sin...see Ritchie (1987)] are required to converge to the solution at which point, the departure point is calcu- lated by Dt x 5 x 2 Dtu x , t 1 .D A M1 22

Smoothness of the future and past trapped sets in Kerr–Newman–Taub-NUT spacetimes

NASA Astrophysics Data System (ADS)

Paganini, Claudio F.; Oancea, Marius A.

2018-03-01

We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr–Newman–Taub-NUT spacetime. We show that from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer.

Physical optics in a uniform gravitational field

NASA Astrophysics Data System (ADS)

Hacyan, Shahen

2012-01-01

The motion of a (quasi-)plane wave in a uniform gravitational field is studied. It is shown that the energy of an elliptically polarized wave does not propagate along a geodesic, but in a direction that is rotated with respect to the gravitational force. The similarity with the walk-off effect in anisotropic crystals or the optical Magnus effect in inhomogeneous media is pointed out.

Joint Data Management for MOVINT Data-to-Decision Making

DTIC Science & Technology

2011-07-01

flux tensor , aligned motion history images, and related approaches have been shown to be versatile approaches [12, 16, 17, 18]. Scaling these...methods include voting , neural networks, fuzzy logic, neuro-dynamic programming, support vector machines, Bayesian and Dempster-Shafer methods. One way...Information Fusion, 2010. [16] F. Bunyak, K. Palaniappan, S. K. Nath, G. Seetharaman, “Flux tensor constrained geodesic active contours with sensor fusion

Geometrization of the Dirac theory of the electron

NASA Technical Reports Server (NTRS)

Fock, V.

1977-01-01

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.

Diviner lunar radiometer gridded brightness temperatures from geodesic binning of modeled fields of view

NASA Astrophysics Data System (ADS)

Sefton-Nash, E.; Williams, J.-P.; Greenhagen, B. T.; Aye, K.-M.; Paige, D. A.

2017-12-01

An approach is presented to efficiently produce high quality gridded data records from the large, global point-based dataset returned by the Diviner Lunar Radiometer Experiment aboard NASA's Lunar Reconnaissance Orbiter. The need to minimize data volume and processing time in production of science-ready map products is increasingly important with the growth in data volume of planetary datasets. Diviner makes on average >1400 observations per second of radiance that is reflected and emitted from the lunar surface, using 189 detectors divided into 9 spectral channels. Data management and processing bottlenecks are amplified by modeling every observation as a probability distribution function over the field of view, which can increase the required processing time by 2-3 orders of magnitude. Geometric corrections, such as projection of data points onto a digital elevation model, are numerically intensive and therefore it is desirable to perform them only once. Our approach reduces bottlenecks through parallel binning and efficient storage of a pre-processed database of observations. Database construction is via subdivision of a geodesic icosahedral grid, with a spatial resolution that can be tailored to suit the field of view of the observing instrument. Global geodesic grids with high spatial resolution are normally impractically memory intensive. We therefore demonstrate a minimum storage and highly parallel method to bin very large numbers of data points onto such a grid. A database of the pre-processed and binned points is then used for production of mapped data products that is significantly faster than if unprocessed points were used. We explore quality controls in the production of gridded data records by conditional interpolation, allowed only where data density is sufficient. The resultant effects on the spatial continuity and uncertainty in maps of lunar brightness temperatures is illustrated. We identify four binning regimes based on trades between the spatial resolution of the grid, the size of the FOV and the on-target spacing of observations. Our approach may be applicable and beneficial for many existing and future point-based planetary datasets.

Geodesic active fields--a geometric framework for image registration.

PubMed

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 the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parekh, V; Jacobs, MA

Purpose: Multiparametric radiological imaging is used for diagnosis in patients. Potentially extracting useful features specific to a patient’s pathology would be crucial step towards personalized medicine and assessing treatment options. In order to automatically extract features directly from multiparametric radiological imaging datasets, we developed an advanced unsupervised machine learning algorithm called the multidimensional imaging radiomics-geodesics(MIRaGe). Methods: Seventy-six breast tumor patients underwent 3T MRI breast imaging were used for this study. We tested the MIRaGe algorithm to extract features for classification of breast tumors into benign or malignant. The MRI parameters used were T1-weighted, T2-weighted, dynamic contrast enhanced MR imaging (DCE-MRI)more » and diffusion weighted imaging(DWI). The MIRaGe algorithm extracted the radiomics-geodesics features (RGFs) from multiparametric MRI datasets. This enable our method to learn the intrinsic manifold representations corresponding to the patients. To determine the informative RGF, a modified Isomap algorithm(t-Isomap) was created for a radiomics-geodesics feature space(tRGFS) to avoid overfitting. Final classification was performed using SVM. The predictive power of the RGFs was tested and validated using k-fold cross validation. Results: The RGFs extracted by the MIRaGe algorithm successfully classified malignant lesions from benign lesions with a sensitivity of 93% and a specificity of 91%. The top 50 RGFs identified as the most predictive by the t-Isomap procedure were consistent with the radiological parameters known to be associated with breast cancer diagnosis and were categorized as kinetic curve characterizing RGFs, wash-in rate characterizing RGFs, wash-out rate characterizing RGFs and morphology characterizing RGFs. Conclusion: In this paper, we developed a novel feature extraction algorithm for multiparametric radiological imaging. The results demonstrated the power of the MIRaGe algorithm at automatically discovering useful feature representations directly from the raw multiparametric MRI data. In conclusion, the MIRaGe informatics model provides a powerful tool with applicability in cancer diagnosis and a possibility of extension to other kinds of pathologies. NIH (P50CA103175, 5P30CA006973 (IRAT), R01CA190299, U01CA140204), Siemens Medical Systems (JHU-2012-MR-86-01) and Nivida Graphics Corporation.« less

Quantum Adiabatic Brachistochrone

NASA Astrophysics Data System (ADS)

Rezakhani, A. T.; Kuo, W.-J.; Hamma, A.; Lidar, D. A.; Zanardi, P.

2009-08-01

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

Quantum adiabatic brachistochrone.

PubMed

Rezakhani, A T; Kuo, W-J; Hamma, A; Lidar, D A; Zanardi, P

2009-08-21

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

An automatic brain tumor segmentation tool.

PubMed

Diaz, Idanis; Boulanger, Pierre; Greiner, Russell; Hoehn, Bret; Rowe, Lindsay; Murtha, Albert

2013-01-01

This paper introduces an automatic brain tumor segmentation method (ABTS) for segmenting multiple components of brain tumor using four magnetic resonance image modalities. ABTS's four stages involve automatic histogram multi-thresholding and morphological operations including geodesic dilation. Our empirical results, on 16 real tumors, show that ABTS works very effectively, achieving a Dice accuracy compared to expert segmentation of 81% in segmenting edema and 85% in segmenting gross tumor volume (GTV).

Geodesy and Cartography (Selected Articles),

DTIC Science & Technology

1979-08-10

C-OO/b73 GEODESY AND CARTOGRAPHY (SELECTED ARTICLES) English pages: 40 Source: GeodezJa i Kartografia, Vol. 27, Nr. 1, 1978, PP. 3-27 Country of...1976. 14) kledzixski, J., Zibek, Z., Czarnecki, K., Rogowski, J.B., Problems in Using Satellite Surveys in an Astronomical-Geodesic Network, Geodezja i...Based on Observations of Low-Low Satellites Using Collocation Methods, Geodezja i Kartografia, Vol. XXVI, No. 4, 1977. [-7. Krynski, J., Schwarz, K.P

Deep Water Ocean Acoustics

DTIC Science & Technology

2016-10-07

range due to either the geodesic correction or the element positioning. Figure 3. The travel time between N1 and S1 obtained from modeling with...chain running due north at 170°E. The effect of these bathymetric interactions is to fill the shadow zone completely by the time the Asian...the width of the envelope reduces with increasing frequency, enabling a higher time resolution. Furthermore, the lag time becomes smaller with

Robust regression on noisy data for fusion scaling laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be; Laboratoire de Physique des Plasmas de l'ERM - Laboratorium voor Plasmafysica van de KMS

2014-11-15

We introduce the method of geodesic least squares (GLS) regression for estimating fusion scaling laws. Based on straightforward principles, the method is easily implemented, yet it clearly outperforms established regression techniques, particularly in cases of significant uncertainty on both the response and predictor variables. We apply GLS for estimating the scaling of the L-H power threshold, resulting in estimates for ITER that are somewhat higher than predicted earlier.

Formation Flying through Geodesic Motion and the Different Geometrical Requirements

DTIC Science & Technology

2006-09-01

APPROXIMATE SOLUTIONS IN A CLOHESSY - WILTSHIRE -TYPE SYSTEM Despite the assumed approximation, the simplified problem (5)+(6) remains complicated for an...analytical approach. For a further simplification let us introduce a CW ( Clohessy - Wiltshire ) referential system [1], [3]. Consider that the trajectory...momentum. Figure 2: The Clohessy - Wiltshire -type referential system, CX1Y1Z1. Neglecting the second order terms, equation (9) reads: (10

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-01-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159

Physical interpretation of antigravity

NASA Astrophysics Data System (ADS)

Bars, Itzhak; James, Albin

2016-02-01

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 regions introduce apparent problems of ghosts that raise several questions of physical interpretation. It was shown that unitarity is not violated, but there may be an instability associated with negative kinetic energies in the antigravity regions. In this paper we show that the apparent problems can be resolved with the interpretation of the theory from the perspective of observers strictly in the gravity region. Such observers cannot experience the negative kinetic energy in antigravity directly, but can only detect in and out signals that interact with the antigravity region. This is no different from a spacetime black box for which the information about its interior is encoded in scattering amplitudes for in/out states at its exterior. Through examples we show that negative kinetic energy in antigravity presents no problems of principles but is an interesting topic for physical investigations of fundamental significance.

Confronting the models of 3:2 quasiperiodic oscillations with the rapid spin of the microquasar GRS 1915+105

NASA Astrophysics Data System (ADS)

Török, G.; Kotrlová, A.; Šrámková, E.; Stuchlík, Z.

2011-07-01

Spectral fitting of the spin a ≡ cJ/GM2 in the microquasar GRS 1915+105 estimate values higher than a = 0.98. However, there are certain doubts about this (nearly) extremal number. Confirming a high value of a > 0.9 would have significant concequences for the theory of high-frequency quasiperiodic oscillations (HF QPOs). Here we discuss its possible implications assuming several commonly used orbital models of 3:2 HF QPOs. We show that the estimate of a > 0.9 is almost inconsistent with two hot-spot (relativistic precession and tidal disruption) models and the warped disc resonance model. In contrast, we demonstrate that the epicyclic resonance and discoseismic models assuming the c- and g-modes are favoured. We extend our discussion to another two microquasars that display the 3:2 HF QPOs. The frequencies of these QPOs scale roughly inversely to the microquasar masses, and the differences in the individual spins, such as a = 0.9 compared to a = 0.7, represent a generic problem for most of the discussed geodesic 3:2 QPO models. To explain the observations of all the three microquasars by one unique mechanism, the models would have to accommodate very large non-geodesic corrections.

Probing extra dimension through gravitational wave observations of compact binaries and their electromagnetic counterparts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Hao; Gu, Bao-Min; Wang, Yong-Qiang

The future gravitational wave (GW) observations of compact binaries and their possible electromagnetic counterparts may be used to probe the nature of the extra dimension. It is widely accepted that gravitons and photons are the only two completely confirmed objects that can travel along null geodesics in our four-dimensional space-time. However, if there exist extra dimensions and only GWs can propagate freely in the bulk, the causal propagations of GWs and electromagnetic waves (EMWs) are in general different. In this paper, we study null geodesics of GWs and EMWs in a five-dimensional anti-de Sitter space-time in the presence of themore » curvature of the universe. We show that for general cases the horizon radius of GW is longer than EMW within equal time. Taking the GW150914 event detected by the Advanced Laser Interferometer Gravitational-Wave Observatory and the X-ray event detected by the Fermi Gamma-ray Burst Monitor as an example, we study how the curvature k and the constant curvature radius l affect the horizon radii of GW and EMW in the de Sitter and Einstein-de Sitter models of the universe. This provides an alternative method for probing extra dimension through future GW observations of compact binaries and their electromagnetic counterparts.« less

Liver DCE-MRI Registration in Manifold Space Based on Robust Principal Component Analysis.

PubMed

Feng, Qianjin; Zhou, Yujia; Li, Xueli; Mei, Yingjie; Lu, Zhentai; Zhang, Yu; Feng, Yanqiu; Liu, Yaqin; Yang, Wei; Chen, Wufan

2016-09-29

A technical challenge in the registration of dynamic contrast-enhanced magnetic resonance (DCE-MR) imaging in the liver is intensity variations caused by contrast agents. Such variations lead to the failure of the traditional intensity-based registration method. To address this problem, a manifold-based registration framework for liver DCE-MR time series is proposed. We assume that liver DCE-MR time series are located on a low-dimensional manifold and determine intrinsic similarities between frames. Based on the obtained manifold, the large deformation of two dissimilar images can be decomposed into a series of small deformations between adjacent images on the manifold through gradual deformation of each frame to the template image along the geodesic path. Furthermore, manifold construction is important in automating the selection of the template image, which is an approximation of the geodesic mean. Robust principal component analysis is performed to separate motion components from intensity changes induced by contrast agents; the components caused by motion are used to guide registration in eliminating the effect of contrast enhancement. Visual inspection and quantitative assessment are further performed on clinical dataset registration. Experiments show that the proposed method effectively reduces movements while preserving the topology of contrast-enhancing structures and provides improved registration performance.

A Large Hemi-Anechoic Enclosure for Community-Compatible Aeroacoustic Testing of Aircraft Propulsion Systems

NASA Technical Reports Server (NTRS)

Cooper, Beth A.

1993-01-01

A large hemi-anechoic (absorptive walls and acoustically hard floor) noise control enclosure has been erected around a complex of test stands at the NASA Lewis Research Center in Cleveland, Ohio. This new state-of-the-art Aeroacoustic Propulsion Laboratory (APL) provides an all-weather, semisecure test environment while limiting noise to acceptable levels in surrounding residential neighborhoods. The 39.6 m (130 ft) diameter geodesic dome structure houses the new Nozzle Aeroacoustic Test Rig (NATR), an ejector-powered M = 0.3 free jet facility for acoustic testing of supersonic aircraft exhaust nozzles and turbomachinery. A multi-axis, force-measuring Powered Lift Facility (PLF) stand for testing of Short Takeoff Vertical Landing (STOVL) vehicles is also located within the dome. The design of the Aeroacoustic Propulsion Laboratory efficiently accomodates the research functions of two separate test rigs, one of which (NATR) requires a specialized environment for taking acoustic measurements. Absorptive fiberglass wedge treatment on the interior surface of the dome provides a hemi-anechoic interior environment for obtaining the accurate acoustic measurements required to meet research program goals. The APL is the first known geodesic dome structure to incorporate transmission-loss properties as well as interior absorption into a free-standing, community-compatible, hemi-anechoic test facility.

Sachs' free data in real connection variables

NASA Astrophysics Data System (ADS)

De Paoli, Elena; Speziale, Simone

2017-11-01

We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.

The Grand Tour via Geodesic Interpolation of 2-frames

NASA Technical Reports Server (NTRS)

Asimov, Daniel; Buja, Andreas

1994-01-01

Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One of the original inspirations for the grand tour was the experience of trying to comprehend an abstract sculpture in a museum. One tends to walk around the sculpture, viewing it from many different angles. A useful class of grand tours is based on the idea of continuously interpolating an infinite sequence of randomly chosen planes. Visiting randomly (more precisely: uniformly) distributed planes guarantees denseness of the interpolating path. In computer implementations, 2-dimensional orthogonal projections are specified by two 1-dimensional projections which map to the horizontal and vertical screen dimensions, respectively. Hence, a grand tour is specified by a path of pairs of orthonormal projection vectors. This paper describes an interpolation scheme for smoothly connecting two pairs of orthonormal vectors, and thus for constructing interpolating grand tours. The scheme is optimal in the sense that connecting paths are geodesics in a natural Riemannian geometry.

Sagnac delay in the Kerr-dS spacetime: Implications for Mach's principle

NASA Astrophysics Data System (ADS)

Karimov, R. Kh.; Izmailov, R. N.; Garipova, G. M.; Nandi, K. K.

2018-02-01

Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass M and cosmological constant Λ on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits M→ 0, spin a→ 0 and Λ → 0, while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.

