Geodesic stability, Lyapunov exponents, and quasinormal modes

International Nuclear Information System (INIS)

Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.

2009-01-01

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.

Rational first integrals of geodesic equations and generalised hidden symmetries

International Nuclear Information System (INIS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-01-01

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson–O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski–Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing–Yano tensors. (paper)

Non-integrability of geodesic flow on certain algebraic surfaces

International Nuclear Information System (INIS)

Waters, T.J.

2012-01-01

This Letter addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface xyz=1. We prove this is the case using the Morales–Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result. -- Highlights: ► The behaviour of geodesics on surfaces defined by algebraic expressions is studied. ► The non-integrability of the geodesic equations is rigorously proved using differential Galois theory. ► Morales–Ramis theory and Kovacic's algorithm is used and the normal variational equation is of Fuchsian type. ► Some extensions and limitations are discussed.

Geodesic distance in planar graphs

International Nuclear Information System (INIS)

Bouttier, J.; Di Francesco, P.; Guitter, E.

2003-01-01

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

International Nuclear Information System (INIS)

Rowland, D R

2006-01-01

Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics

Geodesics in Goedel-type space-times

International Nuclear Information System (INIS)

Calvao, M.O.; Soares, I.D.; Tiomno, J.

1988-01-01

The geodesic curves of the homogeneous Goedel-type space-times, which constitute a two-parameter ({ l and Ω}) class of solutions presented to several theories of gravitation (general relativity, Einstein-Cartan and higher derivative) are investigated. The qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion are examined. It is shown that some of the qualitative features of the free motion in Godel's universe (l 2 =2Ω 2 ) are preserved in all space-times, namely the projections of the geodesics onto the 2-surface (r,ψ) are simple closed curves, and the geodesics for which the ratio of azymuthal angular momentum to total energy, υ is equal to zero always cross the origin r = o. However, two new cases appear: (i) radially unbounded geodesics with υ assuming any (real) value, which may occur only for the causal space-times (l 2 ≥ 4 Ω 2 ), and (ii) geodesics with υ bounded both below and above, which always occur for the circular family (l 2 [pt

Geodesic patterns

KAUST Repository

Pottmann, Helmut; Huang, Qixing; Deng, Bailin; Schiftner, Alexander; Kilian, Martin; Guibas, Leonidas J.; Wallner, Johannes

2010-01-01

Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.

Geodesic patterns

KAUST Repository

Pottmann, Helmut

2010-07-26

Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.

Geodesic flows in a charged black hole spacetime with quintessence

Energy Technology Data Exchange (ETDEWEB)

Nandan, Hemwati [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Uniyal, Rashmi [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Government Degree College, Department of Physics, Tehri Garhwal, Uttarakhand (India)

2017-08-15

We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)

Geodesic flows in a charged black hole spacetime with quintessence

International Nuclear Information System (INIS)

Nandan, Hemwati; Uniyal, Rashmi

2017-01-01

We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)

An exact Jacobi map in the geodesic light-cone gauge

CERN Document Server

Fanizza, G.; Marozzi, G.; Veneziano, G.

2013-11-07

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodetic-deviation equation, and thus to derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J^A_B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J^A_B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on l...

Space–time and spatial geodesic orbits in Schwarzschild geometry

Science.gov (United States)

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.

Geodesic in Godel type universes

International Nuclear Information System (INIS)

Galvao, M.O.

1985-01-01

We find out the timelike and null geodesics of a certain family of Goedel-like universes, carrying out, at first, a qualitative analysis through the method of the effective potential and, subsequently, proceeding to the exact integration of the equations of motion. (author) [pt

Geodesic congruences in warped spacetimes

International Nuclear Information System (INIS)

Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan

2011-01-01

In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. 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.

Efficiently computing exact geodesic loops within finite steps.

Science.gov (United States)

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

Singularities in geodesic surface congruence

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2008-01-01

In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.

Some remarks on geodesics in gauge groups and harmonic maps

International Nuclear Information System (INIS)

Valli, G.

1987-08-01

The following topics are discussed: Euler's equations for geodesics in the gauge groups and in gauge orbits of connections, conserved quantities and moment map, existence and uniqueness of solutions for the Cauchy problem, stationary solutions and harmonic bundles, harmonic gauges on Riemann surfaces and Lax pairs, low geodesics in gauge groups over Riemann surfaces produce, by Hodge decomposition, paths of holomorphic differentials. 19 refs

Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures

Directory of Open Access Journals (Sweden)

Ishikawa Goo

2015-06-01

Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.

Black hole decay as geodesic motion

International Nuclear Information System (INIS)

Gupta, Kumar S.; Sen, Siddhartha

2003-01-01

We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes

Polyaffine parametrization of image registration based on geodesic flows

DEFF Research Database (Denmark)

Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.

2012-01-01

Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which ...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....

Geodesics and symmetries of doubly spinning black rings

International Nuclear Information System (INIS)

Durkee, Mark

2009-01-01

This paper studies various properties of the Pomeransky-Sen'kov doubly spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the ergoregion. These geodesics are used to construct geometrically motivated coordinates that cover the black hole horizon. Finally, I relate this weak form of separability to the existence of a conformal Killing tensor in a particular four-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a related conformal Killing-Yano tensor only exists in the singly spinning case.

Large deviations for solutions to stochastic recurrence equations under Kesten's condition

DEFF Research Database (Denmark)

Buraczewski, Dariusz; Damek, Ewa; Mikosch, Thomas Valentin

2013-01-01

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten’s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise...... sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest...... step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies...

Improved iterative oscillation tests for first-order deviating differential equations

Directory of Open Access Journals (Sweden)

George E. Chatzarakis

2018-01-01

Full Text Available In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \\(\\lim \\sup\\ and \\(\\lim \\inf\\ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.

Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

International Nuclear Information System (INIS)

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

2009-01-01

In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a nondegenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4, 5, 6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.

Geodesic structure of Lifshitz black holes in 2+1 dimensions

International Nuclear Information System (INIS)

Cruz, Norman; Olivares, Marco; Villanueva, J.R.

2013-01-01

We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with z=3 and d=1 as found in Ayon-Beato et al. (Phys. Rev. D 80:104029, 2009). By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic p, σ, and ζ functions. (orig.)

Do electromagnetic waves always propagate along null geodesics?

International Nuclear Information System (INIS)

Asenjo, Felipe A; Hojman, Sergio A

2017-01-01

We find exact solutions to Maxwell equations written in terms of four-vector potentials in non–rotating, as well as in Gödel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non–rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gödel and Kerr spacetimes do not exhibit that behavior. (paper)

Integrability of geodesics and action-angle variables in Sasaki-Einstein space T{sup 1,1}

Energy Technology Data Exchange (ETDEWEB)

Visinescu, Mihai [National Institute of Physics and Nuclear Engineering, Department Theoretical Physics, Magurele, Bucharest (Romania)

2016-09-15

We briefly describe the construction of Staekel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T{sup 1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed. (orig.)

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

Science.gov (United States)

Deng, Gao-Ming; Huang, Yong-Chang

2018-03-01

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.

Lagrangian averaging with geodesic mean.

Science.gov (United States)

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.

Perfect fluid cosmology with geodesic world lines

International Nuclear Information System (INIS)

Raychaudhuri, A.K.; Maity, S.R.

1978-01-01

It is shown that for a perfect fluid with an equation of state p = p (rho), if the world lines are geodesics, then they are hypersurface orthogonal and the scalars p, rho, sigma 2 , and theta 2 are all constants over these hypersurfaces, irrespective of any spatial-homogeneity assumption. However, an examination of some simple cases does not reveal any spatially nonhomogeneous solution with these properties

Arcmancer: Geodesics and polarized radiative transfer library

Science.gov (United States)

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.

An explicit local uniform large deviation bound for Brownian bridges

NARCIS (Netherlands)

Wittich, O.

2005-01-01

By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.

Newtonian potential and geodesic completeness in infinite derivative gravity

Science.gov (United States)

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.

Stringy Jacobi fields in Morse theory

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2007-01-01

We consider the variation of the surface spanned by closed strings in a spacetime manifold. Using the Nambu-Goto string action, we induce the geodesic surface equation and the geodesic surface deviation equation which yields a Jacobi field, and we define the index form of a geodesic surface as in the case of point particles to discuss conjugate strings on the geodesic surface

Statistics of geodesics in large quadrangulations

International Nuclear Information System (INIS)

Bouttier, J; Guitter, E

2008-01-01

We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to the notion of 'spine trees', amenable to a direct enumeration. We obtain the generating functions for quadrangulations with a marked geodesic of fixed length, as well as with a set of 'confluent geodesics', i.e. a collection of non-intersecting minimal paths connecting two given points. In the limit of quadrangulations with a large area n, we find in particular an average number 3 x 2 i of geodesics between two fixed points at distance i >> 1 from each other. We show that, for generic endpoints, two confluent geodesics remain close to each other and have an extensive number of contacts. This property fails for a few 'exceptional' endpoints which can be linked by truly distinct geodesics. Results are presented both in the case of finite length i and in the scaling limit i ∼ n 1/4 . In particular, we give the scaling distribution of the exceptional points

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

International Nuclear Information System (INIS)

Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi; Sasaki, Misao

2014-01-01

In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing

Geodesics of black holes with dark energy

Science.gov (United States)

Ghaderi, K.

2017-12-01

Dark energy is the most popular hypothesis to explain recent observations suggesting that the world will increasingly expand. One of the models of dark energy is quintessence which is highly plausible. In this paper, we investigate the effect of dark energy on the null geodesics of Schwarzschild, Reissner-Nordström, Schwarzschild-de Sitter and Bardeen black holes. Using the definition of effective potential, the radius of the circular orbits, the period, the instability of the circular orbits, the force exerted on the photons and the deviation angle of light in quintessence field are calculated and the results are analyzed and discussed.

Entropy Measures as Geometrical Tools in the Study of Cosmology

Directory of Open Access Journals (Sweden)

Gilbert Weinstein

2017-12-01

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

General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations

OpenAIRE

Ren, Jiagang; Wu, Jing; Zhang, Hua

2015-01-01

In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.

EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.

Oscillations in deviating difference equations using an iterative technique

Directory of Open Access Journals (Sweden)

George E Chatzarakis

2017-07-01

Full Text Available Abstract The paper deals with the oscillation of the first-order linear difference equation with deviating argument and nonnegative coefficients. New sufficient oscillation conditions, involving limsup, are given, which essentially improve all known results, based on an iterative technique. We illustrate the results and the improvement over other known oscillation criteria by examples, numerically solved in Matlab.

Geodesics in (Rn, d1

Directory of Open Access Journals (Sweden)

Mehmet KILIÇ

2016-09-01

Full Text Available The notion of geodesic, which may be regarded as an extension of the line segment in Euclidean geometry to the space we study in, has an important place in many branches of geometry, such as Riemannian geometry, Metric geometry, to name but a few. In this article, the concept of geodesic in a metric space will be introduced, then geodesics in the space (Rn, d1 will be characterized. Furthermore, some examples will be presented to demonstrate the effectiveness of the main result.

Kastor-Traschen black holes, null geodesics and conformal circles

International Nuclear Information System (INIS)

Casey, Stephen

2012-01-01

The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant Λ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the projection to the space of orbits of the timelike conformal retraction. It is found that these projected light rays arise as integral curves of a system of third-order ordinary differential equations. This system is not uniquely defined, however, and we use the inherent freedom to construct a new system whose integral curves coincide with the projection of distinguished null curves of Kastor-Traschen arising from a magnetic flow. We discuss our results in the one-centre case and demonstrate a link to conformal circles in the limit Λ → 0. We also show how to construct analytic expressions for the projected null geodesics of this metric by exploiting a well-known diffeomorphism between the K-T metric and extremal Reissner-Nordstrom-de Sitter. We make some remarks about the two-centre solution and demonstrate a link with the one-centre case. (paper)

Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations

International Nuclear Information System (INIS)

Roeckner, Michael; Zhang, Tusheng; Zhang Xicheng

2010-01-01

In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Roeckner and Zhang in Probab. Theory Relat. Fields 145(1-2), 211-267, 2009).

Geodesics on a hot plate: an example of a two-dimensional curved space

International Nuclear Information System (INIS)

Erkal, Cahit

2006-01-01

The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion

Geodesics on a hot plate: an example of a two-dimensional curved space

Energy Technology Data Exchange (ETDEWEB)

Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)

2006-07-01

The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.

From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos

Science.gov (United States)

Kuznetsov, Sergey P.

2016-12-01

Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.

Kinematics of relative motion of test particles in general relativity

International Nuclear Information System (INIS)

Bazanski, S.L.

1977-01-01

A detailed mathematical study of the concept of geodesic deviation in pseudo-riemannian geometry is presented. A generalization of this concept to geodesic deviations of a higher order is then introduced and the second geodesic deviation is investigated in some detail. A geometric interpretation of the set of generalized geodesic deviations is given and applied in general relativity to determine a covariant and local description (with a desired order of accuracy) of test motions which take place in a certain finite neighbourhood of a given world line of an observer. The proper time evolution of two other objects related to geodesic deviation is also discussed: the space separation vector and the telescopic vector. This last name is given here to a field of null vectors along observer's world line which always point towards the same adjacent world line. The telescopic equations allow to determine the evolution of the frequency shift of electromagnetic radiation sent from and received on neighbouring world lines. On the basis of these equations also certain relations have been derived which connect the frequencies or frequency shifts with the curvature of space-time

Diffeomorphometry and geodesic positioning systems for human anatomy.

Science.gov (United States)

Miller, Michael I; Younes, Laurent; Trouvé, Alain

2014-03-01

The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry . Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning . As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates . These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system . We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

Vacuum non-expanding horizons and shear-free null geodesic congruences

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2009-01-01

We investigate the geometry of a particular class of null surfaces in spacetime called vacuum non-expanding horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex worldline in a complex four-dimensional space, each such choice induces a CR structure on the horizon, and a particular worldline (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.

Geodesics in thermodynamic state spaces of quantum gases

International Nuclear Information System (INIS)

Oshima, H.; Obata, T.; Hara, H.

2002-01-01

The geodesics for ideal quantum gases are numerically studied. We show that 30 ideal quantum state is connected to an ideal classical state by geodesics and that the bundle of geodesics for Bose gases have a tendency of convergence

Revisiting scalar geodesic synchrotron radiation in Kerr spacetime

International Nuclear Information System (INIS)

Macedo, Caio F.B.; Crispino, Luis C.B.

2011-01-01

Full text: The Kerr solution [R. P. Kerr, Phys. Rev. D 11, 5 (1963)] is one of the most important black hole solutions of Einstein equations. It describes a chargeless rotating black hole, with Schwarzschild black hole as a particular case. It is estimated, inferred using distinct methods, that most black hole candidates have a considerable value of the rotation parameter [E. Berti, V. Cardoso, and A. Starinets, Classical Quantum Gravity 26, 163001 (2009)]. Although the Schwarzschild solution is suitable for a great variety of phenomena in star and black hole physics, the Kerr solution becomes very important in the explanation of the electrodynamical aspects of accretion disks for binary X-ray sources [The Kerr Spacetime: Rotating Black Holes in General Relativity, edited by D. L. Wiltshire, M. Visser, and S. M. Scott (Cambridge University Press, Cambridge, 2009)]. Thus, the investigation of how radiation emission processes are modified by the nontrivial curvature of rotating black holes is particularly important. As a first approximation to the problem, one can consider a moving particle, minimally coupled to the massless scalar field, in circular geodesic motion. The radiation emitted in this configuration is called scalar geodesic synchrotron radiation. In this work, we revisit the main aspects of scalar geodesic synchrotron radiation in Kerr spacetime, including some effects occurring in the high-frequency approximation. Our results can be readily compared with the results of the equivalent phenomena in Schwarzschild spacetime. (author)

Congruences of totally geodesic surfaces

International Nuclear Information System (INIS)

Plebanski, J.F.; Rozga, K.

1989-01-01

A general theory of congruences of totally geodesic surfaces is presented. In particular their classification, based on the properties of induced affine connections, is provided. In the four-dimensional case canonical forms of the metric tensor admitting congruences of two-dimensional totally geodesic surfaces of rank one are given. Finally, congruences of two-dimensional extremal surfaces are studied. (author)

Geodesic exponential kernels: When Curvature and Linearity Conflict

DEFF Research Database (Denmark)

Feragen, Aase; Lauze, François; Hauberg, Søren

2015-01-01

manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic...

On certain geodesic conjugacies of flat cylinders

Indian Academy of Sciences (India)

Moreover, these base points must lie on different parallels. By continuity of F ◦α we conclude that the above parallel geodesics fill out a neighborhood of (r0, 0) in S. We conclude that f (r) = 0 for all r close to r0. This proves that R \\ A must be open. D. We call a closed geodesic slant if it is not a parallel geodesic. We have the ...