Myocardial Iron Loading Assessment by Automatic Left Ventricle Segmentation with Morphological Operations and Geodesic Active Contour on T2* images

NASA Astrophysics Data System (ADS)

Luo, Yun-Gang; Ko, Jacky Kl; Shi, Lin; Guan, Yuefeng; Li, Linong; Qin, Jing; Heng, Pheng-Ann; Chu, Winnie Cw; Wang, Defeng

2015-07-01

Myocardial iron loading thalassemia patients could be identified using T2* magnetic resonance images (MRI). To quantitatively assess cardiac iron loading, we proposed an effective algorithm to segment aligned free induction decay sequential myocardium images based on morphological operations and geodesic active contour (GAC). Nine patients with thalassemia major were recruited (10 male and 16 female) to undergo a thoracic MRI scan in the short axis view. Free induction decay images were registered for T2* mapping. The GAC were utilized to segment aligned MR images with a robust initialization. Segmented myocardium regions were divided into sectors for a region-based quantification of cardiac iron loading. Our proposed automatic segmentation approach achieve a true positive rate at 84.6% and false positive rate at 53.8%. The area difference between manual and automatic segmentation was 25.5% after 1000 iterations. Results from T2* analysis indicated that regions with intensity lower than 20 ms were suffered from heavy iron loading in thalassemia major patients. The proposed method benefited from abundant edge information of the free induction decay sequential MRI. Experiment results demonstrated that the proposed method is feasible in myocardium segmentation and was clinically applicable to measure myocardium iron loading.

Dynamics of kinetic geodesic-acoustic modes and the radial electric field in tokamak neoclassical plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Belli, E.; Bodi, K.; Candy, J.; Chang, C. S.; 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.

2009-06-01

We present edge gyrokinetic simulations of tokamak plasmas using the fully non-linear (full-f) continuum code TEMPEST. A non-linear 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 the damping observed in our TEMPEST q-scans and consistent with the experimental measurements of the scaling of the GAM amplitude with edge q95 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 parallel flow characteristics qualitatively like those observed in experiments.

Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q; Belli, E; Bodi, K

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 dependencemore » 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.« less

Features of quark and lepton mixing from differential geometry of curves on surfaces

NASA Astrophysics Data System (ADS)

Bordes, José; Hong-Mo, Chan; Pfaudler, Jakov; Sheung Tsun, Tsou

1998-09-01

It is noted that the Cabibbo-Kobayashi-Moskawa (CKM) matrix elements for both quarks and leptons as conceived in the dualized standard model (DSM) can be interpreted as direction cosines obtained by moving the Darboux trihedron (a 3-frame) along a trajectory on a sphere traced out through changing energy scales by a 3-vector factorized from the mass matrix. From the Darboux analogues of the well-known Serret-Frenet formulas for space curves, it is seen that the corner elements (Vub,Vtd for quarks, and Ue3,Uτ1 for leptons) are associated with the (geodesic) torsion, while the other off-diagonal elements (Vus,Vcd and Vcb,Vts for quarks, and Ue2,Uμ1 and Uμ3,Uτ2 for leptons) with the (respectively, geodesic and normal) curvatures of the trajectory. From this it follows that (i) the corner elements in both matrices are much smaller than the other elements, and (ii) the Uμ3,Uτ2 elements for the lepton CKM matrix are much larger than their counterparts in the quark matrix. Both these conclusions are strongly borne out by experiment, for quarks in hadron decays and for leptons in neutrino oscillations, and by previous explicit calculations within the DSM scheme.

Graph Design via Convex Optimization: Online and Distributed Perspectives

NASA Astrophysics Data System (ADS)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation problems in sensor networks, multi-agent coordination. Distributed optimization aims to optimize a global objective function formed by summation of coupled local functions over a graph via only local communication and computation. We developed a weighted proximal ADMM for distributed optimization using graph structure. This fully distributed, single-loop algorithm allows simultaneous updates and can be viewed as a generalization of existing algorithms. More importantly, we achieve faster convergence by jointly designing graph weights and algorithm parameters. Finally, we propose a new problem on networks called Online Network Formation Problem: starting with a base graph and a set of candidate edges, at each round of the game, player one first chooses a candidate edge and reveals it to player two, then player two decides whether to accept it; player two can only accept limited number of edges and make online decisions with the goal to achieve the best properties of the synthesized network. The network properties considered include the number of spanning trees, algebraic connectivity and total effective resistance. These network formation games arise in a variety of cooperative multiagent systems. We propose a primal-dual algorithm framework for the general online network formation game, and analyze the algorithm performance by the competitive ratio and regret.

The role of laser determined orbits in geodesy and geophysics

NASA Technical Reports Server (NTRS)

Kolenkiewicz, R.; Smith, D. E.; Dunn, P. J.; Torrence, M. H.; Robbins, J. W.

1991-01-01

Some of the results of orbit analysis from the NASA SLR analysis group are presented. The earth's orientation was determined for 5-day intervals to 1.9 mas for the pole and 0.09 msec for length of day. The 3d center of mass station positions was determined to 33 mm over a period of 3 months, and geodesic rates of SLR tracking sites were determined to 5 mm/yr.

Fabrication of self-rolling geodesic objects and photonic crystal tubes

NASA Astrophysics Data System (ADS)

Danescu, A.; Regreny, Ph; Cremillieu, P.; Leclercq, J.-L.

2018-07-01

This paper presents a stress engineering method that allows the design and fabrication of the analogs of single-wall nanotubes in the class of photonic crystals. The macroscopic shape of the final object is obtained through the stress relaxation of a pre-stressed multilayer planar design. We illustrate the extent of the proposed method by various single-layer and multilayer photonic crystals tubes and micron-scale objects with 5-fold symmetry.

Fabrication of self-rolling geodesic objects and photonic crystal tubes.

PubMed

Danescu, A; Regreny, Ph; Cremillieu, P; Leclercq, J-L

2018-07-13

This paper presents a stress engineering method that allows the design and fabrication of the analogs of single-wall nanotubes in the class of photonic crystals. The macroscopic shape of the final object is obtained through the stress relaxation of a pre-stressed multilayer planar design. We illustrate the extent of the proposed method by various single-layer and multilayer photonic crystals tubes and micron-scale objects with 5-fold symmetry.

Lienard--Wiechert fields and general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Newman, E.T.

1974-01-01

An analogy is extablished between the Lienard-Weichart solutions of the Maxwell equations and the Robinson-Trautman solutions of the einstein equations by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) The field is a geodesic field, (2) it has nonvanishing divergence, (3) it is shear free, and (4) it is twist (or curl) free. (auth)

Generalized Newton Method for Energy Formulation in Image Processing

DTIC Science & Technology

2008-04-01

A. Brook, N. Sochen, and N. Kiryati. Deblurring of color images corrupted by impulsive noise . IEEE Transactions on Image Processing, 16(4):1101–1111...tive functionals: variational image deblurring and geodesic active contours for image segmentation. We show that in addition to the fast convergence...inner product, active contours, deblurring . AMS subject classifications. 35A15, 65K10, 90C53 1. Introduction. Optimization of a cost functional is a

On Light-Like Extremal Surfaces in Curved Spacetimes

NASA Astrophysics Data System (ADS)

Huang, Shou-Jun; He, Chun-Lei

2014-01-01

In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of nonlinear geodesic equations. Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.

Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

NASA Astrophysics Data System (ADS)

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. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time- Domain Method, 3rd. ed. Norwood, MA: Artech House, 2005. [2] M. Hayakawa, K. Ohta, A. P. Nickolaenko, and Y. Ando, "Anomalous effect in Schumann resonance phenomena observed in Japan, possibly associated with the Chi-Chi earthquake in Taiwan," Ann. Geophysicae, in press. [3] J. J. Simpson and A. Taflove, "3-D FDTD modeling of ULF/ELF propagation within the global Earth-ionosphere cavity using an optimized geodesic grid," Proc. IEEE AP-S International Symposium, Washington, D.C., July 2005.

Lower bound on the compactness of isotropic ultracompact objects

NASA Astrophysics Data System (ADS)

Hod, Shahar

2018-04-01

Horizonless spacetimes describing spatially regular ultracompact objects which, like black-hole spacetimes, possess closed null circular geodesics (light rings) have recently attracted much attention from physicists and mathematicians. In the present paper we raise the following physically intriguing question: how compact is an ultracompact object? Using analytical techniques, we prove that ultracompact isotropic matter configurations with light rings are characterized by the dimensionless lower bound maxr{2 m (r )/r }>7 /12 on their global compactness parameter.

Geometrizing adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Rezakhani, Ali; Kuo, Wan-Jung; Hamma, Alioscia; Lidar, Daniel; Zanardi, Paolo

2010-03-01

A time-optimal approach to adiabatic quantum computation (AQC) is formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. We demonstrate this geometrization through some examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance. The underlying connection with quantum phase transitions is also explored.

Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices

NASA Technical Reports Server (NTRS)

Hughston, L. P.; Sommers, P.

1973-01-01

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

NASA Astrophysics Data System (ADS)

Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n

In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.

Spectral methods for the spin-2 equation near the cylinder at spatial infinity

NASA Astrophysics Data System (ADS)

Macedo, Rodrigo P.; Valiente Kroon, Juan A.

2018-06-01

We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us to compute the solutions to these equations up to the critical sets where null infinity intersects with spatial infinity. Moreover, we use the convergence rates of the numerical solutions to read-off their regularity properties.

Passive Acoustic Thermometry Using Low-Frequency Deep Water Noise

DTIC Science & Technology

2015-09-30

where potential ice noise sources contributing to the coherent arrivals shown in C-D are located (18b). In the low-frequency band used in this...seismic activity (e.g. along major undersea fault lines) or ice -breaking noise in the Polar Regions (19-22). Ice - generated ambient noise near the...using geodesic paths to obtain a simple estimate of the geographical area from where ice -generated ambient noise is likely to emanate for each site

Modified gravity (MOG), the speed of gravitational radiation and the event GW170817/GRB170817A

NASA Astrophysics Data System (ADS)

Green, M. A.; Moffat, J. W.; Toth, V. T.

2018-05-01

Modified gravity (MOG) is a covariant, relativistic, alternative gravitational theory whose field equations are derived from an action that supplements the spacetime metric tensor with vector and scalar fields. Both gravitational (spin 2) and electromagnetic waves travel on null geodesics of the theory's one metric. MOG satisfies the weak equivalence principle and is consistent with observations of the neutron star merger and gamma ray burster event GW170817/GRB170817A.

Tsunami Propagation Models Based on First Principles

DTIC Science & Technology

2012-11-21

geodesic lines from the epicenter shown in the figure are great circles with a longitudinal separation of 90o, which define a ‘ lune ’ that covers one...past which the waves begin to converge according to Model C. A tsunami propagating in this lune does not encounter any continental landmass until...2011 Japan tsunami in a lune of angle 90o with wavefronts at intervals of 5,000 km The 2011 Japan tsunami was felt throughout the Pacific Ocean

Cosmological bounce and Genesis beyond Horndeski

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolevatov, R.; Mironov, S.; Volkova, V.

2017-08-01

We study 'classical' bouncing and Genesis models in beyond Horndeski theory. We give an example of spatially flat bouncing solution that is non-singular and stable throughout the whole evolution. We also provide an example of stable geodesically complete Genesis with similar features. The model is arranged in such a way that the scalar field driving the cosmological evolution initially behaves like full-fledged beyond Horndeski, whereas at late times it becomes a massless scalar field minimally coupled to gravity.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able tomore » extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.« less

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

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

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

What is general relativity?

NASA Astrophysics Data System (ADS)

Coley, Alan A.; Wiltshire, David L.

2017-05-01

General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: what is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein’s equations? We address these questions. If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe. Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe. This possibility is hinted at by diverse approaches to quantum gravity which find a dynamical reduction to two effective dimensions at high energies on one hand, and by cosmological observations which are beginning to strongly restrict the class of viable inflationary phenomenologies on the other. We suggest that the foundational principles of general relativity will play a central role in reformulating the theory of spacetime structure to meet the challenges of cosmology in the 21st century.

Terrestrial Sagnac delay constraining modified gravity models

NASA Astrophysics Data System (ADS)

Karimov, R. Kh.; Izmailov, R. N.; Potapov, A. A.; Nandi, K. K.

2018-04-01

Modified gravity theories include f(R)-gravity models that are usually constrained by the cosmological evolutionary scenario. However, it has been recently shown that they can also be constrained by the signatures of accretion disk around constant Ricci curvature Kerr-f(R0) stellar sized black holes. Our aim here is to use another experimental fact, viz., the terrestrial Sagnac delay to constrain the parameters of specific f(R)-gravity prescriptions. We shall assume that a Kerr-f(R0) solution asymptotically describes Earth's weak gravity near its surface. In this spacetime, we shall study oppositely directed light beams from source/observer moving on non-geodesic and geodesic circular trajectories and calculate the time gap, when the beams re-unite. We obtain the exact time gap called Sagnac delay in both cases and expand it to show how the flat space value is corrected by the Ricci curvature, the mass and the spin of the gravitating source. Under the assumption that the magnitude of corrections are of the order of residual uncertainties in the delay measurement, we derive the allowed intervals for Ricci curvature. We conclude that the terrestrial Sagnac delay can be used to constrain the parameters of specific f(R) prescriptions. Despite using the weak field gravity near Earth's surface, it turns out that the model parameter ranges still remain the same as those obtained from the strong field accretion disk phenomenon.

Equatorial Geodesics Around the Magnetars

NASA Astrophysics Data System (ADS)

Alfradique, Viviane A. P.; Troconis, Orlenys N.; Negreiros, Rodrigo P.

Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than 1015 G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to 1017G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection.

PubMed

Li, Hongyin; Bai, Yanzheng; Hu, Ming; Luo, Yingxin; Zhou, Zebing

2016-12-23

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to 8 × 10 - 13 m / s 2 / H z 1 / 2 , which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 pm / Hz 1 / 2 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching.

Constraining black holes with light boson hair and boson stars using epicyclic frequencies and quasiperiodic oscillations

NASA Astrophysics Data System (ADS)

Franchini, Nicola; Pani, Paolo; Maselli, Andrea; Gualtieri, Leonardo; Herdeiro, Carlos A. R.; Radu, Eugen; Ferrari, Valeria

2017-06-01

Light bosonic fields are ubiquitous in extensions of the Standard Model. Even when minimally coupled to gravity, these fields might evade the assumptions of the black-hole no-hair theorems and give rise to spinning black holes which can be drastically different from the Kerr metric. Furthermore, they allow for self-gravitating compact solitons, known as (scalar or Proca) boson stars. The quasiperiodic oscillations (QPOs) observed in the x-ray flux emitted by accreting compact objects carry information about the strong-field region, thus providing a powerful tool to constrain deviations from Kerr's geometry and to search for exotic compact objects. By using the relativistic precession model as a proxy to interpret the QPOs in terms of geodesic frequencies, we investigate how the QPO frequencies could be used to test the no-hair theorem and the existence of light bosonic fields near accreting compact objects. We show that a detection of two QPO triplets with current sensitivity can already constrain these models and that the future eXTP mission or a LOFT-like mission can set very stringent constraints on black holes with bosonic hair and on (scalar or Proca) boson stars. The peculiar geodesic structure of compact scalar/Proca boson stars implies that these objects can easily be ruled out as alternative models for x-ray source GRO J1655-40.

High-velocity collision of particles around a rapidly rotating black hole

NASA Astrophysics Data System (ADS)

Harada, T.

2014-03-01

We have derived a general formula for the centre-of-mass (CM) energy for the near-horizon collision of two general geodesic particles around a Kerr black hole. We have found that if the angular momentum of the particle satisfies the critical condition, the CM energy can be arbitrarily high. We have then applied the formula to the collision of a particle orbiting an innermost stable circular orbit (ISCO) and another generic particle near the horizon, and found that the CM energy is arbitrarily high if we take the maximal limit of the black hole spin. In view of the astrophysical significance of the ISCO, this implies that particles can collide around a rapidly rotating black hole with a very high CM energy without any artificial fine-tuning. We have next applied the formula to the collision of general inclined geodesic particles and shown that in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes, not only at the equator but also on a belt centred at the equator between two latitudes. This is also true in the scenario through the collision of a last stable orbit particle. This strongly suggests that if signals due to high-energy collision are to be observed, such signals will be generated primarily on this belt.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

Geodesic topological analysis of trabecular bone microarchitecture from high-spatial resolution magnetic resonance images.