A Continuum Mechanical Approach to Geodesics in Shape Space

Science.gov (United States)

2010-01-01

mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto...P. W. Michor and D. Mumford. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc., 8:1–48, 2006. 37 [33] Peter W. Michor, David ... Cremers . Shape matching by variational computation of geodesics on a manifold. In Pattern Recognition, LNCS 4174, pages 142–151, 2006. [38] P

On integrability of the Killing equation

Science.gov (United States)

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.

Generating geodesic flows and supergravity solutions

NARCIS (Netherlands)

Bergshoeff, E.; Chemissany, W.; Ploegh, A.; Trigiante, M.; Van Riet, T.

2009-01-01

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacellike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike p-brane Solutions when they are lifted over a p-dimensional flat space. In particular, we consider

Craniofacial Reconstruction Evaluation by Geodesic Network

Directory of Open Access Journals (Sweden)

Junli Zhao

2014-01-01

Full Text Available Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.

A regularized approach for geodesic-based semisupervised multimanifold learning.

Science.gov (United States)

Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun

2014-05-01

Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.

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

Science.gov (United States)

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

Symmetries and conserved quantities in geodesic motion

International Nuclear Information System (INIS)

Hojman, S.; Nunez, L.; Patino, A.; Rago, H.

1986-01-01

Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved

Do extended objects move along the geodesics in the Riemann space-time

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

1981-01-01

Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru

New non-linear modified massless Klein-Gordon equation

Energy Technology Data Exchange (ETDEWEB)

Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2017-11-15

The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)

Craniofacial Reconstruction Evaluation by Geodesic Network

OpenAIRE

Zhao, Junli; Liu, Cuiting; Wu, Zhongke; Duan, Fuqing; Wang, Kang; Jia, Taorui; Liu, Quansheng

2014-01-01

Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the or...

Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Sheng-lan Chen

2014-01-01

Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

Geodesic motion and confinement in Goedel's universe

International Nuclear Information System (INIS)

Novello, M.; Soares, I.D.; Tiomno, J.

1982-01-01

A complete study of geodesic motion in Goedel's universe, using the method of the Effective Potential is presented. It then emerges a clear physical picture of free motion and its stability in this universe. Geodesics of a large class have finite intervals in which the particle moves back in time (dt/ds [pt

Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics

Directory of Open Access Journals (Sweden)

Liandong Zhang

2012-01-01

Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.

Instantons from geodesics in AdS moduli spaces

Science.gov (United States)

Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas

2018-03-01

We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.

On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

Directory of Open Access Journals (Sweden)

Youliang Fu

2016-01-01

Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

Geodesic detection of Agulhas rings

Science.gov (United States)

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.

From geodesics of the multipole solutions to the perturbed Kepler problem

International Nuclear Information System (INIS)

Hernandez-Pastora, J. L.; Ospino, J.

2010-01-01

A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2 4 -pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.

The geometry of geodesics

CERN Document Server

Busemann, Herbert

2005-01-01

A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

Timelike geodesics around a charged spherically symmetric dilaton black hole

Directory of Open Access Journals (Sweden)

Blaga C.

2015-01-01

Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.

Spherical null geodesics of rotating Kerr black holes

International Nuclear Information System (INIS)

Hod, Shahar

2013-01-01

The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r ph (a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii r ph (a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√(3)−√(59))/4≲cosi ph (a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=√(4/7), above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

Do extended bodies move alon.o the geodesics of the Riemannian space-time

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

1980-01-01

Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8

Equations of motion derived from a generalization of Einstein's equation for the gravitational field

International Nuclear Information System (INIS)

Mociutchi, C.

1980-01-01

The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

Directory of Open Access Journals (Sweden)

Timothy M. Adamo

2009-09-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

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Timothy M. Adamo

2012-01-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation.

Science.gov (United States)

Adamo, Timothy M; Newman, Ezra T; Kozameh, Carlos

2012-01-01

A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, [Formula: see text]-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Nonlinear excitation of geodesic acoustic modes by drift waves

International Nuclear Information System (INIS)

Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.

2007-01-01

In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs

Wigner transformation in curved space-time and the curvature correction of the Vlasov equation for semiclassical gravitating systems

International Nuclear Information System (INIS)

Winter, J.

1985-01-01

A covariant generalization of the Wigner transformation of quantum equations is proposed for gravitating many-particle systems, which modifies the Einstein-Liouville equations for the coupled gravity-matter problem by inclusion of quantum effects of the matter moving in its self-consistent classical gravitational field, in order to extend their realm of validity to higher particle densities. The corrections of the Vlasov equation (Liouville equation in one-particle phase space) are exhibited as combined effects of quantum mechanics and the curvature of space-time arranged in a semiclassical expansion in powers of h 2 , the first-order term of which is explicitly calculated. It is linear in the Riemann tensor and in its gradient; the Riemann tensor occurs in a similar position as the tensor of the Yang-Mills field strength in a corresponding Vlasov equation for systems with local gauge invariance in the purely classical limit. The performance of the Wigner transformation is based on expressing the equation of motion for the two-point function of the Klein-Gordon field, in particular the Beltrami operator, in terms of a midpoint and a distance vector covariantly defined for the two points. This implies the calculation of deviations of the geodesic between these points, the standard concept of which has to be refined to include infinitesimal variations of the second order. A differential equation for the second-order deviation is established

Equatorial Geodesics Around the Magnetars

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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 visualization of null geodesics for the bonnor massive dipole

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G. Andree Oliva Mercado

2015-08-01

Full Text Available In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.

Semi-local inversion of the geodesic ray transform in the hyperbolic plane

International Nuclear Information System (INIS)

Courdurier, Matias; Saez, Mariel

2013-01-01

The inversion of the ray transform on the hyperbolic plane has applications in geophysical exploration and in medical imaging techniques (such as electrical impedance tomography). The geodesic ray transform has been studied in more general geometries and including attenuation, but all of the available inversion formulas require knowledge of the ray transform for all the geodesics. In this paper we present a different inversion formula for the ray transform on the hyperbolic plane, which has the advantage of only requiring knowledge of the ray transform in a reduced family of geodesics. The required family of geodesics is directly related to the set where the original function is to be recovered. (paper)

Null solution of the Yang-Mills equations

International Nuclear Information System (INIS)

Tafel, J.

1986-05-01

We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays. (orig.)

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

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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.

Are eikonal quasinormal modes linked to the unstable circular null geodesics?

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R.A. Konoplya

2017-08-01

Full Text Available In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein–Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein–Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

Are eikonal quasinormal modes linked to the unstable circular null geodesics?

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Konoplya, R. A.; Stuchlík, Z.

2017-08-01

In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

Superintegrability of geodesic motion on the sausage model

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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.

Antiperiodic Solutions for a Kind of Nonlinear Duffing Equations with a Deviating Argument and Time-Varying Delay

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Changjin Xu

2014-01-01

Full Text Available This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results.

Tidal forces in Kiselev black hole

Energy Technology Data Exchange (ETDEWEB)

Shahzad, M.U. [University of Central Punjab, CAMS, UCP Business School, Lahore (Pakistan); Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan)

2017-06-15

The aim of this paper is to examine the tidal forces occurring in a Kiselev black hole surrounded by radiation and dust fluids. It is noted that the radial and angular components of the tidal force change the sign between event and Cauchy horizons. We solve the geodesic deviation equation for radially free-falling bodies toward Kiselev black holes. We explain the geodesic deviation vector graphically and point out the location of the event and Cauchy horizons for specific values of the radiation and dust parameters. (orig.)

Dynamics of relative motion of test particles in general relativity

International Nuclear Information System (INIS)

Bazanski, S.L.

1977-01-01

Several variational principles which lead to the first and the second geodesic deviation equations, recently formulated by the author and used for the description of the relative motion of test particles in general relativity are presented. Relations between these principles are investigated and exhibited. The Hamilton-Jacobi equation is also studied for these generalized deviations and the conservation laws appearing here are discussed

Stability of geodesic imcompleteness for Robertson-Walker space-times

International Nuclear Information System (INIS)

Beem, J.K.