PubMed

Carballido-Gamio, Julio; Krug, Roland; Huber, Markus B; Hyun, Ben; Eckstein, Felix; Majumdar, Sharmila; Link, Thomas M

2009-02-01

In vivo assessment of trabecular bone microarchitecture could improve the prediction of fracture risk and the efficacy of osteoporosis treatment and prevention. Geodesic topological analysis (GTA) is introduced as a novel technique to quantify the trabecular bone microarchitecture from high-spatial resolution magnetic resonance (MR) images. Trabecular bone parameters that quantify the scale, topology, and anisotropy of the trabecular bone network in terms of its junctions are the result of GTA. The reproducibility of GTA was tested with in vivo images of human distal tibiae and radii (n = 6) at 1.5 Tesla; and its ability to discriminate between subjects with and without vertebral fracture was assessed with ex vivo images of human calcanei at 1.5 and 3.0 Tesla (n = 30). GTA parameters yielded an average reproducibility of 4.8%, and their individual areas under the curve (AUC) of the receiver operating characteristic curve analysis for fracture discrimination performed better at 3.0 than at 1.5 Tesla reaching values of up to 0.78 (p < 0.001). Logistic regression analysis demonstrated that fracture discrimination was improved by combining GTA parameters, and that GTA combined with bone mineral density (BMD) allow for better discrimination than BMD alone (AUC = 0.95; p < 0.001). Results indicate that GTA can substantially contribute in studies of osteoporosis involving imaging of the trabecular bone microarchitecture. Copyright 2009 Wiley-Liss, Inc.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection

PubMed Central

Li, Hongyin; Bai, Yanzheng; Hu, Ming; Luo, Yingxin; Zhou, Zebing

2016-01-01

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to 8×10−13m/s2/Hz1/2, which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 pm/Hz1/2 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching. PMID:28025534

Colliding holes in Riemann surfaces and quantum cluster algebras

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2018-01-01

In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

Computerized Liver Volumetry on MRI by Using 3D Geodesic Active Contour Segmentation

PubMed Central

Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji

2014-01-01

OBJECTIVE Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. SUBJECTS AND METHODS Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. RESULTS The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p < 0.001). CONCLUSION The MRI liver volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time. PMID:24370139

Computerized liver volumetry on MRI by using 3D geodesic active contour segmentation.

PubMed

Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji

2014-01-01

Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p < 0.001). The MRI liver volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time.

Correlative Feature Analysis for Multimodality Breast CAD

DTIC Science & Technology

2009-09-01

Imaging 20, 1275–1284 2001. 22V. Caselles, R . Kimmel, and G. Sapiro, “Geodesic active contours,” Int. J. Comput. Vis. 22, 61–79 1997. 23R. Malladi , J...A. R . Jamieson, C. A. Sennett, and S. A. Jensen, “Evaluation of computer-aided diagnosis on a large clinical full-field digital mammographic dataset...Academic Radiology, 15, 1437-1445 (2008). Conference Proceeding Papers [1] Y. Yuan, M. L. Giger, K. Suzuki, H. Li, and A. R . Jamieson, “A

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

Proceedings of a workshop: Multidisciplinary Use of the Very Long Baseline Array

NASA Technical Reports Server (NTRS)

1984-01-01

The National Research Council organized a workshop to gather together experts in very long baseline interometry, astronomy, space navigation, general relativity and the earth sciences. The purpose of the workshop was to provide a forum for consideration of the various possible multi-disciplinary uses of the very long baseline array. Geophysical investigations received major attention. Geodesic uses of the very long baseline array were identified as were uses for fundamental astronomy investigations. Numerous specialized uses were identified.

Absence of positive solutions to the system of differential inequalities on manifolds

NASA Astrophysics Data System (ADS)

Sun, Yuhua

2018-01-01

We investigate the nonexistence of positive solutions to a certain system of differential inequalities on a complete connected non-compact Riemannian manifold. We show that if for some reference point x0, the volume of geodesic ball μ(B(x0, r)) ≤ Crp ln q r holds for all large enough r and for some constant C, then there exists no positive solution to the system. Here the exponents p and q are sharp and cannot be relaxed.

Galaxy travel via Alcubierre's warp drive

NASA Astrophysics Data System (ADS)

Fil'chenkov, M.; Laptev, Yu.

2017-10-01

The possibilities of interstellar flights for extraterrestrial civilizations have been considered. A superluminal motion (hypermotion) via M. Alcubierre's warp drive is considered. Parameters of the warp drive have been estimated. The equations of starship geodesics have been solved. The starship velocity has been shown to exceed the speed of light, with the local velocity relative to the deformed space-time being subluminal. Hawking's radiation does not prove to affect the ship interior considerably. Difficulties related to a practical realization of the hypermotion are indicated.

The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

Schröder, Jörg; von Hoegen, Markus; Neff, Patrizio

2017-10-01

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \\varvec{F} to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.

Ruijsenaars-Schneider three-body models with N = 2 supersymmetry

NASA Astrophysics Data System (ADS)

Galajinsky, Anton

2018-04-01

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N = 2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.

Observations from Sarmizegetusa Sanctuary

NASA Astrophysics Data System (ADS)

Barbosu, M.

2000 years ago, Sarmizegetusa Regia was the capital of ancient Dacia (today: Romania). It is known that the Dacian high priests used the Sanctuary of Sarmizegetusa not only for religious ceremonies, but also for astronomical observations. After having completed geodesic measurements, we analyzed the architecture of the sanctuary with its main points, directions and circles. We discuss here what kind of astronomical observations could have been made with the scientific knowledge of that time. The final section of this work is dedicated to the remarkable resemblance between Sarmizegztusa and Stonehenge.

Cosmological aspects of the Eisenhart-Duval lift

NASA Astrophysics Data System (ADS)

Cariglia, M.; Galajinsky, A.; Gibbons, G. W.; Horvathy, P. A.

2018-04-01

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton-Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart-Duval framework is presented.

Chaos in pseudo-Newtonian black holes with halos

NASA Astrophysics Data System (ADS)

Guéron, E.; Letelier, P. S.

2001-03-01

Newtonian as well as special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole with a dipolar halo. The black hole is modeled by either the usual monopole potential or the Paczyńki-Wiita pseudo-Newtonian potential. The full general relativistic similar case is also considered. The Poincaré section method and the Lyapunov characteristic exponents show that the orbits for the pseudo-Newtonian potential models are more unstable than the corresponding general relativistic geodesics.

Perfect relativistic magnetohydrodynamics around black holes in horizon penetrating coordinates

NASA Astrophysics Data System (ADS)

Cherubini, Christian; Filippi, Simonetta; Loppini, Alessandro; Moradi, Rahim; Ruffini, Remo; Wang, Yu; Xue, She-Sheng

2018-03-01

Plasma accreting processes on black holes represent a central problem for relativistic astrophysics. In this context, here we specifically revisit the classical Ruffini-Wilson work developed for analytically modeling via geodesic equations the accretion of perfect magnetized plasma on a rotating Kerr black hole. Introducing the horizon penetrating coordinates found by Doran 25 years later, we revisit the entire approach studying Maxwell invariants, electric and magnetic fields, volumetric charge density and electromagnetic total energy. We finally discuss the physical implications of this analysis.

Gravity with free initial conditions: A solution to the cosmological constant problem testable by CMB B -mode polarization

NASA Astrophysics Data System (ADS)

Totani, Tomonori

2017-10-01

In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a motivation to solve the cosmological constant problem. This was done by setting four constraints on metric variations in the action principle, which is reasonable because the gravity's physical degrees of freedom are at most six. However, there are two problems about this theory; the three constraints in addition to the unimodular condition were introduced without clear physical meanings, and the flat Minkowski spacetime is unstable against perturbations. Here a new set of gravitational field equations is derived by replacing the three constraints with new ones requiring that geodesic paths remain geodesic against metric variations. The instability problem is then naturally solved. Implications for the cosmological constant Λ are unchanged; the theory converges into EFE with nonzero Λ by inflation, but Λ varies on scales much larger than the present Hubble horizon. Then galaxies are formed only in small Λ regions, and the cosmological constant problem is solved by the anthropic argument. Because of the increased degrees of freedom in metric dynamics, the theory predicts new non-oscillatory modes of metric anisotropy generated by quantum fluctuation during inflation, and CMB B -mode polarization would be observed differently from the standard predictions by general relativity.

Riemann curvature of a boosted spacetime geometry

NASA Astrophysics Data System (ADS)

Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco

2016-10-01

The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.

General relativistic radiative transfer code in rotating black hole space-time: ARTIST

NASA Astrophysics Data System (ADS)

Takahashi, Rohta; Umemura, Masayuki

2017-02-01

We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.

Shadows of rotating five-dimensional charged EMCS black holes

NASA Astrophysics Data System (ADS)

Amir, Muhammed; Singh, Balendra Pratap; Ghosh, Sushant G.

2018-05-01

Higher-dimensional theories admit astrophysical objects like supermassive black holes, which are rather different from standard ones, and their gravitational lensing features deviate from general relativity. It is well known that a black hole shadow is a dark region due to the falling geodesics of photons into the black hole and, if detected, a black hole shadow could be used to determine which theory of gravity is consistent with observations. Measurements of the shadow sizes around the black holes can help to evaluate various parameters of the black hole metric. We study the shapes of the shadow cast by the rotating five-dimensional charged Einstein-Maxwell-Chern-Simons (EMCS) black holes, which is characterized by four parameters, i.e., mass, two spins, and charge, in which the spin parameters are set equal. We integrate the null geodesic equations and derive an analytical formula for the shadow of the five-dimensional EMCS black hole, in turn, to show that size of black hole shadow is affected due to charge as well as spin. The shadow is a dark zone covered by a deformed circle, and the size of the shadow decreases with an increase in the charge q when compared with the five-dimensional Myers-Perry black hole. Interestingly, the distortion increases with charge q. The effect of these parameters on the shape and size of the naked singularity shadow of the five-dimensional EMCS black hole is also discussed.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

Giant wormholes in ghost-free bigravity theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sushkov, Sergey V.; Volkov, Mikhail S., E-mail: sergey_sushkov@mail.ru, E-mail: volkov@lmpt.univ-tours.fr

2015-06-01

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we callmore » W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.« less

Giant wormholes in ghost-free bigravity theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sushkov, Sergey V.; Volkov, Mikhail S.; Laboratoire de Mathématiques et Physique Théorique CNRS-UMR 7350, Université de Tours, Parc de Grandmont, 37200 Tours

2015-06-09

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we callmore » W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.« less

What's the point? Hole-ography in Poincaré AdS

NASA Astrophysics Data System (ADS)

Espíndola, Ricardo; Güijosa, Alberto; Landetta, Alberto; Pedraza, Juan F.

2018-01-01

In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincaré wedge of AdS_3 via hole-ography, i.e., in terms of differential entropy of the dual CFT_2. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincaré AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincaré is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincaré wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincaré AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Test-particle motion in the nonsymmetric gravitation theory

NASA Astrophysics Data System (ADS)

Moffat, J. W.

1987-06-01

A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.

Gully erosion balance in the context of pedological-sedimentological research, geodesic measurements and Aerial Laser Scanning (Lublin Upland, E Poland)

NASA Astrophysics Data System (ADS)

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 measurements of the gully floor and edges were performed. The basic image was obtained from ALS (Aerial Laser Scanning) data. Pedo-geomorphic research permitted the determination of phases of development of the gully. Dates 14C obtained from sediments on the fan at the mouth of the gully were also used.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Galaxy rotation curves via conformal factors

NASA Astrophysics Data System (ADS)

Sporea, Ciprian A.; Borowiec, Andrzej; Wojnar, Aneta

2018-04-01

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in the Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other, the so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions n ≥slant 3 and to the case of tensor fields of any order.

Rigidity in vacuum under conformal symmetry

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Vega, Carlos

2018-04-01

Motivated in part by Eardley et al. (Commun Math Phys 106(1):137-158, 1986), in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a timelike conformal Killing field X, then M must split as a metric product, and X must be Killing. This gives a partial proof of the Bartnik splitting conjecture in the vacuum setting.

Topological geons with self-gravitating phantom scalar field

NASA Astrophysics Data System (ADS)

Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

2017-12-01

A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kerner, Ryan; Mann, R.B.

We investigate quantum tunnelling methods for calculating black hole temperature, specifically the null-geodesic method of Parikh and Wilczek and the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of these methods to a broad class of spacetimes with event horizons, including Rindler and nonstatic spacetimes such as Kerr-Newman and Taub-NUT. We obtain a general form for the temperature of Taub-NUT-AdS black holes that is commensurate with other methods. We examine the limitations of these methods for extremal black holes, taking the extremal Reissner-Nordstrom spacetime as a case in point.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krtous, Pavel; Frolov, Valeri P.; Kubiznak, David

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

Orbital resonances around black holes.

PubMed

Brink, Jeandrew; Geyer, Marisa; Hinderer, Tanja

2015-02-27

We compute the length and time scales associated with resonant orbits around Kerr black holes for all orbital and spin parameters. Resonance-induced effects are potentially observable when the Event Horizon Telescope resolves the inner structure of Sgr A*, when space-based gravitational wave detectors record phase shifts in the waveform during the resonant passage of a compact object spiraling into the black hole, or in the frequencies of quasiperiodic oscillations for accreting black holes. The onset of geodesic chaos for non-Kerr spacetimes should occur at the resonance locations quantified here.

Motion Among Random Obstacles on a Hyperbolic Space

NASA Astrophysics Data System (ADS)

Orsingher, Enzo; Ricciuti, Costantino; Sisti, Francesco

2016-02-01

We consider the motion of a particle along the geodesic lines of the Poincaré half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.

Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-02-01

A random motion on the Poincaré half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are admitted. The main results concern the mean hyperbolic distance (and also the conditional mean distance) in all versions of the motion envisaged. Also an analogous motion on orthogonal circles of the sphere is examined and the evolution of the mean distance from the starting point is investigated.

Galaxy rotation curves via conformal factors.

PubMed

Sporea, Ciprian A; Borowiec, Andrzej; Wojnar, Aneta

2018-01-01

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in the Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other, the so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

KB3D Reference Manual. Version 1.a

NASA Technical Reports Server (NTRS)

Munoz, Cesar; Siminiceanu, Radu; Carreno, Victor A.; Dowek, Gilles

2005-01-01

This paper is a reference manual describing the implementation of the KB3D conflict detection and resolution algorithm. The algorithm has been implemented in the Java and C++ programming languages. The reference manual gives a short overview of the detection and resolution functions, the structural implementation of the program, inputs and outputs to the program, and describes how the program is used. Inputs to the program can be rectangular coordinates or geodesic coordinates. The reference manual also gives examples of conflict scenarios and the resolution outputs the program produces.

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Of spheres and squares: Can Sloterdijk help us rethink the architecture of climate science?

PubMed

Skrydstrup, Martin

2016-12-01

This article explores how different visions and values of science translate into different architectural shapes. I bring Peter Sloterdijk's 'spherology' to bear on my ethnographic fieldwork at the NEEM ice core base in Greenland, a significant node in the global infrastructure of climate science. I argue that the visual form of the geodesic dome of the camp materializes specific values and visions of this branch of paleoclimate science, which I elaborate vis-a-vis the pragmatic claims of the scientists/designers and the particular architectural history of Danish ice core drilling in Greenland. I argue that this aesthetic history articulates with Buckminster Fuller's ideas of a 'new nature' and 'scalar connections' encapsulated in his geodesic form. Second, I argue that the aesthetic production of space in the camp replicates the modern distinction between science and society, in so far as the lab space is rectangular and the recreational space is spherical. Third, I argue that NEEM scientists and Sloterdijk are essentially engaged in a common project: the scientists work hard to align air bubbles in the cores with atmospheric fluctuations in the hemisphere on the evidentiary terrain of ice, and Sloterdijk attempts to connect micro-uteri with macro-uteri in an attempt to fundamentally rethink space. Fuller's notion of 'Spaceship Earth', appropriated by Sloterdijk in his thinking about anthropogenic climate change, lends itself well to capturing the scalar alignments and the isolated NEEM base - on a mission to save planet Earth. In conclusion, I argue that Sloterdijk's spherology may serve as a point of departure for rethinking the aesthetic grammar of the architecture of science.

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

NASA Astrophysics Data System (ADS)

Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

2012-10-01

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.

2015-09-01

We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.