1981-01-01

Let (M,g) be a Lorentzian warped product space-time M = (a, b) X H,g = -dt 2 x fh, where -infinity -infinity and (H,h) is homogeneous, then the past incompleteness of every timelike geodesic of (M,g) is stable under small C 0 perturbations in the space Lor(M) of Lorentzian metrics for M. Also it is shown that if (H,h) is isotropic and (M,g) contains a past-inextendible, past-incomplete null geodesic, then the past incompleteness of all null geodesics is stable under small C 1 perturbations in Lor(M). Given either the isotropy or homogeneity of the Riemannian factor, the background space-time (M,g) is globally hyperbolic. The results of this paper, in particular, answer a question raised by D. Lerner for big bang Robertson-Walker cosmological models affirmatively. (author)

Optimized curve design for image analysis using localized geodesic distance transformations

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Braithwaite, Billy; Niska, Harri; Pöllänen, Irene; Ikonen, Tiia; Haataja, Keijo; Toivanen, Pekka; Tolonen, Teemu

2015-03-01

We consider geodesic distance transformations for digital images. Given a M × N digital image, a distance image is produced by evaluating local pixel distances. Distance Transformation on Curved Space (DTOCS) evaluates shortest geodesics of a given pixel neighborhood by evaluating the height displacements between pixels. In this paper, we propose an optimization framework for geodesic distance transformations in a pattern recognition scheme, yielding more accurate machine learning based image analysis, exemplifying initial experiments using complex breast cancer images. Furthermore, we will outline future research work, which will complete the research work done for this paper.

3D Facial Similarity Measure Based on Geodesic Network and Curvatures

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Junli Zhao

2014-01-01

Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.

Bus Travel Time Deviation Analysis Using Automatic Vehicle Location Data and Structural Equation Modeling

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Xiaolin Gong

2015-01-01

Full Text Available To investigate the influences of causes of unreliability and bus schedule recovery phenomenon on microscopic segment-level travel time variance, this study adopts Structural Equation Modeling (SEM to specify, estimate, and measure the theoretical proposed models. The SEM model establishes and verifies hypotheses for interrelationships among travel time deviations, departure delays, segment lengths, dwell times, and number of traffic signals and access connections. The finally accepted model demonstrates excellent fitness. Most of the hypotheses are supported by the sample dataset from bus Automatic Vehicle Location system. The SEM model confirms the bus schedule recovery phenomenon. The departure delays at bus terminals and upstream travel time deviations indeed have negative impacts on travel time fluctuation of buses en route. Meanwhile, the segment length directly and negatively impacts travel time variability and inversely positively contributes to the schedule recovery process; this exogenous variable also indirectly and positively influences travel times through the existence of signalized intersections and access connections. This study offers a rational approach to analyzing travel time deviation feature. The SEM model structure and estimation results facilitate the understanding of bus service performance characteristics and provide several implications for bus service planning, management, and operation.

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

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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.

Geodesics in hypercomplex number systems. Application to commutative quaternions

International Nuclear Information System (INIS)

Catoni, Francesco; Zampetti, Paolo; Cannata, Roberto; Bordoni, Luciana

1997-10-01

The functions of hypercomplex variable can be related to the physical fields. Following the Einstein's ideas, by which the Theory of General Relativity was developed, they want to verify if a generalisation is possible, in order to described the motion of a body in a gravitational field, by the geodesics in spaces ''deformed'' by functional transformations of hypercomplex variables. These number systems introduce new space symmetries. This paper is just a first step in the more extended study. As a first application they consider the ''commutative quaternions'' system that may be considered as a composition of complex and hyperbolic numbers. By using in this system the same functional transformations valid for the two dimensional case, elliptical geodesics are obtained, with the eccentricity related to the angle between the orbit plane and a reference plane. These geodesics do not describe the Kepler orbits, but they show a space anisotropy that might be related to planet orbits of the solar system

Surfaces foliated by planar geodesics: a model forcurved wood design

DEFF Research Database (Denmark)

Brander, David; Gravesen, Jens

2017-01-01

Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle......Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle...

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstroem space-time: Analytical solutions

International Nuclear Information System (INIS)

Grunau, Saskia; Kagramanova, Valeria

2011-01-01

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstroem space-time in terms of the Weierstrass weierp, σ, and ζ elliptic functions. Based on the study of the polynomials in the θ and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstroem space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstroem space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

Science.gov (United States)

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.

Some investigations of null and time like geodesics in Schwarzschild and Schwarzschild de sitter black hole with a straight string passing through it

International Nuclear Information System (INIS)

Paudel, Eak Raj

2007-01-01

Gravitational field of Schwarzschild and Schwarzschild de-sitter Black hole with a straight string passing through it. In such space analytical and numerical solutions of null and time like geodesics are investigated. The string parameter a + is found to affect both the angle of deflection in null geodesics and the precession of perihelion on time like geodesics .It is seen that the deflection of null and time like geodesics near the gravitating mass of de-sitter space time increases with t he gravitational field of a straight string in flat space time has the property that the Newtonian potential vanishes yet there are non trivial gravitational effects. A test particle is neither attracted nor repelled by a string, yet the conical nature of space outside of string produces observable effects such as light deflection . Schwarzschild Black hole is a mathematical solution to the Einstein's field equations and corresponds to the gravitational field of massive compact spherically symmetric ob normal. References 1. Aryal, M.M, A. Vilenkin and L.H Ford, 1986, Phys.Rev. D32 ,2262 2. Moriyasu ,K ., 1980 , An introduction to gauge Invariance 3. Vilenkin A., 1985 , Physical reports , cosmic strings and Domain walls 4. Berry, M. , 1976 , Principle of cosmology and Gravitation 5. Mishner , C.W ., K.S .Throne , J.A wheeler , 1973. (Author)

A prescribing geodesic curvature problem

International Nuclear Information System (INIS)

Chang, K.C.; Liu, J.Q.

1993-09-01

Let D be the unit disk and k be a function on S 1 = δD. Find a flat metric which is pointwise conformal to the standard metric and has k as the geodesic curvature of S 1 . A sufficient condition for the existence of such a metric is that the harmonic extension of k in D has saddle points. (author). 11 refs

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

DEFF Research Database (Denmark)

Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole

2011-01-01

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......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...

On Geodesic Exponential Kernels

DEFF Research Database (Denmark)

Feragen, Aasa; Lauze, François; Hauberg, Søren

2015-01-01

This extended abstract summarizes work presented at CVPR 2015 [1]. Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, ......, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models....

Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

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Kun-Lin Wu

2016-01-01

Full Text Available In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.

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

Science.gov (United States)

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.

Solutions of the spin coefficient equations with nongeodesic eigenrays

International Nuclear Information System (INIS)

Kota, J.; Lukacs, B.; Perjes, Z.

1982-01-01

Among the many significant results obtained by spin coefficient techniques in general relativity, the exact integrals of gravitational equations have enjoyed particular attention. These integration procedures were first carried out with respect to a congruence of null geodesic curves. The authors show that spin coefficient equations can sometimes be exactly solved when the selected null congruence is nongeodesic. They derive metrics with this property and, among them, a new solution of the coupled Einstein-Maxwell equations. (Auth.)

About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument

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I. Orazov

2013-01-01

Full Text Available We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument. A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem.

Maxwell fields and shear-free null geodesic congruences

International Nuclear Information System (INIS)

Newman, Ezra T

2004-01-01

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the worldline. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, the following strange interpretation can be given. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x a take complex values, i.e., x a → z a = x a + iy a with complex metric g η ab dz a dz b , the real vacuum Maxwell equations can be extended into the complex space and rewritten as curl W=i W radical, div W=0 with W=E+iB. This subcase of Maxwell fields can then be extended into the complex space so as to have as source, a complex analytic worldline, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space (z a = x a ), they possess a real principal null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex worldline is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Null geodesics and embedding diagrams of the interior Schwarzschild--de Sitter spacetimes with uniform density

International Nuclear Information System (INIS)

Stuchlik, Zdenek; Hledik, Stanislav; Soltes, Jiri; Ostgaard, Erlend

2001-01-01

Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild--de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an 'effective potential.' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild--de Sitter spacetimes

Entanglement Equilibrium and the Einstein Equation.

Science.gov (United States)

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.

Large deviations and idempotent probability

CERN Document Server

Puhalskii, Anatolii

2001-01-01

In the view of many probabilists, author Anatolii Puhalskii''s research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel com...

Adaptive geodesic transform for segmentation of vertebrae on CT images

Science.gov (United States)

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.

Null geodesics in black hole metrics with non-zero cosmological constant

International Nuclear Information System (INIS)

Stuchlik, Z.; Calvani, M.