A topo-graph model for indistinct target boundary definition from anatomical images.

PubMed

Cui, Hui; Wang, Xiuying; Zhou, Jianlong; Gong, Guanzhong; Eberl, Stefan; Yin, Yong; Wang, Lisheng; Feng, Dagan; Fulham, Michael

2018-06-01

It can be challenging to delineate the target object in anatomical imaging when the object boundaries are difficult to discern due to the low contrast or overlapping intensity distributions from adjacent tissues. We propose a topo-graph model to address this issue. The first step is to extract a topographic representation that reflects multiple levels of topographic information in an input image. We then define two types of node connections - nesting branches (NBs) and geodesic edges (GEs). NBs connect nodes corresponding to initial topographic regions and GEs link the nodes at a detailed level. The weights for NBs are defined to measure the similarity of regional appearance, and weights for GEs are defined with geodesic and local constraints. NBs contribute to the separation of topographic regions and the GEs assist the delineation of uncertain boundaries. Final segmentation is achieved by calculating the relevance of the unlabeled nodes to the labels by the optimization of a graph-based energy function. We test our model on 47 low contrast CT studies of patients with non-small cell lung cancer (NSCLC), 10 contrast-enhanced CT liver cases and 50 breast and abdominal ultrasound images. The validation criteria are the Dice's similarity coefficient and the Hausdorff distance. Student's t-test show that our model outperformed the graph models with pixel-only, pixel and regional, neighboring and radial connections (p-values <0.05). Our findings show that the topographic representation and topo-graph model provides improved delineation and separation of objects from adjacent tissues compared to the tested models. Copyright © 2018 Elsevier B.V. All rights reserved.

Comparison of collision operators for the geodesic acoustic mode

NASA Astrophysics Data System (ADS)

Li, Yang; Gao, Zhe

2015-04-01

The collisional damping rate and real frequency of the geodesic acoustic mode (GAM) are solved from a drift kinetic model with different collision operators. As the ion collision rate increases, the damping rate increases at low collision rate but decays at high ion collision rate. Different collision operators do not change the overall trend but influence the magnitude of the damping rate. The collision damping is much overestimated with the number-conserving-only Krook operator; on the other hand, using the Lorentz operator with a constant collision rate, the damping is overestimated at low collision rate but underestimated at high collision rate. The results from the Krook operator with both number and energy conservation terms, the Lorentz operator with an energy-dependent collision rate and the full Hirshman-Sigmar-Clarke collision operator are very close. Meanwhile, as the ion collision rate increases, the GAM frequency decreases from the collisionless value, \\sqrt {7/4+τ} {vti}/R , to \\sqrt {1+τ} {vti}/R for the number-conserving-only Krook operator, but to \\sqrt {5/3+τ} {vti}/R for the other four operators, which conserve both number and energy, where τ, vti and R are the ratio of electron temperature to ion temperature, the ion thermal velocity and the major radius, respectively. The results imply that the property of energy conservation of the collision operator is important to the dynamics of the GAM as well as that of number conservation, which may provide guidance in choosing collision operators in further study of the zonal flow (ZF) dynamics, such as the nonlinear simulation of the ZF-turbulence system.

Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak

NASA Astrophysics Data System (ADS)

Seidl, J.; Krbec, J.; Hron, M.; Adamek, J.; Hidalgo, C.; Markovic, T.; Melnikov, A. V.; Stockel, J.; Weinzettl, V.; Aftanas, M.; Bilkova, P.; Bogar, O.; Bohm, P.; Eliseev, L. G.; Hacek, P.; Havlicek, J.; Horacek, J.; Imrisek, M.; Kovarik, K.; Mitosinkova, K.; Panek, R.; Tomes, M.; Vondracek, P.

2017-12-01

Axisymmetric geodesic acoustic mode (GAM) oscillations of the magnetic field, plasma potential and electron temperature have been identified on the COMPASS tokamak. This work brings an overview of their electromagnetic properties studied by multi-pin reciprocating probes and magnetic diagnostics. The n  =  0 fluctuations form a continuous spectrum in limited plasmas but change to a single dominant peak in diverted configuration. At the edge of diverted plasmas the mode exhibits a non-local structure with a constant frequency over a radial extent of at least several centimeters. Nevertheless, the frequency still reacts on temporal changes of plasma temperature caused by an auxiliary NBI heating as well as those induced by periodic sawtooth crashes. Radial wavelength of the mode is found to be about 1-4 cm, with values larger for the plasma potential than for the electron temperature. The mode propagates radially outward and its radial structure induces oscillations of a poloidal E  ×  B velocity, that can locally reach the level of the mean poloidal flow. Bicoherence analysis confirms a non-linear interaction of GAM with a broadband ambient turbulence. The mode exhibits strong axisymmetric magnetic oscillations that are studied both in the poloidal and radial components of the magnetic field. Their poloidal standing-wave structure was confirmed and described for the first time in diverted plasmas. In limited plasmas their amplitude scales with safety factor. Strong suppression of the magnetic GAM component, and possibly of GAM itself, is observed during co-current but not counter-current NBI.

CT liver volumetry using geodesic active contour segmentation with a level-set algorithm

NASA Astrophysics Data System (ADS)

Suzuki, Kenji; Epstein, Mark L.; Kohlbrenner, Ryan; Obajuluwa, Ademola; Xu, Jianwu; Hori, Masatoshi; Baron, Richard

2010-03-01

Automatic liver segmentation on CT images is challenging because the liver often abuts other organs of a similar density. Our purpose was to develop an accurate automated liver segmentation scheme for measuring liver volumes. We developed an automated volumetry scheme for the liver in CT based on a 5 step schema. First, an anisotropic smoothing filter was applied to portal-venous phase CT images to remove noise while preserving the liver structure, followed by an edge enhancer to enhance the liver boundary. By using the boundary-enhanced image as a speed function, a fastmarching algorithm generated an initial surface that roughly estimated the liver shape. A geodesic-active-contour segmentation algorithm coupled with level-set contour-evolution refined the initial surface so as to more precisely fit the liver boundary. The liver volume was calculated based on the refined liver surface. Hepatic CT scans of eighteen prospective liver donors were obtained under a liver transplant protocol with a multi-detector CT system. Automated liver volumes obtained were compared with those manually traced by a radiologist, used as "gold standard." The mean liver volume obtained with our scheme was 1,520 cc, whereas the mean manual volume was 1,486 cc, with the mean absolute difference of 104 cc (7.0%). CT liver volumetrics based on an automated scheme agreed excellently with "goldstandard" manual volumetrics (intra-class correlation coefficient was 0.95) with no statistically significant difference (p(F<=f)=0.32), and required substantially less completion time. Our automated scheme provides an efficient and accurate way of measuring liver volumes.

Predicting Structural Behavior of Filament Wound Composite Pressure Vessel Using Three Dimensional Shell Analysis

NASA Astrophysics Data System (ADS)

Madhavi, M.; Venkat, R.

2014-01-01

Fiber reinforced polymer composite materials with their higher specific strength, moduli and tailorability characteristics will result in reduction of weight of the structure. The composite pressure vessels with integrated end domes develop hoop stresses that are twice longitudinal stresses and when isotropic materials like metals are used for development of the hardware and the material is not fully utilized in the longitudinal/meridional direction resulting in over weight components. The determination of a proper winding angles and thickness is very important to decrease manufacturing difficulties and to increase structural efficiency. In the present study a methodology is developed to understand structural characteristics of filament wound pressure vessels with integrated end domes. Progressive ply wise failure analysis of composite pressure vessel with geodesic end domes is carried out to determine matrix crack failure, burst pressure values at various positions of the shell. A three dimensional finite element analysis is computed to predict the deformations and stresses in the composite pressure vessel. The proposed method could save the time to design filament wound structures, to check whether the ply design is safe for the given input conditions and also can be adapted to non-geodesic structures. The results can be utilized to understand structural characteristics of filament wound pressure vessels with integrated end domes. This approach can be adopted for various applications like solid rocket motor casings, automobile fuel storage tanks and chemical storage tanks. Based on the predictions a composite pressure vessel is designed and developed. Hydraulic test is performed on the composite pressure vessel till the burst pressure.

Particles motion on topological Lifshitz black holes in 3+1 dimensions

NASA Astrophysics Data System (ADS)

Olivares, Marco; Rojas, Germán; Vásquez, Yerko; Villanueva, J. R.

2013-09-01

In the present paper we study the causal structure of a topological black hole presented by Mann R.B. (in J. High Energy Phys. 06:075, 2009) by mean the standard Lagrangian procedure, which allow us analyze qualitatively the behavior of test particles using the effective potential. Then, the geodesic motion of massive and massless particles is obtained analytically. We find that confined orbits are forbidden on this spacetime, however radial photons can escape to infinity in an infinite proper time but in a finite coordinate time, this correspond to an interesting and novel result.

Entanglement Equilibrium and the Einstein Equation.

PubMed

Jacobson, Ted

2016-05-20

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

On the number of infinite geodesics and ground states in disordered systems

NASA Astrophysics Data System (ADS)

Wehr, Jan

1997-04-01

We study first-passage percolation models and their higher dimensional analogs—models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to +∞. As corollaries we show that in any dimension d≥2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or +∞. Proofs employ simple large-deviation estimates and ergodic arguments.

Conformal Yano-Killing Tensors in General Relativity

NASA Astrophysics Data System (ADS)

Jezierski, Jacek

2011-09-01

How CYK tensors appear in General Relativity? Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness, which guarantees well defined total angular momentum [2, 3, 4] Conserved quantities - asymptotic charges (ℐ, 𝓲0) [2, 3, 4, 5, 6, 9] Quasi-local mass and "rotational energy" for Kerr black hole [5] Constants of motion along geodesics and symmetric Killing tensors [5, 6] Spacetimes possessing CYK tensor [10]: Minkowski (quadratic polynomials) [5] (Anti-)deSitter (natural construction) [7, 8, 9] Kerr (type D spacetime) [5] Taub-NUT (new symmetric conformal Killing tensors) [6] Other applications: Symmetries of Dirac operator Symmetries of Maxwell equations

Collisional Penrose process with spinning particles

NASA Astrophysics Data System (ADS)

Mukherjee, Sajal

2018-03-01

In this article, we have investigated collisional Penrose process (CPP) using spinning particles in a Kerr spacetime. Recent studies have shown that the collision between two spinning particles can produce a significantly high energy in the center of mass frame. Here, we explicitly compute the energy extraction and efficiency as measured by an observer at infinity. We consider the colliding particles as well as the escaping particles may contain spins. It has been shown that the energy extraction is larger than the non-spinning case and also their possibility to escape to infinity is wider than the geodesics.

Indirect (source-free) integration method. II. Self-force consistent radial fall

NASA Astrophysics Data System (ADS)

Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane

2016-12-01

We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force (SF). The Mode-Sum regularization is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the SF through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in [Int. J. Geom. Meth. Mod. Phys. 11 (2014) 1450090].

Born again universe

NASA Astrophysics Data System (ADS)

Graham, Peter W.; Kaplan, David E.; Rajendran, Surjeet

2018-02-01

We present a class of nonsingular, bouncing cosmologies that evade singularity theorems through the use of vorticity in compact extra dimensions. The vorticity combats the focusing of geodesics during the contracting phase. The construction requires fluids that violate the null energy condition (NEC) in the compact dimensions, where they can be provided by known stable NEC violating sources such as Casimir energy. The four dimensional effective theory contains an NEC violating fluid of Kaluza-Klein excitations of the higher dimensional metric. These spacetime metrics could potentially allow dynamical relaxation to solve the cosmological constant problem. These ideas can also be used to support traversable Lorentzian wormholes.

Vacuum Decay via Lorentzian Wormholes

NASA Astrophysics Data System (ADS)

Rosales, J. L.

We speculate about the space-time description due to the presence of Lorentzian worm-holes (handles in space-time joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordström space-times is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the value of the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete space-times should be acutally negligible in our physical Universe.

Regge calculus and observations. II. Further applications.

NASA Astrophysics Data System (ADS)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

Relaxation Dynamics in the Merging of N Independent Condensates

NASA Astrophysics Data System (ADS)

Aidelsburger, M.; Ville, J. L.; Saint-Jalm, R.; Nascimbène, S.; Dalibard, J.; Beugnon, J.

2017-11-01

Controlled quantum systems such as ultracold atoms can provide powerful platforms to study nonequilibrium dynamics of closed many-body quantum systems, especially since a complete theoretical description is generally challenging. In this Letter, we present a detailed study of the rich out-of-equilibrium dynamics of an adjustable number N of uncorrelated condensates after connecting them in a ring-shaped optical trap. We observe the formation of long-lived supercurrents and confirm the scaling of their winding number with N in agreement with the geodesic rule. Moreover, we provide insight into the microscopic mechanism that underlies the smoothening of the phase profile.

Clock synchronization by accelerated observers - Metric construction for arbitrary congruences of world lines

NASA Technical Reports Server (NTRS)

Henriksen, R. N.; Nelson, L. A.

1985-01-01

Clock synchronization in an arbitrarily accelerated observer congruence is considered. A general solution is obtained that maintains the isotropy and coordinate independence of the one-way speed of light. Attention is also given to various particular cases including, rotating disk congruence or ring congruence. An explicit, congruence-based spacetime metric is constructed according to Einstein's clock synchronization procedure and the equation for the geodesics of the space-time was derived using Hamilton-Jacobi method. The application of interferometric techniques (absolute phase radio interferometry, VLBI) to the detection of the 'global Sagnac effect' is also discussed.

Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

DTIC Science & Technology

2011-04-01

L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

Neutrino Masses in the Landscape and Global-Local Dualities in Eternal Inflation

NASA Astrophysics Data System (ADS)

Mainemer Katz, Dan

In this dissertation we study two topics in Theoretical Cosmology: one more formal, the other more phenomenological. We work in the context of eternally inflating cosmologies. These arise in any fundamental theory that contains at least one stable or metastable de Sitter vacuum. Each topic is presented in a different chapter: Chapter 1 deals with the measure problem in eternal inflation. Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light- cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin's CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic. The chapter closely follows our paper. Chapter 2 deals with the question of whether neutrino masses could be anthropically explained. The sum of active neutrino masses is well constrained, 58 meV ≤ mupsilon [is approximately less than] 0.23 eV, but the origin of this scale is not well understood. Here we investigate the possibility that it arises by environmental selection in a large landscape of vacua. Earlier work had noted the detrimental effects of neutrinos on large scale structure. However, using Boltzmann codes to compute the smoothed density contrast on Mpc scales, we find that dark matter halos form abundantly for mupsilon [is approximately greater than] 10eV. This finding rules out an anthropic origin of mupsilon, unless a different catastrophic boundary can be identified. Here we argue that galaxy formation becomes inefficient for mupsilon [is approximately greater than] 10 eV. We show that in this regime, structure forms late and is dominated by cluster scales, as in a top-down scenario. This is catastrophic: baryonic gas will cool too slowly to form stars in an abundance comparable to our universe. With this novel cooling boundary, we find that the anthropic prediction for mupsilon agrees at better than 2sigma with current observational bounds. A degenerate hierarchy is mildly preferred. The chapter closely follows our paper.

Gray matter segmentation of the spinal cord with active contours in MR images.

PubMed

Datta, Esha; Papinutto, Nico; Schlaeger, Regina; Zhu, Alyssa; Carballido-Gamio, Julio; Henry, Roland G

2017-02-15

Fully or partially automated spinal cord gray matter segmentation techniques for spinal cord gray matter segmentation will allow for pivotal spinal cord gray matter measurements in the study of various neurological disorders. The objective of this work was multi-fold: (1) to develop a gray matter segmentation technique that uses registration methods with an existing delineation of the cord edge along with Morphological Geodesic Active Contour (MGAC) models; (2) to assess the accuracy and reproducibility of the newly developed technique on 2D PSIR T1 weighted images; (3) to test how the algorithm performs on different resolutions and other contrasts; (4) to demonstrate how the algorithm can be extended to 3D scans; and (5) to show the clinical potential for multiple sclerosis patients. The MGAC algorithm was developed using a publicly available implementation of a morphological geodesic active contour model and the spinal cord segmentation tool of the software Jim (Xinapse Systems) for initial estimate of the cord boundary. The MGAC algorithm was demonstrated on 2D PSIR images of the C2/C3 level with two different resolutions, 2D T2* weighted images of the C2/C3 level, and a 3D PSIR image. These images were acquired from 45 healthy controls and 58 multiple sclerosis patients selected for the absence of evident lesions at the C2/C3 level. Accuracy was assessed though visual assessment, Hausdorff distances, and Dice similarity coefficients. Reproducibility was assessed through interclass correlation coefficients. Validity was assessed through comparison of segmented gray matter areas in images with different resolution for both manual and MGAC segmentations. Between MGAC and manual segmentations in healthy controls, the mean Dice similarity coefficient was 0.88 (0.82-0.93) and the mean Hausdorff distance was 0.61 (0.46-0.76) mm. The interclass correlation coefficient from test and retest scans of healthy controls was 0.88. The percent change between the manual segmentations from high and low-resolution images was 25%, while the percent change between the MGAC segmentations from high and low resolution images was 13%. Between MGAC and manual segmentations in MS patients, the average Dice similarity coefficient was 0.86 (0.8-0.92) and the average Hausdorff distance was 0.83 (0.29-1.37) mm. We demonstrate that an automatic segmentation technique, based on a morphometric geodesic active contours algorithm, can provide accurate and precise spinal cord gray matter segmentations on 2D PSIR images. We have also shown how this automated technique can potentially be extended to other imaging protocols. Copyright © 2016 Elsevier Inc. All rights reserved.

Integrated metagenomics and molecular ecological network analysis of bacterial community composition during the phytoremediation of cadmium-contaminated soils by bioenergy crops.

PubMed

Chen, Zhaojin; Zheng, Yuan; Ding, Chuanyu; Ren, Xuemin; Yuan, Jian; Sun, Feng; Li, Yuying

2017-11-01

Two energy crops (maize and soybean) were used in the remediation of cadmium-contaminated soils. These crops were used because they are fast growing, have a large biomass and are good sources for bioenergy production. The total accumulation of cadmium in maize and soybean plants was 393.01 and 263.24μg pot -1 , respectively. The rhizosphere bacterial community composition was studied by MiSeq sequencing. Phylogenetic analysis was performed using 16S rRNA gene sequences. The rhizosphere bacteria were divided into 33 major phylogenetic groups according to phyla. The dominant phylogenetic groups included Proteobacteria, Acidobacteria, Actinobacteria, Gemmatimonadetes, and Bacteroidetes. Based on principal component analysis (PCA) and unweighted pair group with arithmetic mean (UPGMA) analysis, we found that the bacterial community was influenced by cadmium addition and bioenergy cropping. Three molecular ecological networks were constructed for the unplanted, soybean- and maize-planted bacterial communities grown in 50mgkg -1 cadmium-contaminated soils. The results indicated that bioenergy cropping increased the complexity of the bacterial community network as evidenced by a higher total number of nodes, the average geodesic distance (GD), the modularity and a shorter geodesic distance. Proteobacteria and Acidobacteria were the keystone bacteria connecting different co-expressed operational taxonomic units (OTUs). The results showed that bioenergy cropping altered the topological roles of individual OTUs and keystone populations. This is the first study to reveal the effects of bioenergy cropping on microbial interactions in the phytoremediation of cadmium-contaminated soils by network reconstruction. This method can greatly enhance our understanding of the mechanisms of plant-microbe-metal interactions in metal-polluted ecosystems. Copyright © 2017 Elsevier Inc. All rights reserved.

Robustness analysis of superpixel algorithms to image blur, additive Gaussian noise, and impulse noise

NASA Astrophysics Data System (ADS)

Brekhna, Brekhna; Mahmood, Arif; Zhou, Yuanfeng; Zhang, Caiming

2017-11-01

Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Anisotropic, nonsingular early universe model leading to a realistic cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dechant, Pierre-Philippe; Lasenby, Anthony N.; Hobson, Michael P.

2009-02-15

We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'big bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the big bang. We demonstrate that there exist geodesics extending through the big bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the big bang, rendering it, at worst, a quasiregular singularity. The model is thus reminiscent ofmore » the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasiregular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropization and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [T. S. Pereira, C. Pitrou, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 9 (2007) 6.][C. Pitrou, T. S. Pereira, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 4 (2008) 4.][A. Guemruekcueoglu, C. Contaldi, and M. Peloso, J. Cosmol. Astropart. Phys. 11 (2007) 005.]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalizes the known bouncing solution in closed FRW universes.« less

Light rays and the tidal gravitational pendulum

NASA Astrophysics Data System (ADS)

Farley, A. N. St J.

2018-05-01

Null geodesic deviation in classical general relativity is expressed in terms of a scalar function, defined as the invariant magnitude of the connecting vector between neighbouring light rays in a null geodesic congruence projected onto a two-dimensional screen space orthogonal to the rays, where λ is an affine parameter along the rays. We demonstrate that η satisfies a harmonic oscillator-like equation with a λ-dependent frequency, which comprises terms accounting for local matter affecting the congruence and tidal gravitational effects from distant matter or gravitational waves passing through the congruence, represented by the amplitude, of a complex Weyl driving term. Oscillating solutions for η imply the presence of conjugate or focal points along the rays. A polarisation angle, is introduced comprising the orientation of the connecting vector on the screen space and the phase, of the Weyl driving term. Interpreting β as the polarisation of a gravitational wave encountering the light rays, we consider linearly polarised waves in the first instance. A highly non-linear, second-order ordinary differential equation, (the tidal pendulum equation), is then derived, so-called due to its analogy with the equation describing a non-linear, variable-length pendulum oscillating under gravity. The variable pendulum length is represented by the connecting vector magnitude, whilst the acceleration due to gravity in the familiar pendulum formulation is effectively replaced by . A tidal torque interpretation is also developed, where the torque is expressed as a coupling between the moment of inertia of the pendulum and the tidal gravitational field. Precessional effects are briefly discussed. A solution to the tidal pendulum equation in terms of familiar gravitational lensing variables is presented. The potential emergence of chaos in general relativity is discussed in the context of circularly, elliptically or randomly polarised gravitational waves encountering the null congruence.

From Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics

NASA Astrophysics Data System (ADS)

Perez-Giz, Gabriel

2011-12-01

A direct observational detection of gravitational waves -- perhaps the most fundamental prediction of a theory of curved spacetime -- looms close at hand. Stellar mass compact objects spiraling into supermassive black holes have received particular attention as sources of gravitational waves detectable by space-based gravitational wave observatories. A well-established approach models such an extreme mass ratio inspirals (EMRI) as an adiabatic progression through a series of Kerr geodesics. Thus, the direct detection of gravitational radiation from EMRIs and the extraction of astrophysical information from those waveforms require a thorough knowledge of the underlying geodesic dynamics. This dissertation adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We deduce a topological taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some orbital angular momentum value in the strong-field regime below which zoom-whirl behavior becomes unavoidable. We then generalize the taxonomy to help identify nonequatorial orbits whose radial and polar frequencies are rationally related, or in resonance. The thesis culminates by describing how those resonant orbits can be leveraged for an order of magnitude or more reduction in the computational cost of adiabatic order EMRI trajectories, which are so prohibitively expensive that no such relativistically correct inspirals have been generated to date.

Particle motion and Penrose processes around rotating regular black hole

NASA Astrophysics Data System (ADS)

Abdujabbarov, Ahmadjon

2016-07-01

The neutral particle motion around rotating regular black hole that was derived from the Ayón-Beato-García (ABG) black hole solution by the Newman-Janis algorithm in the preceding paper (Toshmatov et al., Phys. Rev. D, 89:104017, 2014) has been studied. The dependencies of the ISCO (innermost stable circular orbits along geodesics) and unstable orbits on the value of the electric charge of the rotating regular black hole have been shown. Energy extraction from the rotating regular black hole through various processes has been examined. We have found expression of the center of mass energy for the colliding neutral particles coming from infinity, based on the BSW (Baňados-Silk-West) mechanism. The electric charge Q of rotating regular black hole decreases the potential of the gravitational field as compared to the Kerr black hole and the particles demonstrate less bound energy at the circular geodesics. This causes an increase of efficiency of the energy extraction through BSW process in the presence of the electric charge Q from rotating regular black hole. Furthermore, we have studied the particle emission due to the BSW effect assuming that two neutral particles collide near the horizon of the rotating regular extremal black hole and produce another two particles. We have shown that efficiency of the energy extraction is less than the value 146.6 % being valid for the Kerr black hole. It has been also demonstrated that the efficiency of the energy extraction from the rotating regular black hole via the Penrose process decreases with the increase of the electric charge Q and is smaller in comparison to 20.7 % which is the value for the extreme Kerr black hole with the specific angular momentum a= M.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

NASA Astrophysics Data System (ADS)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Information Geometry for Landmark Shape Analysis: Unifying Shape Representation and Deformation

PubMed Central

Peter, Adrian M.; Rangarajan, Anand

2010-01-01

Shape matching plays a prominent role in the comparison of similar structures. We present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation. The theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the information matrix of the density. We first show that given two shapes parameterized by Gaussian mixture models (GMMs), the well-known Fisher information matrix of the mixture model is also a Riemannian metric (actually, the Fisher-Rao Riemannian metric) and can therefore be used for computing shape geodesics. The Fisher-Rao metric has the advantage of being an intrinsic metric and invariant to reparameterization. The geodesic—computed using this metric—establishes an intrinsic deformation between the shapes, thus unifying both shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is not available in closed form for the GMM. Consequently, shape comparisons are computationally very expensive. To address this, we develop a new Riemannian metric based on generalized ϕ-entropy measures. In sharp contrast to the Fisher-Rao metric, the new metric is available in closed form. Geodesic computations using the new metric are considerably more efficient. We validate the performance and discriminative capabilities of these new information geometry-based metrics by pairwise matching of corpus callosum shapes. We also study the deformations of fish shapes that have various topological properties. A comprehensive comparative analysis is also provided using other landmark-based distances, including the Hausdorff distance, the Procrustes metric, landmark-based diffeomorphisms, and the bending energies of the thin-plate (TPS) and Wendland splines. PMID:19110497

QPO observations related to neutron star equations of state

NASA Astrophysics Data System (ADS)

Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr

We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. 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. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density ρc . These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.

Neutron star equation of state and QPO observations

NASA Astrophysics Data System (ADS)

Urbanec, Martin; Stuchlík, Zdeněk; Török, Gabriel; Bakala, Pavel; Čermák, Petr

2007-12-01

Assuming a resonant origin of the twin peak 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 kilohertz 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. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density rho_{c}. These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR, rho_{c}, Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR, rho_{c}, Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR, rho_{c}, Ω, EOS) into the chromosome we use the Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.

Behavior of a test gyroscope moving towards a rotating traversable wormhole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Chandrachur; Pradhan, Parthapratim, E-mail: chandrachur.chakraborty@tifr.res.in, E-mail: pppradhan77@gmail.com

2017-03-01

The geodesic structure of the Teo wormhole is briefly discussed and some observables are derived that promise to be of use in detecting a rotating traversable wormhole indirectly, if it does exist. We also deduce the exact Lense-Thirring (LT) precession frequency of a test gyroscope moving toward a rotating traversable Teo wormhole. The precession frequency diverges on the ergoregion, a behavior intimately related to and governed by the geometry of the ergoregion, analogous to the situation in a Kerr spacetime. Interestingly, it turns out that here the LT precession is inversely proportional to the angular momentum ( a ) ofmore » the wormhole along the pole and around it in the strong gravity regime, a behavior contrasting with its direct variation with a in the case of other compact objects. In fact, divergence of LT precession inside the ergoregion can also be avoided if the gyro moves with a non-zero angular velocity in a certain range. As a result, the spin precession frequency of the gyro can be made finite throughout its whole path, even very close to the throat, during its travel to the wormhole. Furthermore, it is evident from our formulation that this spin precession not only arises due to curvature or rotation of the spacetime but also due to the non-zero angular velocity of the spin when it does not move along a geodesic in the strong gravity regime. If in the future, interstellar travel indeed becomes possible through a wormhole or at least in its vicinity, our results would prove useful in determining the behavior of a test gyroscope which is known to serve as a fundamental navigation device.« less

Geometrically Induced Interactions and Bifurcations

NASA Astrophysics Data System (ADS)

Binder, Bernd

2010-01-01

In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.

Entanglement entropy in Galilean conformal field theories and flat holography.

PubMed

Bagchi, Arjun; Basu, Rudranil; Grumiller, Daniel; Riegler, Max

2015-03-20

We present the analytical calculation of entanglement entropy for a class of two-dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.

Optimal protocols for slowly driven quantum systems.

PubMed

Zulkowski, Patrick R; DeWeese, Michael R

2015-09-01

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.

(2+1)-Dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

NASA Astrophysics Data System (ADS)

Xu, Wei; Zou, De-Cheng

2017-06-01

In (2+1)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter k=1 and k≠1), in the Einstein-Power-Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with k≠1, we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.

On the competition of forces in the Kerr field

NASA Astrophysics Data System (ADS)

Semerak, O.

1994-11-01

'Rotosphere', where the component of 4-acceleration, radial relative to the symmetry axis, of the stationary observer depends on his angular velocity in a way going against our intuition, is demarcated in the Kerr spacetime. Stationary observers with extremal value of this acceleration ('extremelly accelerated observers') are introduced and their privileged relation to circular geodesics in the equatorial plane is found. Possible translation of the results into 'force' language is based on the definition of the 'centrifugal force' with respect to the zero-angular-momentum observers. It yields, in particular, a simple interpretation of the behavior of acceleration of the stationary observer in terms of gravitational, Coriolis and centrifugal forces.

On the time arrows, and randomness in cosmological signals

NASA Astrophysics Data System (ADS)

Gurzadyan, V. G.; Sargsyan, S.; Yegorian, G.

2013-09-01

Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian) dynamics are outlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.

Hidden symmetries and supergravity solutions

NASA Astrophysics Data System (ADS)

Santillan, Osvaldo P.

2012-04-01

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally, the Papadopoulos list [G. Papadopoulos, Class. Quantum Grav. 25, 105016 (2008)], 10.1088/0264-9381/25/10/105016 for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.

Nonlinear Decay and Plasma Heating by a Toroidal Alfvén Eigenmode

NASA Astrophysics Data System (ADS)

Qiu, Z.; Chen, L.; Zonca, F.; Chen, W.

2018-03-01

We demonstrate theoretically that a toroidal Alfvén eigenmode (TAE) can parametrically decay into a geodesic acoustic mode and kinetic TAE in a toroidal plasma. The corresponding threshold condition for the TAE amplitude is estimated to be |δ B⊥/B0|˜O (10-4). Here, δ B⊥ and B0 are, respectively, the perturbed magnetic field of the pump TAE and the equilibrium magnetic field. This novel decay process, in addition to contributing to the nonlinear saturation of energetic-particle or α -particle driven TAE instability, could also contribute to the heating as well as regulating the transports of thermal plasmas.

Working covariance model selection for generalized estimating equations.

PubMed

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

A quantum measure of the multiverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vilenkin, Alexander, E-mail: vilenkin@cosmos.phy.tufts.edu

2014-05-01

It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ''watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standardmore » Born rule of QM.« less

More on boundary holographic Witten diagrams

NASA Astrophysics Data System (ADS)

Sato, Yoshiki

2018-01-01

In this paper we discuss geodesic Witten diagrams in general holographic conformal field theories with boundary or defect. In boundary or defect conformal field theory, two-point functions are nontrivial and can be decomposed into conformal blocks in two distinct ways; ambient channel decomposition and boundary channel decomposition. In our previous work [A. Karch and Y. Sato, J. High Energy Phys. 09 (2017) 121., 10.1007/JHEP09(2017)121] we only consider two-point functions of same operators. We generalize our previous work to a situation where operators in two-point functions are different. We obtain two distinct decomposition for two-point functions of different operators.

New singularities in unexpected places

NASA Astrophysics Data System (ADS)

Barrow, John D.; Graham, Alexander A. H.

2015-09-01

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

On twisting type [N] ⊗ [N] Ricci flat complex spacetimes with two homothetic symmetries

NASA Astrophysics Data System (ADS)

Chudecki, Adam; Przanowski, Maciej

2018-04-01

In this article, H H spaces of type [N] ⊗ [N] with twisting congruence of null geodesics defined by the 4-fold undotted and dotted Penrose spinors are investigated. It is assumed that these spaces admit two homothetic symmetries. The general form of the homothetic vector fields is found. New coordinates are introduced, which enable us to reduce the H H system of partial differential equations to one ordinary differential equation (ODE) on one holomorphic function. In a special case, this is a second-order ODE and its general solution is explicitly given. In the generic case, one gets rather involved fifth-order ODE.