1990-02-01

We study the radial motion along null geodesics in the Reissner-Nordstroem-de Sitter and Kerr-de Sitter space-times. We analyze the properties of the effective potential and we discuss circular orbits. We find that the radii of circular geodesics in the Reissner-Nordstroem-de Sitter space-time do not depend on the cosmological constant, and we explain this property using the optical reference geometry. In addition, we describe the unusual consequences of the interplay between rotation of the source and cosmological repulsion. (author). 16 refs, 8 figs

Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance

OpenAIRE

Wang, Zaihong

2013-01-01

We study the existence of periodic solutions of Liénard equation with a deviating argument $x\\mathrm{\\prime \\prime }+f\\left(x\\right)x\\mathrm{\\text{'}}+{n}^{\\mathrm{2}}x+g\\left(x\\left(t-\\tau \\right)\\right)=p\\left(t\\right),$ where $f,g,p:\\mathrm{R}\\to \\mathrm{R}$ are continuous and $p$ is $\\mathrm{2}\\pi $ -periodic, $\\mathrm{0}\\le \\tau

Can geodesics in extra dimensions solve the cosmological horizon problem?

International Nuclear Information System (INIS)

Chung, Daniel J. H.; Freese, Katherine

2000-01-01

We demonstrate a non-inflationary solution to the cosmological horizon problem in scenarios in which our observable universe is confined to three spatial dimensions (a three-brane) embedded in a higher dimensional space. A signal traveling along an extra-dimensional null geodesic may leave our three-brane, travel into the extra dimensions, and subsequently return to a different place on our three-brane in a shorter time than the time a signal confined to our three-brane would take. Hence, these geodesics may connect distant points which would otherwise be ''outside'' the four dimensional horizon (points not in causal contact with one another). (c) 2000 The American Physical Society

The Jacobi metric for timelike geodesics in static spacetimes

Science.gov (United States)

Gibbons, G. W.

2016-01-01

It is shown that the free motion of massive particles moving in static spacetimes is given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the massless limit Jacobi's metric coincides with the energy independent Fermat or optical metric. For stationary metrics, it is known that the motion of massless particles is given by the geodesics of an energy independent Finslerian metric of Randers type. The motion of massive particles is governed by neither a Riemannian nor a Finslerian metric. The properies of the Jacobi metric for massive particles moving outside the horizon of a Schwarschild black hole are described. By constrast with the massless case, the Gaussian curvature of the equatorial sections is not always negative.

The generalized good cut equation

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2010-01-01

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.

On geodesics with negative energies in the ergoregions of dirty black holes

Science.gov (United States)

Zaslavskii, O. B.

2015-03-01

We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov and V. D. Vertogradov, Mod. Phys. Lett.29, 1450110 (2014), arXiv:1304.7360.

Properties of an Arithmetic Code for Geodesic Flows

International Nuclear Information System (INIS)

Chaves, Daniel P B; Palazzo, Reginaldo Jr; Rios Leite, Jose R

2011-01-01

Topological analysis of chaotic dynamical systems emerged in the nineties as a powerful tool in the study of strange attractors in low-dimensional dynamical systems. It is based on identifying the stretching and squeezing mechanisms responsible for creating a strange attractor and organize all the unstable periodic orbits in this attractor. This method is concerned with the manifold generated by the chaotic system. Furthermore, as a mathematical object, the manifolds have a well studied geometric and algebraic structure, particularly for the case of compact surfaces. Intending to use this structure in the analysis and application of chaotic systems through their topological characteristics, we determine properties of geodesic codes for compact surfaces necessary for the construction of encoders from the symbolic sequences of experimental data generated by the unstable periodic orbits of the strange attractor (related to the behavior changes of the system with the variation of control parameters) to the geodesic code sequences, which permits to use the surface structure to study the system orbits.

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

Science.gov (United States)

2015-03-26

encompass the quad-rotor. This cage will behave like a faraday cage of sorts, shielding the quad-rotor’s RCS phenomenology from the radar’s antenna...test volume. Second, because the quad-rotor’s structural geometry is a cause for concern, a geodesic cage , in the shape of a sphere, will be built to...be the development of the geodesic cage that will encompass the quad-rotor along with an analysis of its scattering statistics as function of the

Vector-tensor interaction of gravitation

Energy Technology Data Exchange (ETDEWEB)

Zhang Yuan-zhong; Guo han-ying

1982-11-01

In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.

Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

Energy Technology Data Exchange (ETDEWEB)

Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)

2009-12-31

A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.

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

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I. [National Research Centre Kurchatov Institute (Russian Federation); Konovaltseva, L. V. [Peoples’ Friendship University of Russia (Russian Federation)

2015-12-15

A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

Energy Technology Data Exchange (ETDEWEB)

Florinski, V. [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States); Guo, X. [Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Balsara, D. S.; Meyer, C. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States)

2013-04-01

This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

International Nuclear Information System (INIS)

Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.

2013-01-01

This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

Geodesic atlas-based labeling of anatomical trees

DEFF Research Database (Denmark)

Feragen, Aasa; Petersen, Jens; Owen, Megan

2015-01-01

We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...... equally complete airway trees, and comparable in performance to that of experts in pulmonary medicine, emphasizing the suitability of the labeling algorithm for clinical use....

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

Science.gov (United States)

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 \

One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance

Science.gov (United States)

Fröb, Markus B.

2018-02-01

We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.

Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

Science.gov (United States)

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.

On the Robinson theorem and shearfree geodesic null congruences

International Nuclear Information System (INIS)

Tafel, J.

1985-01-01

Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)

Conventional Gymnasium vs. Geodesic Field House. A Comparative Study of High School Physical Education and Assembly Facilities.

Science.gov (United States)

Educational Facilities Labs., Inc., New York, NY.

A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…

New perspectives for high accuracy SLR with second generation geodesic satellites

Science.gov (United States)

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

Geodesic least squares regression for scaling studies in magnetic confinement fusion

International Nuclear Information System (INIS)

Verdoolaege, Geert

2015-01-01

In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices

Ergodic Properties of the Quantum Geodesic Flow on Tori

Energy Technology Data Exchange (ETDEWEB)

Klimek, SLawomir [Indiana University Purdue University Indianapolis, Department of Mathematics (United States); Kondracki, Witold [Polish Academy of Sciences, Institute of Mathematics (Poland)

2005-05-15

We study ergodic averages for a class of pseudo-differential operators on the flat N-dimensional torus with respect to the Schroedinger evolution. The later can be consider a quantization of the geodesic flow on T{sup N}. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.

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

Energy Technology Data Exchange (ETDEWEB)

Zhang, H; Yan, L; Huang, K; Kong, F; Jin, J [Georgia Regents University, Augusta, GA (Georgia)

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 two 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.

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

Science.gov (United States)

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.

AdS/CFT prescription for angle-deficit space and winding geodesics

International Nuclear Information System (INIS)

Aref’eva, Irina Ya.; Khramtsov, Mikhail A.

2016-01-01

We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS_3 space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical bulk-boundary propagator for a scalar field in the space with conical defect and use it to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of ℤ_r-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.

Investigation of energetic particle induced geodesic acoustic mode

Science.gov (United States)

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.

Lagrangian analysis of invariant third-order equations of motion in relativistic classical particle mechanics

International Nuclear Information System (INIS)

Matsyuk, R.Ya.

1985-01-01

The problem on the existence of the invariant third-order Euler-Poisson equations in the pseudo-Euclidean space is investigated. The locally variational problem is determined by the Lagrangian density over the space of the second-order jets. The one - parameter family of the invariant third-order Euler-Poisson equations is groved to be the only one in the three-dimensional pseudo-Euclidean space. No invariant third-order Euler-Poisson equations exist in the four-dimensional pseudo-Euclidean space. It is shown that the Mathisson equation and the equation of geodesic circles in particular cases may be considered in the context of the Ostrogradiskij mechanics and the Kavaguchi geometry

Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

Energy Technology Data Exchange (ETDEWEB)

Lakhin, V.P. [NRC “Kurchatov Institute”, Moscow (Russian Federation); Sorokina, E.A., E-mail: sorokina.ekaterina@gmail.com [NRC “Kurchatov Institute”, Moscow (Russian Federation); Peoples' Friendship University of Russia, Moscow (Russian Federation)

2014-01-24

The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.

Chiral equations and fiber bundles

International Nuclear Information System (INIS)

Mateos, T.; Becerril, R.

1992-01-01

Using the hypothesis g = g (lambda i ), the chiral equations (rhog, z g -1 ), z -bar + (rhog, z -barg -1 ), z = 0 are reduced to a Killing equation of a p-dimensional space V p , being lambda i lambda i (z, z-bar) 'geodesic' parameters of V p . Supposing that g belongs to a Lie group G, one writes the corresponding Lie algebra elements (F) in terms of the Killing vectors of V p and the generators of the subalgebra of F of dimension d = dimension of the Killing space. The elements of the subalgebras belong to equivalence classes which in the respective group form a principal fiber bundle. This is used to integrate the matrix g in terms of the complex variables z and z-bar ( Author)

The topology of geodesically complete space-times

International Nuclear Information System (INIS)

Lee, C.W.