Classical conformal blocks and accessory parameters from isomonodromic deformations

NASA Astrophysics Data System (ADS)

Lencsés, Máté; Novaes, Fábio

2018-04-01

Classical conformal blocks appear in the large central charge limit of 2D Virasoro conformal blocks. In the AdS3 /CFT2 correspondence, they are related to classical bulk actions and used to calculate entanglement entropy and geodesic lengths. In this work, we discuss the identification of classical conformal blocks and the Painlevé VI action showing how isomonodromic deformations naturally appear in this context. We recover the accessory parameter expansion of Heun's equation from the isomonodromic τ -function. We also discuss how the c = 1 expansion of the τ -function leads to a novel approach to calculate the 4-point classical conformal block.

TEMPEST Simulations of Collisionless Damping of Geodesic-Acoustic Mode in Edge Plasma Pedestal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q; Xiong, Z; Nevins, W M

The fully nonlinear (full-f) 4D TEMPEST gyrokinetic continuum code produces frequency, collisionless damping of GAM and zonal flow with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon}-scan and the tokamak safety factor q-scan in homogeneous plasmas. The TEMPEST simulation shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude.

Engaging spaces: Intimate electro-acoustic display in alternative performance venues

NASA Astrophysics Data System (ADS)

Bahn, Curtis; Moore, Stephan

2004-05-01

In past presentations to the ASA, we have described the design and construction of four generations of unique spherical speakers (multichannel, outward-radiating geodesic speaker arrays) and Sensor-Speaker-Arrays, (SenSAs: combinations of various sensor devices with outward-radiating multichannel speaker arrays). This presentation will detail the ways in which arrays of these speakers have been employed in alternative performance venues-providing presence and intimacy in the performance of electro-acoustic chamber music and sound installation, while engaging natural and unique acoustical qualities of various locations. We will present documentation of the use of multichannel sonic diffusion arrays in small clubs, ``black-box'' theaters, planetariums, and art galleries.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conroy, Aindriú; Mazumdar, Anupam; Koshelev, Alexey S., E-mail: a.conroy@lancaster.ac.uk, E-mail: alexey@ubi.pt, E-mail: a.mazumdar@lancaster.ac.uk

Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any ansatz -dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies withinmore » an infinite derivative theory of gravity, without assuming any ansatz to solve the full equations of motion.« less

An information geometric approach to least squares minimization

NASA Astrophysics Data System (ADS)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

Antigravity and the big crunch/big bang transition

NASA Astrophysics Data System (ADS)

Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

2012-08-01

We point out a new phenomenon which seems to be generic in 4d effective theories of scalar fields coupled to Einstein gravity, when applied to cosmology. A lift of such theories to a Weyl-invariant extension allows one to define classical evolution through cosmological singularities unambiguously, and hence construct geodesically complete background spacetimes. An attractor mechanism ensures that, at the level of the effective theory, generic solutions undergo a big crunch/big bang transition by contracting to zero size, passing through a brief antigravity phase, shrinking to zero size again, and re-emerging into an expanding normal gravity phase. The result may be useful for the construction of complete bouncing cosmologies like the cyclic model.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Dynamics of a rigid body in an inhomogenous force field

NASA Astrophysics Data System (ADS)

Resch, Andreas; Laemmerzahl, Claus; Lorek, Dennis; Schaffer, Isabell

Extended rigid bodies do not move on geodesics but couple to the space-time curvature. We discuss this effect at the Newtonian level where the deviation from the ordinary Keplerian orbits occurs in two ways: we obtain an additional force in the equation of motion for the center-of-mass and a torque acting on the rotational degrees of freedom. We give a survey of the dynamics for various initial conditions. We discuss whether these modifications of the equations of motion can explain the so-called flyby anomaly. In particular, the behavior of satellites during a flyby is studied and a comparison with the flyby anomaly of Galileo, NEAR, Cassini and Rosetta is made.

On the Nodal Lines of Eisenstein Series on Schottky Surfaces

NASA Astrophysics Data System (ADS)

Jakobson, Dmitry; Naud, Frédéric

2017-04-01

On convex co-compact hyperbolic surfaces {X=Γ backslash H2}, we investigate the behavior of nodal curves of real valued Eisenstein series {F_λ(z,ξ)}, where {λ} is the spectral parameter, {ξ} the direction at infinity. Eisenstein series are (non-{L^2}) eigenfunctions of the Laplacian {Δ_X} satisfying {Δ_X F_λ=(1/4+λ^2)F_λ}. As {λ} goes to infinity (the high energy limit), we show that, for generic {ξ}, the number of intersections of nodal lines with any compact segment of geodesic grows like {λ}, up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.

Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.

This chapter contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

Inverse Problems for Semilinear Wave Equations on Lorentzian Manifolds

NASA Astrophysics Data System (ADS)

Lassas, Matti; Uhlmann, Gunther; Wang, Yiran

2018-06-01

We consider inverse problems in space-time ( M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations {\\square_g u + H(x, u) = f}, where {\\square_g} denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map {L: f → u|_V}, where V is a neighborhood of a time-like geodesic {μ}, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set, where waves can propagate from {μ} and return back. Moreover, on a given space-time ( M, g), the source-to-solution map determines some coefficients of the Taylor expansion of H in u.

Penrose limits of Abelian and non-Abelian T-duals of AdS 5 × S 5 and their field theory duals

NASA Astrophysics Data System (ADS)

Itsios, Georgios; Nastase, Horatiu; Núñez, Carlos; Sfetsos, Konstantinos; Zacarías, Salomón

2018-01-01

We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on AdS 5 × S 5. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a `flow' in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, which we also provide.

Maximizers in Lipschitz spacetimes are either timelike or null

NASA Astrophysics Data System (ADS)

Graf, Melanie; Ling, Eric

2018-04-01

We prove that causal maximizers in C 0,1 spacetimes are either timelike or null. This question was posed in Sämann and Steinbauer (2017 arXiv:1710.10887) since bubbling regions in C0, α spacetimes (α <1 ) can produce causal maximizers that contain a segment which is timelike and a segment which is null, see Chruściel and Grant (2012 Class. Quantum Grav. 29 145001). While C 0,1 spacetimes do not produce bubbling regions, the causal character of maximizers for spacetimes with regularity at least C 0,1 but less than C 1,1 was unknown until now. As an application we show that timelike geodesically complete spacetimes are C 0,1-inextendible.

Dynamics of charges and solitons

NASA Astrophysics Data System (ADS)

Barros, Manuel; Ferrández, Ángel; Garay, Óscar J.

2018-02-01

We first show that trajectories traced by charges moving in rotational magnetic fields are, basically, the non-parallel geodesics of surfaces of revolution with coincident axis. Thus, people living in a surface of revolution are not able to sense the magnetic Hall effect induced by the surrounding magnetic field and perceive charges as influenced, exclusively, by the gravity action on the surface of revolution. Secondly, the extended Hasimoto transformations are introduced and then used to identify trajectories of charges moving through a Killing rotational magnetic field in terms of non-circular elastic curves. As a consequence, we see that in this case charges evolve along trajectories which are obtained as extended Hasimoto transforms of solitons of the filament equation.

STU black holes and SgrAstar

NASA Astrophysics Data System (ADS)

Cvetič, M.; Gibbons, G. W.; Pope, C. N.

2017-08-01

The equations of null geodesics in the STU family of rotating black hole solutions of supergravity theory, which may be considered as deformations of the vacuum Kerr metric, are completely integrable. We propose that they be used as a foil to test, for example, with what precision the gravitational field external to the black hole at the centre of our galaxy is given by the Kerr metric. By contrast with some metrics proposed in the literature, the STU metrics satisfy by construction the dominant and strong energy conditions. Our considerations may be extended to include the effects of a cosmological term. We show that these metrics permit a straightforward calculation of the properties of black hole shadows.

Observational signatures of spherically-symmetric black hole spacetimes

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Fromm, Christian; Rezzolla, Luciano; Olivares, Hector

2017-12-01

A binary system composed of a supermassive black hole and a pulsar orbiting around it is studied. The motivation for this study arises from the fact that pulsar timing observations have proven to be a powerful tool in identifying physical features of the orbiting companion. In this study, taking into account a general spherically-symmetric metric, we present analytic calculations of the geodesic motion, and the possible deviations with respect to the standard Schwarzschild case of General Relativity. In particular, the advance at periastron is studied with the aim of identifying corrections to General Relativity. A discussion of the motion of a pulsar very close the supermassive central black hole in our Galaxy (Sgr A*) is reported.

Acoustic metric of the compressible draining bathtub

NASA Astrophysics Data System (ADS)

Cherubini, C.; Filippi, S.

2011-10-01

The draining bathtub flow, a cornerstone in the theory of acoustic black holes, is here extended to the case of exact solutions for compressible nonviscous flows characterized by a polytropic equation of state. Investigating the analytical configurations obtained for selected values of the polytropic index, it is found that each of them becomes nonphysical at the so called limiting circle. By studying the null geodesics structure of the corresponding acoustic line elements, it is shown that such a geometrical locus coincides with the acoustic event horizon. This region is characterized also by an infinite value of space-time curvature, so the acoustic analogy breaks down there. Possible applications for artificial and natural vortices are finally discussed.

Fullerenes formation in flames

NASA Technical Reports Server (NTRS)

Howard, Jack B.

1993-01-01

Fullerenes are composed of carbon atoms arranged in approximately spherical or ellipsoidal cages resembling the geodesic domes designed by Buckminster Fuller, after whom the molecules were named. The approximately spherical fullerene, which resembles a soccer ball and contains sixty atoms (C60), is called buckminsterfullerene. The fullerene containing seventy carbon atoms (C70) is approximately ellipsoidal, similar to a rugby ball. Fullerenes were first detected in 1985, in carbon vapor produced by laser evaporation of graphite. The closed shell structure, which has no edge atoms vulnerable to reaction, was proposed to explain the observed high stability of certain carbon clusters relative to that of others at high temperatures and in the presence of an oxidizing gas.

A superparticle on the super Riemann surface

NASA Astrophysics Data System (ADS)

Matsumoto, Shuji; Uehara, Shozo; Yasui, Yukinori

1990-02-01

The free motion of a nonrelativistic superparticle on the super Riemann surface (SRS) of genus h≥2 is investigated. Geodesics or classical paths are given explicitly on the super Poincaré upper half-plane SH, a universal covering space of the SRS, and the paths with some suitable initial conditions yield periodic orbits on the SRS. The periodic orbits are unstable and the system is chaotic. Quantum mechanics is solved on the universal covering space SH and the heat kernel is given on the SRS. This leads to a superanalog of the Selberg trace formula. The Selberg super zeta function is introduced whose zero points and poles determine the energy spectrum on the SRS.

Accelerated orbits in black hole fields: the static case

NASA Astrophysics Data System (ADS)

Bini, Donato; de Felice, Fernando; Geralico, Andrea

2011-11-01

We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of their Frenet-Serret parameters and apply it to explicit cases as those of spatially circular orbits which witness the equilibrium under conflicting types of interactions. In our general analysis, we solve the equations of motion offering a detailed picture of the dynamics having in mind a check with a possible astronomical setup. We focus on certain ambiguities which plague the interpretation of the measurements preventing one from identifying the particular structure carried by the particle.

Holographic repulsion and confinement in gauge theory

NASA Astrophysics Data System (ADS)

Husain, Viqar; Kothawala, Dawood

2013-02-01

We show that for asymptotically anti-de Sitter (AdS) backgrounds with negative energy, such as the AdS soliton and regulated negative-mass AdS-Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark-antiquark (q \\bar{q}) potential can be interpreted as affine time along null geodesics on the minimal string worldsheet and that its intrinsic curvature provides a signature of transition to confinement phase. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity. Communicated by P R L V Moniz

Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions

NASA Astrophysics Data System (ADS)

Blair, Matthew D.; Sogge, Christopher D.

2017-12-01

We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors (Blair and Sogge in Anal PDE 8:747-764, 2015) and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these estimates, which involves a phase space decomposition of these modes that is essentially invariant under the bicharacteristic/geodesic flow. In a companion paper (Blair and Sogge in J Differ Geom, 2015), it will be seen that these sharpened estimates yield improved L q ( M) bounds on eigenfunctions in the presence of nonpositive curvature when {2 < q < 2(d+1)/d-1}.

The kinematic component of the cosmological redshift

NASA Astrophysics Data System (ADS)

Chodorowski, Michał J.

2011-05-01

It is widely believed that the cosmological redshift is not a Doppler shift. However, Bunn & Hogg have recently pointed out that to solve this problem properly, one has to transport parallelly the velocity four-vector of a distant galaxy to the observer's position. Performing such a transport along the null geodesic of photons arriving from the galaxy, they found that the cosmological redshift is purely kinematic. Here we argue that one should rather transport the velocity four-vector along the geodesic connecting the points of intersection of the world-lines of the galaxy and the observer with the hypersurface of constant cosmic time. We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula. Instead, for small redshifts it coincides with the well-known non-relativistic decomposition of the redshift into a Doppler (kinematic) component and a gravitational one. We perform such a decomposition for arbitrary large redshifts and derive a formula for the kinematic component of the cosmological redshift, valid for any Friedman-Lemaître-Robertson-Walker (FLRW) cosmology. In particular, in a universe with Ωm= 0.24 and ΩΛ= 0.76, a quasar at a redshift 6, at the time of emission of photons reaching us today had the recession velocity v= 0.997c. This can be contrasted with v= 0.96c, had the redshift been entirely kinematic. Thus, for recession velocities of such high-redshift sources, the effect of deceleration of the early Universe clearly prevails over the effect of its relatively recent acceleration. Last but not the least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies' four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities.

Measures for a multidimensional multiverse

NASA Astrophysics Data System (ADS)

Chung, Hyeyoun

2015-04-01

We explore the phenomenological implications of generalizing the causal patch and fat geodesic measures to a multidimensional multiverse, where the vacua can have differing numbers of large dimensions. We consider a simple model in which the vacua are nucleated from a D -dimensional parent spacetime through dynamical compactification of the extra dimensions, and compute the geometric contribution to the probability distribution of observations within the multiverse for each measure. We then study how the shape of this probability distribution depends on the time scales for the existence of observers, for vacuum domination, and for curvature domination (tobs,tΛ , and tc, respectively.) In this work we restrict ourselves to bubbles with positive cosmological constant, Λ . We find that in the case of the causal patch cutoff, when the bubble universes have p +1 large spatial dimensions with p ≥2 , the shape of the probability distribution is such that we obtain the coincidence of time scales tobs˜tΛ˜tc . Moreover, the size of the cosmological constant is related to the size of the landscape. However, the exact shape of the probability distribution is different in the case p =2 , compared to p ≥3 . In the case of the fat geodesic measure, the result is even more robust: the shape of the probability distribution is the same for all p ≥2 , and we once again obtain the coincidence tobs˜tΛ˜tc . These results require only very mild conditions on the prior probability of the distribution of vacua in the landscape. Our work shows that the observed double coincidence of time scales is a robust prediction even when the multiverse is generalized to be multidimensional; that this coincidence is not a consequence of our particular Universe being (3 +1 )-dimensional; and that this observable cannot be used to preferentially select one measure over another in a multidimensional multiverse.

VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)

NASA Astrophysics Data System (ADS)

Karney, C. F. F.; Deakin, R. E.

2010-06-01

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).

Gravitational collapse in Husain space-time for Brans-Dicke gravity theory with power-law potential

NASA Astrophysics Data System (ADS)

Rudra, Prabir; Biswas, Ritabrata; Debnath, Ujjal

2014-12-01

The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, ω, and the potential-scalar field dependency parameter n respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/inhomogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases (through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's EoS satisfies a wide range of phenomena: from dust to exotic fluid like dark energy. We have used the EoS parameter k to determine the end state of collapse in different cosmological era. Our main target is to check low ω (more deviations from Einstein gravity-more Brans Dicke effect) and negative k zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter k, the collapse results in a black hole, whereas for negative values of k, naked singularity is the only outcome. It is also to be noted that "low ω" leads to the possibility of getting more naked singularities even for a non-accelerating universe.

Gravitational Collapse in Husain space-time for Brans-Dicke Gravity Theory with Power-law Potential.