1983-01-01

Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)

A Finsler geodesic spray paradigm for wildfire spread modelling

DEFF Research Database (Denmark)

Markvorsen, Steen

2015-01-01

represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... and thence eventually constitute the local and global structure of the wildfire spread....

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

Science.gov (United States)

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.

Calculating observables in inhomogeneous cosmologies. Part I: general framework

Science.gov (United States)

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.

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

Science.gov (United States)

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

Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity

International Nuclear Information System (INIS)

Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston

2010-01-01

The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.

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

International Nuclear Information System (INIS)

Yehia, Hamad M

2013-01-01

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 S 2 is constructed. (paper)

Surface current equilibria from a geometric point of view

International Nuclear Information System (INIS)

Kaiser, R.; Salat, A.

1993-04-01

This paper addresses the inverse problem of the existence of surface current MHD equilibria in toroidal geometry with vanishing magnetic field inside. Inverse means that the plasma-vacuum interface rather than the external wall or conductors are given and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: What toroidal surfaces with analytic parameterization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering and are described by a function satisfying a nonlinear partial differential equation of the Hamilton-Jacobi type whose coefficients are combinations of the metric elements of the surface. All known equilibria - equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform - turn out to be solutions of separable cases of that equation and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behaviour of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry KAM-type behaviour is observed, i.e. destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry an analytic criterion is

Average geodesic distance of skeleton networks of Sierpinski tetrahedron

Science.gov (United States)

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.

Geodesic acoustic modes in noncircular cross section tokamaks

Energy Technology Data Exchange (ETDEWEB)

Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com; Lakhin, V. P. [National Research Center “Kurchatov Institute,” (Russian Federation); Konovaltseva, L. V. [People’s Friendship University of Russia (Russian Federation); Ilgisonis, V. I. [National Research Center “Kurchatov Institute,” (Russian Federation)

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.

Fundamental geodesic deformations in spaces of treelike shapes

DEFF Research Database (Denmark)

Feragen, Aasa; Lauze, Francois Bernard; Nielsen, Mads

2010-01-01

This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which...... is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees....

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

Science.gov (United States)

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.

Testing the equivalence principle on cosmological scales

Science.gov (United States)

Bonvin, Camille; Fleury, Pierre

2018-05-01

The equivalence principle, that is one of the main pillars of general relativity, is very well tested in the Solar system; however, its validity is more uncertain on cosmological scales, or when dark matter is concerned. This article shows that relativistic effects in the large-scale structure can be used to directly test whether dark matter satisfies Euler's equation, i.e. whether its free fall is characterised by geodesic motion, just like baryons and light. After having proposed a general parametrisation for deviations from Euler's equation, we perform Fisher-matrix forecasts for future surveys like DESI and the SKA, and show that such deviations can be constrained with a precision of order 10%. Deviations from Euler's equation cannot be tested directly with standard methods like redshift-space distortions and gravitational lensing, since these observables are not sensitive to the time component of the metric. Our analysis shows therefore that relativistic effects bring new and complementary constraints to alternative theories of gravity.

Cosmological models in globally geodesic coordinates. II. Near-field approximation

International Nuclear Information System (INIS)

Liu Hongya

1987-01-01

A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system

Moderate Deviation Principles for Stochastic Differential Equations with Jumps

Science.gov (United States)

2014-01-15

N ŕ’"(dt; dy) and the controls ’" : X [0; T ] ! [0;1) are predictable processes satisfying LT (’") Ma2 (") for some constantM . Here LT denotes...space. Although in the moderate deviations problem one has the stronger bound LT (’") Ma2 (") on the cost of controls, the mere tightness of ’" does not...suitable quadratic form. For " > 0 and M ə, consider the spaces SM+;" : = f’ : X [0; T ]! R+j LT (’) Ma2 (")g (2.5) SM" : = f : X [0; T ]! Rj

Anatomy of geodesic Witten diagrams

Energy Technology Data Exchange (ETDEWEB)

Chen, Heng-Yu; Kuo, En-Jui [Department of Physics and Center for Theoretical Sciences, National Taiwan University,Taipei 10617, Taiwan (China); Kyono, Hideki [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)

2017-05-12

We revisit the so-called “Geodesic Witten Diagrams” (GWDs) https://www.doi.org/10.1007/JHEP01(2016)146, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related “split representation” for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

The centripetal force law and the equation of motion for a particle on a curved hypersurface

International Nuclear Information System (INIS)

Hu, L.D.; Lian, D.K.; Liu, Q.H.

2016-01-01

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. (orig.)

Sensitivity Analysis of Deviation Source for Fast Assembly Precision Optimization

Directory of Open Access Journals (Sweden)

Jianjun Tang

2014-01-01

Full Text Available Assembly precision optimization of complex product has a huge benefit in improving the quality of our products. Due to the impact of a variety of deviation source coupling phenomena, the goal of assembly precision optimization is difficult to be confirmed accurately. In order to achieve optimization of assembly precision accurately and rapidly, sensitivity analysis of deviation source is proposed. First, deviation source sensitivity is defined as the ratio of assembly dimension variation and deviation source dimension variation. Second, according to assembly constraint relations, assembly sequences and locating, deviation transmission paths are established by locating the joints between the adjacent parts, and establishing each part’s datum reference frame. Third, assembly multidimensional vector loops are created using deviation transmission paths, and the corresponding scalar equations of each dimension are established. Then, assembly deviation source sensitivity is calculated by using a first-order Taylor expansion and matrix transformation method. Finally, taking assembly precision optimization of wing flap rocker as an example, the effectiveness and efficiency of the deviation source sensitivity analysis method are verified.

Twisting null geodesic congruences, scri, H-space and spin-angular momentum

International Nuclear Information System (INIS)

Kozameh, Carlos; Newman, E T; Silva-Ortigoza, Gilberto

2005-01-01

The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat spacetime with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world line in a four-parameter complex space. Surprisingly, this parameter space turns out to be the H-space that is associated with the real physical spacetime under consideration. The main development in this work is the demonstration of how this complex world line can be made both unique and also given a physical meaning. More specifically, by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world line is uniquely determined and becomes (by several arguments) identified as the 'complex centre of mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum. One should think of this work as developing a generalization of the properties of the algebraically special spacetimes in the sense that the term that is forced here to vanish is automatically vanishing (among many other terms) for all the algebraically special metrics. This is demonstrated in the several given examples. It was, in fact, an understanding of the algebraically special metrics and their associated shear-free null congruence that led us to this construction of the asymptotically shear-free congruences and the unique complex world line. The Robinson-Trautman metrics and the Kerr and charged Kerr metrics with their properties are explicit examples of the construction given here

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

Science.gov (United States)

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

Asymptotically shear-free and twist-free null geodesic congruences

International Nuclear Information System (INIS)

Kozameh, Carlos; Newman, Ezra T

2007-01-01

The Robinson-Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property

Divided Spheres Geodesics and the Orderly Subdivision of the Sphere

CERN Document Server

Popko, Edward S

2012-01-01

This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.

Geodesic Monitoring of Settling in Vertical Fuel Tanks

Directory of Open Access Journals (Sweden)

Luis Enrique Acosta-González

2017-07-01

Full Text Available The behavior of the settling in a vertical tank used for fuel storage was studied. Monitoring was conducted using the geodesic model for the geometric leveling of high accuracy category II. The original project varied during construction by replacing deep foundations with a surface one applying compaction techniques to improve soil resistance. The deformation values obtained provided valuable information on the implementation of the proposed foundation alternative depending on time and loads. The maximum settling was reported to be 132,6 mm. The displacements in the control points located in the perimeter of the tank had a distinct nature with a maximum of 44,2 mm, which caused the foundation structure to crack.

Comments on the Gravitational lensing Magnification

OpenAIRE

Takashi, HAMANA; Astronomical Institute, Tohoku University

1998-01-01

We rederive a relation between gravitational lensing magnification relative to the standard Friedmann distance and one relative to the Dyer-Roeder distance by investigating the null geodesic deviation equation. We show that the relation comes from a natural consequence of the definition of the lensing magnification matrices and is not based on the averaging of the magnifications, which has conventionally been used to derive it. We therefore conclude that the relation is true for each individu...