NASA Astrophysics Data System (ADS)

Rudra, Prabir

2016-07-01

The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, ω, and the potential-scalar field dependency parameter 'n' respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/inhomogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases(through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's equation of state satisfies a wide range of phenomena : from dust to exotic fluid like dark energy. We have used the equation of state parameter 'k' to determine the end state of collapse in different cosmological era. Our main target is to check low ω (more deviations from Einstein gravity-more Brans Dicke effect) and negative 'k' zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter 'k', the collapse results in a black hole, whereas for negative values of 'k', naked singularity is the only outcome. It is also to be noted that "low ω" leads to the possibility of getting more naked singularities even for a non-accelerating universe.

Automatic detection and quantification of pulmonary arterio-venous malformations in hereditary hemorrhagic telangiectasia

NASA Astrophysics Data System (ADS)

Fetita, Catalin; Fortemps de Loneux, Thierry; Kouvahe, Amélé Florence; El Hajjam, Mostafa

2017-03-01

Hereditary hemorrhagic telangiectasia (HHT) is an autosomic dominant disorder, which is characterized by the development of multiple arterio-venous malformations in the skin, mucous membranes, and/or visceral organs. Pulmonary Arterio-Venous Malformation (PAVM) is an abnormal connection where feeding arteries shunt directly into draining veins with no intervening capillary bed. This condition may lead to paradoxical embolism and hemorrhagic complications. PAVMs patients should systematically be screened as the spontaneous complication rate is high, reaching almost 50%. Chest enhanced contrast CT scanner is the reference screening and follow-up examination. When performed by experienced operators as the prime treatment, percutaneous embolization of PAVMs is a safe, efficient and sustained therapy. The accuracy of PAVM detection and quantification of its progression over time is the key of embolotherapy success. In this paper, we propose an automatic method for PAVM detection and quantification relying on a modeling of vessel deformation, i.e. local caliber increase, based on mathematical morphology. The pulmonary field and vessels are first segmented using geodesic operators. The vessel caliber is estimated by means of a granulometric measure and the local caliber increase is detected by using a geodesic operator, the h-maxdomes. The detection sensitivity can be tuned up according to the choice of the h value which models the irregularity of the vessel caliber along its axis and the PAVM selection is performed according to a clinical criterion of >3 mm diameter of the feeding artery of the PAVM. The developed method was tested on a 20 patient dataset. A sensitivity study allowed choosing the irregularity parameter to maximize the true positive ratio reaching 85.4% in average. A specific false positive reduction procedure targeting the vessel trunks of the arterio-venous tree near mediastinum allows a precision increase from 13% to 67% with an average number of 1.15 false positives per scan.

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan; Wardell, Barry

2017-04-01

If a small "particle" of mass μ M (with μ ≪1 ) orbits a black hole of mass M , the leading-order radiation-reaction effect is an O (μ2) "self-force" acting on the particle, with a corresponding O (μ ) "self-acceleration" of the particle away from a geodesic. Such "extreme-mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the "toy model" problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th-order puncture field, followed by an ei m ϕ ("m -mode") Fourier decomposition and a separate time-domain numerical evolution in 2 +1 dimensions for each m . We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and J+ . Our numerical evolution uses Berger-Oliger mesh refinement with 4th-order finite differencing in space and time. Our computational scheme allows computation for highly eccentric orbits and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage; these appear to be caused by the passage of the orbit through the strong-field region close to the background Kerr black hole.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

Power law inflation with electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu

2013-07-15

We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as inmore » Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.« less

Gravitational instantons from minimal surfaces

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Hortaçsu, M.; Kalayci, J.; Nutku, Y.

1999-02-01

Physical properties of gravitational instantons which are derivable from minimal surfaces in three-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi type 0264-9381/16/2/024/img9, or E(2), which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form, which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

New two-metric theory of gravity with prior geometry

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1973-01-01

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Hidden symmetries on Kerr-NUT-(A)dS metrics of Einstein-Sasaki type

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2013-01-01

The hidden symmetries of higher dimensional Euclideanised Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

NASA Astrophysics Data System (ADS)

Rodríguez, J. F.; Rueda, J. A.; Ruffini, R.

2018-01-01

We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

A Yang-Mills field on the extremal Reissner-Nordström black hole

NASA Astrophysics Data System (ADS)

Bizoń, Piotr; Kahl, Michał

2016-09-01

We consider a spherically symmetric (magnetic) SU(2) Yang-Mills field propagating on the exterior of the extremal Reissner-Nordström black hole. Taking advantage of the conformal symmetry, we reduce the problem to the study of the Yang-Mills equation in a geodesically complete spacetime with two asymptotically flat ends. We prove the existence of infinitely many static solutions (two of which are found in closed form) and determine the spectrum of their linear perturbations and quasinormal modes. Finally, using the hyperboloidal approach to the initial value problem, we describe the process of relaxation to the static endstates of evolution, both stable (for generic initial data) and unstable (for codimension-one initial data).

Photon orbits and thermodynamic phase transition of d -dimensional charged AdS black holes

NASA Astrophysics Data System (ADS)

Wei, Shao-Wen; Liu, Yu-Xiao

2018-05-01

We study the relationship between the null geodesics and thermodynamic phase transition for the charged AdS black hole. In the reduced parameter space, we find that there exist nonmonotonic behaviors of the photon sphere radius and the minimum impact parameter for the pressure below its critical value. The study also shows that the changes of the photon sphere radius and the minimum impact parameter can serve as order parameters for the small-large black hole phase transition. In particular, these changes have an universal exponent of 1/2 near the critical point for any dimension d of spacetime. These results imply that there may exist universal critical behavior of gravity near the thermodynamic critical point of the black hole system.

Mean and oscillating plasma flows and turbulence interactions across the L-H confinement transition.

PubMed

Conway, G D; Angioni, C; Ryter, F; Sauter, P; Vicente, J

2011-02-11

A complex interaction between turbulence driven E × B zonal flow oscillations, i.e., geodesic acoustic modes (GAMs), the turbulence, and mean equilibrium flows is observed during the low to high (L-H) plasma confinement mode transition in the ASDEX Upgrade tokamak. Below the L-H threshold at low densities a limit-cycle oscillation forms with competition between the turbulence level and the GAM flow shearing. At higher densities the cycle is diminished, while in the H mode the cycle duration becomes too short to sustain the GAM, which is replaced by large amplitude broadband flow perturbations. Initially GAM amplitude increases as the H-mode transition is approached, but is then suppressed in the H mode by enhanced mean flow shear.

Local Neighbourhoods for First-Passage Percolation on the Configuration Model

NASA Astrophysics Data System (ADS)

Dereich, Steffen; Ortgiese, Marcel

2018-04-01

We consider first-passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen uniformly at random, a sender and a recipient, and all edges along the geodesic connecting the two vertices are coloured in red (in the case that both vertices are in the same component). In this article we prove local limit theorems for the coloured graph around the recipient in the spirit of Benjamini and Schramm. We consider the explosive regime, in which case the random distances are of finite order, and the Malthusian regime, in which case the random distances are of logarithmic order.

An experimental trip to the Calculus of Variations

NASA Astrophysics Data System (ADS)

Arroyo, Josu

2008-04-01

This paper presents a collection of experiments in the Calculus of Variations. The implementation of the Gradient Descent algorithm built on cubic-splines acting as "numerically friendly" elementary functions, give us ways to solve variational problems by constructing the solution. It wins a pragmatic point of view: one gets solutions sometimes as fast as possible, sometimes as close as possible to the true solutions. The balance speed/precision is not always easy to achieve. Starting from the most well-known, classic or historical formulation of a variational problem, section 2 describes briefly the bridge between theoretical and computational formulations. The next sections show the results of several kind of experiments; from the most basics, as those about geodesics, to the most complex, as those about vesicles.

Antisymmetric tensor generalizations of affine vector fields.

PubMed

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

Lagrangian submanifolds with constant angle functions of the nearly Kähler S3 ×S3

NASA Astrophysics Data System (ADS)

Bektaş, Burcu; Moruz, Marilena; Van der Veken, Joeri; Vrancken, Luc

2018-04-01

We study Lagrangian submanifolds of the nearly Kähler S3 ×S3 with respect to their so called angle functions. We show that if all angle functions are constant, then the submanifold is either totally geodesic or has constant sectional curvature and there is a classification theorem that follows from Dioos et al. (2018). Moreover, we show that if precisely one angle function is constant, then it must be equal to 0 , π/3 or 2π/3. Using then two remarkable constructions together with the classification of Lagrangian submanifolds of which the first component has nowhere maximal rank from, Bektaş et al. (2018), we obtain a classification of such Lagrangian submanifolds.

Naked singularities as particle accelerators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patil, Mandar; Joshi, Pankaj S.

We investigate here the particle acceleration by naked singularities to arbitrarily high center of mass energies. Recently it has been suggested that black holes could be used as particle accelerators to probe the Planck scale physics. We show that the naked singularities serve the same purpose and probably would do better than their black hole counterparts. We focus on the scenario of a self-similar gravitational collapse starting from a regular initial data, leading to the formation of a globally naked singularity. It is seen that when particles moving along timelike geodesics interact and collide near the Cauchy horizon, the energymore » of collision in the center of mass frame will be arbitrarily high, thus offering a window to Planck scale physics.« less

Geometric optics for a coupling model of electromagnetic and gravitational fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jing, Jiliang, E-mail: jljing@hunnu.edu.cn; Chen, Songbai; Pan, Qiyuan

2016-04-15

The coupling between the electromagnetic and gravitational fields results in “faster than light” photons, and then the first and third laws of geometric optics are invalid in usual spacetime. By introducing an effective spacetime, we find that the wave vector can be casted into null and then it obeys the geodesic equation, the polarization vector is perpendicular to the rays, and the number of photons is conserved. That is to say, the laws of geometric optics are valid for the modified theory in the effective spacetime. We also show that the focusing theorem of light rays for the modified theorymore » in the effective spacetime can be cast into the usual form.« less

STU black holes and SgrA{sup *}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cvetič, M.; Gibbons, G.W.; Pope, C.N., E-mail: cvetic@physics.upenn.edu, E-mail: gwg1@cam.ac.uk, E-mail: pope@physics.tamu.edu

The equations of null geodesics in the STU family of rotating black hole solutions of supergravity theory, which may be considered as deformations of the vacuum Kerr metric, are completely integrable. We propose that they be used as a foil to test, for example, with what precision the gravitational field external to the black hole at the centre of our galaxy is given by the Kerr metric. By contrast with some metrics proposed in the literature, the STU metrics satisfy by construction the dominant and strong energy conditions. Our considerations may be extended to include the effects of a cosmologicalmore » term. We show that these metrics permit a straightforward calculation of the properties of black hole shadows.« less

Interacting vector fields in relativity without relativity

NASA Astrophysics Data System (ADS)

Anderson, Edward; Barbour, Julian

2002-06-01

Barbour, Foster and Ó Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of three-dimensional metric-matter configurations. In fact gravity, the universal light-cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity - and more - without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang-Mills fields minimally coupled to gravity.

Gravitational Lensing from a Spacetime Perspective.

PubMed

Perlick, Volker

2004-01-01

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

EXACT RELATIVISTIC NEWTONIAN REPRESENTATION OF GRAVITATIONAL STATIC SPACETIME GEOMETRIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava, E-mail: sghosh@jcbose.ac.in, E-mail: ta.sa.nbu@hotmail.com, E-mail: aru_bhadra@yahoo.com

2016-09-01

We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, starting directly from a generalized scalar relativistic gravitational action in a Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of the Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite usefulmore » in studying a wide range of astrophysical phenomena, especially in strong field gravity.« less

3D effects on transport and plasma control in the TJ-II stellarator

NASA Astrophysics Data System (ADS)

Castejón, F.; Alegre, D.; Alonso, A.; Alonso, J.; Ascasíbar, E.; Baciero, A.; de Bustos, A.; Baiao, D.; Barcala, J. M.; Blanco, E.; Borchardt, M.; Botija, J.; Cabrera, S.; de la Cal, E.; Calvo, I.; Cappa, A.; Carrasco, R.; Castro, R.; De Castro, A.; Catalán, G.; Chmyga, A. A.; Chamorro, M.; Dinklage, A.; Eliseev, L.; Estrada, T.; Fernández-Marina, F.; Fontdecaba, J. M.; García, L.; García-Cortés, I.; García-Gómez, R.; García-Regaña, J. M.; Guasp, J.; Hatzky, R.; Hernanz, J.; Hernández, J.; Herranz, J.; Hidalgo, C.; Hollmann, E.; Jiménez-Denche, A.; Kirpitchev, I.; Kleiber, R.; Komarov, A. D.; Kozachoek, A. S.; Krupnik, L.; Lapayese, F.; Liniers, M.; Liu, B.; López-Bruna, D.; López-Fraguas, A.; López-Miranda, B.; López-Razola, J.; Losada, U.; de la Luna, E.; Martín de Aguilera, A.; Martín-Díaz, F.; Martínez, M.; Martín-Gómez, G.; Martín-Hernández, F.; Martín-Rojo, A. B.; Martínez-Fernández, J.; McCarthy, K. J.; Medina, F.; Medrano, M.; Melón, L.; Melnikov, A. V.; Méndez, P.; Merino, R.; Miguel, F. J.; van Milligen, B.; Molinero, A.; Momo, B.; Monreal, P.; Moreno, R.; Navarro, M.; Narushima, Y.; Nedzelskiy, I. S.; Ochando, M. A.; Olivares, J.; Oyarzábal, E.; de Pablos, J. L.; Pacios, L.; Panadero, N.; Pastor, I.; Pedrosa, M. A.; de la Peña, A.; Pereira, A.; Petrov, A.; Petrov, S.; Portas, A. B.; Poveda, E.; Rattá, G. A.; Rincón, E.; Ríos, L.; Rodríguez, C.; Rojo, B.; Ros, A.; Sánchez, J.; Sánchez, M.; Sánchez, E.; Sánchez-Sarabia, E.; Sarksian, K.; Satake, S.; Sebastián, J. A.; Silva, C.; Solano, E. R.; Soleto, A.; Sun, B. J.; Tabarés, F. L.; Tafalla, D.; Tallents, S.; Tolkachev, A.; Vega, J.; Velasco, G.; Velasco, J. L.; Wolfers, G.; Yokoyama, M.; Zurro, B.

2017-10-01

The effects of 3D geometry are explored in TJ-II from two relevant points of view: neoclassical transport and modification of stability and dispersion relation of waves. Particle fuelling and impurity transport are studied considering the 3D transport properties, paying attention to both neoclassical transport and other possible mechanisms. The effects of the 3D magnetic topology on stability, confinement and Alfvén Eigenmodes properties are also explored, showing the possibility of controlling Alfvén modes by modifying the configuration; the onset of modes similar to geodesic acoustic modes are driven by fast electrons or fast ions; and the weak effect of magnetic well on confinement. Finally, we show innovative power exhaust scenarios using liquid metals.

Fractal active contour model for segmenting the boundary of man-made target in nature scenes

NASA Astrophysics Data System (ADS)

Li, Min; Tang, Yandong; Wang, Lidi; Shi, Zelin

2006-02-01

In this paper, a novel geometric active contour model based on the fractal dimension feature to extract the boundary of man-made target in nature scenes is presented. In order to suppress the nature clutters, an adaptive weighting function is defined using the fractal dimension feature. Then the weighting function is introduced into the geodesic active contour model to detect the boundary of man-made target. Curve driven by our proposed model can evolve gradually from the initial position to the boundary of man-made target without being disturbed by nature clutters, even if the initial curve is far away from the true boundary. Experimental results validate the effectiveness and feasibility of our model.

Verification of TEMPEST with neoclassical transport theory

NASA Astrophysics Data System (ADS)

Xiong, Z.; Cohen, B. I.; Cohen, R. H.; Dorr, M.; Hittinger, J.; Kerbel, G.; Nevins, W. M.; Rognlien, T.; Umansky, M.; Xu, X.

2006-10-01

TEMPEST is an edge gyro-kinetic continuum code developed to study boundary plasma transport over the region extending from the H-mode pedestal across the separatrix to the divertor plates. For benchmark purposes, we present results from the 4D (2r,2v) TEMPEST for both steady-state transport and time-dependent Geodesic Acoustic Modes (GAMs). We focus on an annular region inside the separatrix of a circular cross-section tokamak where analytical and numerical results are available. The parallel flow velocity and radial particle flux are obtained for different collisional regimes and compared with previous neoclassical results. The effect of radial electric field and the transition to steep edge gradients is emphasized. The dynamical response of GAMs is also shown and compared to recent theory.