Comments on the gravitational lensing magnification

OpenAIRE

Hamana, Takashi

1998-01-01

We rederive a relation between gravitational lensing magnification relative to the standard Friedmann distance and one relative to the Dyer-Roeder distance by investigating the null geodesic deviation equation. We show that the relation comes from a natural consequence of the definition of the lensing magnification matrices and is not based on the averaging of the magnifications, which has conventionally been used to derive it. We therefore conclude that the relation is true for each individu...

A hierarchical scheme for geodesic anatomical labeling of airway trees

DEFF Research Database (Denmark)

Feragen, Aasa; Petersen, Jens; Owen, Megan

2012-01-01

We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....... In tree-space, the airway tree topology and geometry change continuously, giving a natural way to automatically handle anatomical differences and noise. The algorithm is made efficient using a hierarchical approach, in which labels are assigned from the top down. We only use features of the airway...

Working covariance model selection for generalized estimating equations.

Science.gov (United States)

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.

Large deviations

CERN Document Server

Varadhan, S R S

2016-01-01

The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.

Drift effects on electromagnetic geodesic acoustic modes

Energy Technology Data Exchange (ETDEWEB)

Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)

2015-02-15

A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)

A geodesic atmospheric model with a quasi-Lagrangian vertical coordinate

International Nuclear Information System (INIS)

Heikes, Ross; Konor, Celal; Randall, David A

2006-01-01

The development of the Coupled Colorado State Model (CCoSM) is ultimately motivated by the need to predict and study climate change. All components of CCoSM innovatively blend unique design ideas and advanced computational techniques. The atmospheric model combines a geodesic horizontal grid with a quasi-Lagrangian vertical coordinate to improve the quality of simulations, particularly that of moisture and cloud distributions. Here we briefly describe the dynamical core, physical parameterizations and computational aspects of the atmospheric model, and present our preliminary numerical results. We also briefly discuss the rational behind our design choices and selection of computational techniques

Optics of relativistic sources in a spherically symmetric gravitational field

International Nuclear Information System (INIS)

Campbell, G.A.

1975-01-01

The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)

Geodesic acoustic modes excited by finite beta drift waves

DEFF Research Database (Denmark)

Chakrabarti, Nikhil Kumar; Guzdar, P.N.; Kleva, R.G.

2008-01-01

Presented in this paper is a mode-coupling analysis for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by finite beta drift waves. The finite beta effects give rise to a strong stabilizing influence on the parametric excitation process. The dominant finite beta...... effect is the combination of the Maxwell stress, which has a tendency to cancel the primary drive from the Reynolds stress, and the finite beta modification of the drift waves. The zonal magnetic field is also excited at the GAM frequency. However, it does not contribute to the overall stability...... of the three-wave process for parameters of relevance to the edge region of tokamaks....

Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

International Nuclear Information System (INIS)

Iftikhar, Sehrish; Sharif, M.

2015-01-01

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole

Wasserstein gradient flows from large deviations of many-particle limits

NARCIS (Netherlands)

Duong, M.H.; Laschos, V.; Renger, D.R.M.

2013-01-01

We study the Fokker–Planck equation as the many-particle limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the path-space rate functional, which characterises the large deviations from the expected trajectories, in such a way that the free

The Raychaudhuri equation in homogeneous cosmologies

International Nuclear Information System (INIS)

Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A.

2014-01-01

In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories

Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak

Czech Academy of Sciences Publication Activity Database

Seidl, Jakub; Krbec, Jaroslav; Hron, Martin; Adámek, Jiří; Hidalgo, C.; Markovič, Tomáš; Melnikov, A.V.; Stöckel, Jan; Weinzettl, Vladimír; Aftanas, Milan; Bílková, Petra; Bogár, Ondrej; Böhm, Petr; Eliseev, L.G.; Háček, Pavel; Havlíček, Josef; Horáček, Jan; Imríšek, Martin; Kovařík, Karel; Mitošinková, Klára; Pánek, Radomír; Tomeš, Matěj; Vondráček, Petr

2017-01-01

Roč. 57, č. 12 (2017), č. článku 126048. ISSN 0029-5515 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA AV ČR(CZ) GA16-24724S; GA ČR(CZ) GA15-10723S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : geodesic acoustic mode * tokamak * turbulence * COMPASS Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016

Closed string field theory: Quantum action and the Batalin-Vilkovsky master equation

International Nuclear Information System (INIS)

Zwiebach, B.

1993-01-01

The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L ∞ encoding the gauge symmetry of the classical theory. The higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation and thus consistent BRST quantization of the quantum action. From the L ∞ algebra, and the BV equation on the off-shell state space we derive the L ∞ algebra, and the BV equation on physical states that were recently constructed in d=2 string theory. The string diagrams are surfaces with minimal area metrics, foliated by closed geodesics of length 2π. These metrics generalize quadratic differentials in that foliation bands can cross. The string vertices are succinctly characterized; they include the surfaces whose foliation bands are all of height smaller than 2π. (orig.)

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

Science.gov (United States)

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.

CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

Directory of Open Access Journals (Sweden)

Evert van Aart

2011-01-01

Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.

Quasilocal contribution to the scalar self-force: Geodesic motion

International Nuclear Information System (INIS)

Ottewill, Adrian C.; Wardell, Barry

2008-01-01

We consider a scalar charge travelling in a curved background space-time. We calculate the quasilocal contribution to the scalar self-force experienced by such a particle following a geodesic in a general space-time. We also show that if we assume a massless field and a vacuum background space-time, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analogs are of immediate physical interest for the calculation of radiation-reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results

Large Deviations for Two-Time-Scale Diffusions, with Delays

International Nuclear Information System (INIS)

Kushner, Harold J.

2010-01-01

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.

Mean E×B shear effect on geodesic acoustic modes in Tokamaks

International Nuclear Information System (INIS)

Singh, Rameswar; Gurcan, Ozgur D.

2015-01-01

E × B shearing effect on geodesic acoustic mode (GAM) is investigated for the first time both as an initial value problem in the shearing frame and as an eigenvalue value problem in the lab frame. The nontrivial effects are that E × B shearing couples the standard GAM perturbations to their complimentary poloidal parities. The resulting GAM acquires an effective inertia increasing in time leading to GAM damping. Eigenmode analysis shows that GAMs are radially localized by E × B shearing with the mode width being inversely proportional and radial wave number directly proportional to the shearing rate for weak shear. (author)

Deviations from LTE in a stellar atmosphere

International Nuclear Information System (INIS)

Kalkofen, W.; Klein, R.I.; Stein, R.F.

1979-01-01

Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section αsub(ν) grows with frequency ν faster than ν 2 ; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of αsub(ν). Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature. (author)

Deviations from LTE in a stellar atmosphere

Science.gov (United States)

Kalkofen, W.; Klein, R. I.; Stein, R. F.

1979-01-01

Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.

YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME

Energy Technology Data Exchange (ETDEWEB)

Yang Xiaolin; Wang Jiancheng, E-mail: yangxl@ynao.ac.cn [National Astronomical Observatories, Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011 (China)

2013-07-01

Following the work of Dexter and 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 and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and 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/{approx}yangxl/yxl.html.

YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME

International Nuclear Information System (INIS)

Yang Xiaolin; Wang Jiancheng

2013-01-01

Following the work of Dexter and 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 and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and 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.

Comment on ''Modified photon equation of motion as a test for the principle of equivalence''

International Nuclear Information System (INIS)

Nityananda, R.

1992-01-01

In a recent paper, a modification of the geodesic equation was proposed for spinning photons containing a spin-curvature coupling term. The difference in arrival times of opposite circular polarizations starting simultaneously from a source was computed, obtaining a result linear in the coupling parameter. It is pointed out here that this linear term violates causality and, more generally, Fermat's principle, implying calculational errors. Even if these are corrected, there is a violation of covariance in the way the photon spin was introduced. Rectifying this makes the effect computed vanish entirely

a Fuzzy Automatic CAR Detection Method Based on High Resolution Satellite Imagery and Geodesic Morphology

Science.gov (United States)

Zarrinpanjeh, N.; Dadrassjavan, F.

2017-09-01

Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.

GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION

Directory of Open Access Journals (Sweden)

Serge Beucher

2011-05-01

Full Text Available The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstruction supposes the use of a marker function f which is not necessarily related to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristic regions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy to handle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in image reconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of the function reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.

Structural Equations and Causation

OpenAIRE

Hall, Ned

2007-01-01

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

International Nuclear Information System (INIS)

Soda, Jiro.