The centripetal force law and the equation of motion for a particle on a curved hypersurface

NASA Astrophysics Data System (ADS)

Hu, L. D.; Lian, D. K.; Liu, Q. H.

2016-12-01

It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable.

On the null trajectories in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

Villanueva, J. R.; Olivares, Marco

2013-06-01

In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the conformal Weyl gravity. Then, we study the radial motion from the point of view of the proper and coordinate frames, and compare it with that found in spacetimes of general relativity. The angular motion is also examined qualitatively by means of an effective potential; quantitatively, the equation of motion is solved in terms of wp-Weierstrass elliptic function. Thus, we find the deflection angle for photons without using any approximation, which is a novel result for this kind of gravity.

Holographic signatures of cosmological singularities.

PubMed

Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T

2014-09-19

To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.

Experimental evidence of turbulence regulation by time-varying E  ×  B flows

NASA Astrophysics Data System (ADS)

Silva, C.; Henriques, R.; Hidalgo, C.; Fernandes, H.

2018-02-01

The interaction between zonal flows and turbulence is a self-regulating mechanism. Understanding this interaction is crucial to control plasma confinement. Results presented in this paper aim at understanding the conditions under which geodesic acoustic modes (GAMs) influence turbulent transport. This is achieved by performing perturbative experiments where GAMs are stimulated and externally controlled. Experiments on ISTTOK revealed that increasing the GAM shear rate over its natural value leads to a reduction of the turbulent transport and to an enhancement in particle confinement. Taking advantage of our unique experimental tools, it is shown that GAMs play an important role in the regulation of the fluctuations, constituting further evidence that the GAM shear rate is enough to regulate the ambient fluctuations without totally suppressing the turbulence.

Virtual Environments in Scientific Visualization

NASA Technical Reports Server (NTRS)

Bryson, Steve; Lisinski, T. A. (Technical Monitor)

1994-01-01

Virtual environment technology is a new way of approaching the interface between computers and humans. Emphasizing display and user control that conforms to the user's natural ways of perceiving and thinking about space, virtual environment technologies enhance the ability to perceive and interact with computer generated graphic information. This enhancement potentially has a major effect on the field of scientific visualization. Current examples of this technology include the Virtual Windtunnel being developed at NASA Ames Research Center. Other major institutions such as the National Center for Supercomputing Applications and SRI International are also exploring this technology. This talk will be describe several implementations of virtual environments for use in scientific visualization. Examples include the visualization of unsteady fluid flows (the virtual windtunnel), the visualization of geodesics in curved spacetime, surface manipulation, and examples developed at various laboratories.

Electromagnetic Chirps from Neutron Star–Black Hole Mergers

NASA Astrophysics Data System (ADS)

Schnittman, Jeremy D.; Dal Canton, Tito; Camp, Jordan; Tsang, David; Kelly, Bernard J.

2018-02-01

We calculate the electromagnetic signal of a gamma-ray flare coming from the surface of a neutron star shortly before merger with a black hole companion. Using a new version of the Monte Carlo radiation transport code Pandurata that incorporates dynamic spacetimes, we integrate photon geodesics from the neutron star surface until they reach a distant observer or are captured by the black hole. The gamma-ray light curve is modulated by a number of relativistic effects, including Doppler beaming and gravitational lensing. Because the photons originate from the inspiraling neutron star, the light curve closely resembles the corresponding gravitational waveform: a chirp signal characterized by a steadily increasing frequency and amplitude. We propose to search for these electromagnetic chirps using matched filtering algorithms similar to those used in LIGO data analysis.

Integrability of spinning particle motion in higher-dimensional rotating black hole spacetimes.

PubMed

Kubizňák, David; Cariglia, Marco

2012-02-03

We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing-Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et al. [Phys. Rev. Lett. 98, 061102 (2007)] on complete integrability of geodesic motion in these spacetimes.

Maximal analytic extension and hidden symmetries of the dipole black ring

NASA Astrophysics Data System (ADS)

Armas, Jay

2011-12-01

We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell’s theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple asymptotically flat regions and, in the non-extremal case, are also maximal and timelike complete. Moreover, we find that in both cases, the causal structure of the maximally extended spacetime resembles that of the four-dimensional Reissner-Nordström black hole. Furthermore, motivated by the physical interpretation of one of these extensions, we find a separable solution to the Hamilton-Jacobi equation corresponding to zero energy null geodesics and relate it to the existence of a conformal Killing tensor and a conformal Killing-Yano tensor in a specific dimensionally reduced spacetime.

Numerical treatment of a geometrically nonlinear planar Cosserat shell model

NASA Astrophysics Data System (ADS)

Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

2016-05-01

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.

Classical and quantum dynamics in an inverse square potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx; Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx; Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx

2014-10-15

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence ofmore » bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.« less

Geometric Lie algebra in matter, arts and mathematics with incubation of the periodic systems of the elements

NASA Astrophysics Data System (ADS)

Trell, Erik; Edeagu, Samuel; Animalu, Alexander

2017-01-01

From a brief recapitulation of the foundational works of Marius Sophus Lie and Herrmann Günther Grassmann, and including missing African links, a rhapsodic survey is made of the straight line of extension and existence that runs as the very fibre of generation and creation throughout Nature's all utterances, which must therefore ultimately be the web of Reality itself of which the Arts and Sciences are interpreters on equal explorer terms. Assuming their direct approach, the straight line and its archaic and algebraic and artistic bearings and convolutions have been followed towards their inner reaches, which earlier resulted in a retrieval of the baryon and meson elementary particles and now equally straightforward the electron geodesics and the organic build of the periodic system of the elements.

Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca; McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca

2014-08-15

We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the diagonal curvature condition. The metrics we find either correspond to a Benenti system or are warped product metrics where the induced metric on the base manifold corresponds to a Benenti system. Furthermore, we show that most metrics we find are characterized by concircular tensors; these metrics, called Kalnins-Eisenhart-Miller metrics, have an intrinsic characterization which can be used to obtain them on a given space. In conjunction withmore » other results, we show that the metrics we found constitute all separable metrics for Riemannian spaces of constant curvature and de Sitter space.« less

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

ERPs While Judging Meaningfulness of Sentences with and without Homonym or Morpheme Spelling Foils: Comparing 4th to 9th Graders with and without Spelling Disabilities

PubMed Central

Richards, Todd; Pettet, Mark; Askren, Katie; Grabowski, Tom; Yagle, Kevin; Wallis, Peter; Northey, Mary; Abbott, Robert; Berninger, Virginia

2016-01-01

Thirteen students with and twelve students without spelling disabilities judged whether sentences (1/3 all correct spellings, 1/3 with homonym foil, 1/3 with morpheme foil) were meaningful while event-related potentials (ERPs) were measured with EGI Geodesic EEG System 300 (128-channel hydro-cell nets). For N400, Rapid Automatic Switching (RAS) correlated with comprehending sentences with homonym foils in control group but with morpheme foils in SLD group. For P600, dictated spelling correlated with comprehending sentences with morpheme foils in the control group but solving anagrams with homonym foils in the SLD group. Educational significance and neuropsychological significance of these contrasting results are discussed. PMID:28657362

Electromagnetic Chirps from Neutron Star-Black Hole Mergers

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy D.; Dal Canton, Tito; Camp, Jordan B.; Tsang, David; Kelly, Bernard J.

2018-01-01

We calculate the electromagnetic signal of a gamma-ray flare coming from the surface of a neutron star shortly before merger with a black hole companion. Using a new version of the Monte Carlo radiation transport code Pandurata that incorporates dynamic spacetimes, we integrate photon geodesics from the neutron star surface until they reach a distant observer or are captured by the black hole. The gamma-ray light curve is modulated by a number of relativistic effects, including Doppler beaming and gravitational lensing. Because the photons originate from the inspiraling neutron star, the light curve closely resembles the corresponding gravitational waveform: a chirp signal characterized by a steadily increasing frequency and amplitude. We propose to search for these electromagnetic chirps using matched filtering algorithms similar to those used in LIGO data analysis.

Unified treatment of the luminosity distance in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo, Jaiyul; Scaccabarozzi, Fulvio, E-mail: jyoo@physik.uzh.ch, E-mail: fulvio@physik.uzh.ch

Comparing the luminosity distance measurements to its theoretical predictions is one of the cornerstones in establishing the modern cosmology. However, as shown in Biern and Yoo, its theoretical predictions in literature are often plagued with infrared divergences and gauge-dependences. This trend calls into question the sanity of the methods used to derive the luminosity distance. Here we critically investigate four different methods—the geometric approach, the Sachs approach, the Jacobi mapping approach, and the geodesic light cone (GLC) approach to modeling the luminosity distance, and we present a unified treatment of such methods, facilitating the comparison among the methods and checkingmore » their sanity. All of these four methods, if exercised properly, can be used to reproduce the correct description of the luminosity distance.« less

Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light.

PubMed

Beravat, Ramin; Wong, Gordon K L; Frosz, Michael H; Xi, Xiao Ming; Russell, Philip St J

2016-11-01

A century ago, Einstein proposed that gravitational forces were the result of the curvature of space-time and predicted that light rays would deflect when passing a massive celestial object. We report that twisting the periodically structured "space" within a coreless photonic crystal fiber creates a helical channel where guided modes can form despite the absence of any discernible core structure. Using a Hamiltonian optics analysis, we show that the light rays follow closed spiral or oscillatory paths within the helical channel, in close analogy with the geodesics of motion in a two-dimensional gravitational field. The mode diameter shrinks, and its refractive index rises, as the twist rate increases. The birefringence, orbital angular momentum, and dispersion of these unusual modes are explored.

On gravitational chirality as the genesis of astrophysical jets

NASA Astrophysics Data System (ADS)

Tucker, R. W.; Walton, T. J.

2017-02-01

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

Energy conditions and junction conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marolf, Donald; Yaida, Sho; Mathematics Department, UCSB, Santa Barbara, California 93106

2005-08-15

We consider the familiar junction conditions described by Israel for thin timelike walls in Einstein-Hilbert gravity. One such condition requires the induced metric to be continuous across the wall. Now, there are many spacetimes with sources confined to a thin wall for which this condition is violated and the Israel formalism does not apply. However, we explore the conjecture that the induced metric is in fact continuous for any thin wall which models spacetimes containing only positive energy matter. Thus, the usual junction conditions would hold for all positive energy spacetimes. This conjecture is proven in various special cases, includingmore » the case of static spacetimes with spherical or planar symmetry as well as settings without symmetry which may be sufficiently well approximated by smooth spacetimes with well-behaved null geodesic congruences.« less

On the proof of the C 0-inextendibility of the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Sbierski, Jan

2018-02-01

This article presents a streamlined version of the author’s original proof of the C 0-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established in collaboration with Galloway and Ling, that given a C 0-extension of a globally hyperbolic spacetime, one can find a timelike geodesic that leaves this spacetime. This result much simplifies the proof of the inextendibility through the exterior region of the Schwarzschild spacetime. Secondly, we give a more flexible and shorter argument for the inextendibility through the interior region. Furthermore, we present a small new structural result for the boundary of a globally hyperbolic spacetime within a C 0-extension which serves as a new and simpler starting point for the proof.

Connecting Archimedean and Non-Archimedean AdS/CFT

NASA Astrophysics Data System (ADS)

Parikh, Sarthak

This thesis develops a non-Archimedean analog of the usual Archimedean anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. AdS space gets replaced by a Bruhat-Tits tree, which is a regular graph with no cycles. The boundary of the Bruhat-Tits tree is described by an unramified extension of the p-adic numbers, which replaces the real valued Euclidean vector space on which the CFT lives. Conformal transformations on the boundary act as linear fractional transformations. In the first part of the thesis, correlation functions are computed in the simple case of massive, interacting scalars in the bulk. They are found to be surprisingly similar to standard holographic correlation functions down to precise numerical coefficients, when expressed in terms of local zeta functions. Along the way, we show that like in the Archimedean case, CFT conformal blocks are dual to geodesic bulk diagrams, which are bulk exchange diagrams with the bulk points of integration restricted to certain geodesics. Other than these intriguing similarities, significant simplifications also arise. Notably, all derivatives disappear from the operator product expansion, and the conformal block decomposition of the four-point function. Finally, a minimal bulk action is constructed on the Bruhat-Tits tree for a single scalar field with nearest neighbor interactions, which reproduces the two-, three-, and four-point functions of the free O(N) model. In the second part, the p-adic O(N) model is studied at the interacting fixed point. Leading order results for the anomalous dimensions of low dimension operators are obtained in two separate regimes: the epsilon-expansion and the large N limit. Remarkably, formulae for anomalous dimensions in the large N limit are valid equally for Archimedean and non-Archimedean field theories, when expressed in terms of local zeta functions. Finally, higher derivative versions of the O(N) model in the Archimedean case are considered, where the general formula for anomalous dimensions obtained earlier is still valid. Analogies with two-derivative theories hint at the existence of some interesting new field theories in four real Euclidean dimensions.

Local properties and global structure of McVittie spacetimes with non-flat Friedmann-Lemaître-Robertson-Walker backgrounds

NASA Astrophysics Data System (ADS)

Nolan, Brien C.

2017-11-01

McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter) spacetime in an isotropic, Friedmann-Lemaître-Robertson-Walker (FLRW) background universe. The global structure of such spacetimes is well understood when the FLRW background is spatially flat. In this paper, we study the global structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. We derive some basic results on the metric, curvature and matter content of these spacetimes and provide a representation of the metric that makes the study of their global properties possible. In the closed case, we find that at each instant of time, the spacetime is confined to a region bounded by a (positive) minimum and a maximum area radius, and is bounded either to the future or to the past by a scalar curvature singularity. This allowed region only exists when the background scale factor is above a certain minimum, and so is bounded away from the Big Bang singularity, as in the flat case. In the open case, the situation is different, and we focus mainly on this case. In K<0 McVittie spacetimes, radial null geodesics originate in finite affine time in the past at a boundary formed by the union of the Big Bang singularity of the FLRW background and a hypersurface (of varying causal character) which is non-singular in the sense of scalar curvature. Furthermore, in the case of eternally expanding open universes with Λ≥slant0 , we prove that black holes are ubiquitous: ingoing radial null geodesics extend in finite affine time to a hypersurface that forms the boundary of the region from which photons can escape to future null infinity. We determine the structure of the conformal diagrams that can arise in the open case. Finally, we revisit the black hole interpretation of McVittie spacetimes in the spatially flat case, and show that this interpretation holds also in the case of a vanishing cosmological constant, contrary to a previous claim of ours.

Simple inflationary quintessential model. II. Power law potentials

NASA Astrophysics Data System (ADS)

de Haro, Jaume; Amorós, Jaume; Pan, Supriya

2016-09-01

The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive improvement of the observational data.

A special form of SPD covariance matrix for interpretation and visualization of data manipulated with Riemannian geometry

NASA Astrophysics Data System (ADS)

Congedo, Marco; Barachant, Alexandre

2015-01-01

Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In conclusion, we are able to show that the Riemannian concepts of distance, geometric mean, moving along a geodesic, etc. can be readily transposed into a generic data space, whatever this data space represents.

Algorithm for lens calculations in the geometrized Maxwell theory

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Sevastianov, Leonid A.; Gevorkyan, Migran N.; Demidova, Anastasia V.

2018-04-01

Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrized optics is usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrized approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics construction for isotropic and anisotropic media. For effective metric space ray trajectories are obtained in the form of geodesic curves. The introduced algorithm is applied to well-known objects, Maxwell and Luneburg lenses. The similarity of results obtained by classical and geometric approach is demonstrated.

Composing Music with Complex Networks

NASA Astrophysics Data System (ADS)

Liu, Xiaofan; Tse, Chi K.; Small, Michael

In this paper we study the network structure in music and attempt to compose music artificially. Networks are constructed with nodes and edges corresponding to musical notes and their co-occurrences. We analyze sample compositions from Bach, Mozart, Chopin, as well as other types of music including Chinese pop music. We observe remarkably similar properties in all networks constructed from the selected compositions. Power-law exponents of degree distributions, mean degrees, clustering coefficients, mean geodesic distances, etc. are reported. With the network constructed, music can be created by using a biased random walk algorithm, which begins with a randomly chosen note and selects the subsequent notes according to a simple set of rules that compares the weights of the edges, weights of the nodes, and/or the degrees of nodes. The newly created music from complex networks will be played in the presentation.