1989-08-01

On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

The trace formula and the distribution of eigenvalues of Schroedinger operators on manifolds all of whose geodesics are closed

International Nuclear Information System (INIS)

Schubert, R.

1995-05-01

We investigate the behaviour of the remainder term R(E) in the Weyl formula {nvertical stroke E n ≤E}=Vol(M).E d/2 /[(4π) d/2 Γ(d/2+1)]+R(E) for the eigenvalues E n of a Schroedinger operator on a d-dimensional compact Riemannian manifold all of whose geodesics are closed. We show that R(E) is of the form E (d-1)/2 Θ(√E), where Θ(x) is an almost periodic function of Besicovitch class B 2 which has a limit distribution whose density is a box-shaped function. Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits. The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly. (orig.)

Nonlocal analysis of the excitation of the geodesic acoustic mode by drift waves

DEFF Research Database (Denmark)

Guzdar, P.N.; Kleva, R.G.; Chakrabarti, N.

2009-01-01

The geodesic acoustic modes (GAMs) are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical...... of the edge region of tokamaks is presented in this paper. The continuum GAM modes with coupling to the drift waves can create discrete "global" unstable eigenmodes localized in the edge "pedestal" region of the plasma. Multiple resonantly driven unstable radial eigenmodes can coexist on the edge pedestal....

Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren

2010-01-01

, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...

Computational Analysis of Natural Ventilation Flows in Geodesic Dome Building in Hot Climates

Directory of Open Access Journals (Sweden)

Zohreh Soleimani

2016-08-01

Full Text Available For centuries, dome roofs were used in traditional houses in hot regions such as the Middle East and Mediterranean basin due to its thermal advantages, structural benefits and availability of construction materials. This article presents the computational modelling of the wind- and buoyancy-induced ventilation in a geodesic dome building in a hot climate. The airflow and temperature distributions and ventilation flow rates were predicted using Computational Fluid Dynamics (CFD. The three-dimensional Reynolds-Averaged Navier-Stokes (RANS equations were solved using the CFD tool ANSYS FLUENT15. The standard k-epsilon was used as turbulence model. The modelling was verified using grid sensitivity and flux balance analysis. In order to validate the modelling method used in the current study, additional simulation of a similar domed-roof building was conducted for comparison. For wind-induced ventilation, the dome building was modelled with upper roof vents. For buoyancy-induced ventilation, the geometry was modelled with roof vents and also with two windows open in the lower level. The results showed that using the upper roof openings as a natural ventilation strategy during winter periods is advantageous and could reduce the indoor temperature and also introduce fresh air. The results also revealed that natural ventilation using roof vents cannot satisfy thermal requirements during hot summer periods and complementary cooling solutions should be considered. The analysis showed that buoyancy-induced ventilation model can still generate air movement inside the building during periods with no or very low wind.

A FUZZY AUTOMATIC CAR DETECTION METHOD BASED ON HIGH RESOLUTION SATELLITE IMAGERY AND GEODESIC MORPHOLOGY

Directory of Open Access Journals (Sweden)

N. Zarrinpanjeh

2017-09-01

Full Text Available Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.

Analytic continuation of tgensor fields along geodesics by covariant Taylor series

International Nuclear Information System (INIS)

Tsirulev, A.N.

1995-01-01

It is shown that in a certain normal neighborhood of a submanifold-the analog of a normal neighborhood of a point-the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered

On extracting physical content from asymptotically flat spacetime metrics

International Nuclear Information System (INIS)

Kozameh, C; Newman, E T; Silva-Ortigoza, G

2008-01-01

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux

Singular perturbations of manifolds, with applications to the problem of motion in general relativity

International Nuclear Information System (INIS)

Kates, R.E.

1979-01-01

This thesis shows that a small body with possibly strong internal gravity moves through an empty region of a curved, and not necessarily asymptotically flat, external spacetime on an approximate geodesic. By approximate geodesic, the following is meant: Suppose the ratio epsilon = m/L 1 - where m is the body's mass and L is a curvature reference length of the external field - is a small parameter. Then the body's worldline deviates from a geodesic only by distances of at most THETA(epsilon) L over times of order L. The worldline is calculated directly from the Einstein field equation using a singular perturbation technique that has been generalized from the method of matched asymptotic expansions. The need for singular perturbation techniques has long been appreciated in fluid mechanics, where they are now standard procedure in problems in which the straightforward expansion in powers of a small parameter fails to give a correct qualitative picture. In part I of this thesis, singular perturbations on manifolds are formulated in a coordinate-free way suitable for treating problems in general relativity and other field theories. Most importantly for this thesis, the coordinate-free formulation of singular perturbations given in part I is essential for treatment of the problem of motion in part II

Deviations from mass transfer equilibrium and mathematical modeling of mixer-settler contactors

International Nuclear Information System (INIS)

Beyerlein, A.L.; Geldard, J.F.; Chung, H.F.; Bennett, J.E.

1980-01-01

This paper presents the mathematical basis for the computer model PUBG of mixer-settler contactors which accounts for deviations from mass transfer equilibrium. This is accomplished by formulating the mass balance equations for the mixers such that the mass transfer rate of nuclear materials between the aqueous and organic phases is accounted for. 19 refs

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

Science.gov (United States)

Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe

2014-02-01

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

Postoperative radiotherapy for glioma: improved delineation of the clinical target volume using the geodesic distance calculation.

Directory of Open Access Journals (Sweden)

DanFang Yan

Full Text Available OBJECTS: To introduce a new method for generating the clinical target volume (CTV from gross tumor volume (GTV using the geodesic distance calculation for glioma. METHODS: One glioblastoma patient was enrolled. The GTV and natural barriers were contoured on each slice of the computer tomography (CT simulation images. Then, a graphic processing unit based on a parallel Euclidean distance transform was used to generate the CTV considering natural barriers. Three-dimensional (3D visualization technique was applied to show the delineation results. Speed of operation and precision were compared between this new delineation method and the traditional method. RESULTS: In considering spatial barriers, the shortest distance from the point sheltered from these barriers equals the sum of the distance along the shortest path between the two points; this consists of several segments and evades the spatial barriers, rather than being the direct Euclidean distance between two points. The CTV was generated irregularly rather than as a spherical shape. The time required to generate the CTV was greatly reduced. Moreover, this new method improved inter- and intra-observer variability in defining the CTV. CONCLUSIONS: Compared with the traditional CTV delineation, this new method using geodesic distance calculation not only greatly shortens the time to modify the CTV, but also has better reproducibility.

The Distance Standard Deviation

OpenAIRE

Edelmann, Dominic; Richards, Donald; Vogel, Daniel

2017-01-01

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. New representations for the distance standard deviation are obtained in terms of Gini's mean difference and in terms of the moments of spacings of order statistics. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini's mean difference. Further, it is ...

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

International Nuclear Information System (INIS)

Kupeli, A.H.

1988-01-01

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 μ/ is chosen to be the null vector of the GKS transformation, this property is stated as σ = 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 less symmetries including special cases of the Kota--Perjes and Lukacs solutions

The Kerr/fluid duality and the singularity of solutions to the fluid equation

International Nuclear Information System (INIS)

Fujisawa, Ippei; Nakayama, Ryuichi

2016-01-01

An equation for a viscous incompressible fluid on a spheroidal surface that is dual to the perturbation around the near-near-horizon extreme Kerr (near-NHEK) black hole is derived. It is also shown that an expansion scalar θ of a congruence of null geodesics on the perturbed horizon of the perturbed near-NHEK spacetime, which is dual to a viscous incompressible fluid, is not in general positive semidefinite, even if initial conditions on the velocity are smooth. Unless the initial conditions are appropriately adjusted, caustics of null congruence will occur on the perturbed horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime, which is dual to a viscous incompressible fluid on S 2 . An initial condition that θ be positive semidefinite at any point on S 2 is a necessary condition for the existence of smooth solutions to the incompressible Navier-Stokes equation on S 2

Quantum maps of geodesic flows on surfaces of constant negative curvature

International Nuclear Information System (INIS)

Bogomolny, E.B.; Carioli, M.

1992-01-01

The Selberg zeta function Z(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds Z(s) can be exactly rewritten as the Fredholm determinant det(1-T s ), where T s is the generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is presented, yielding a method to find not only the spectrum but also the eigenvalues of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically. (author) 15 refs., 10 figs

Lipschitz Metrics for a Class of Nonlinear Wave Equations

Science.gov (United States)

Bressan, Alberto; Chen, Geng

2017-12-01

The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.

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

Science.gov (United States)

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%.

Geodesic mode instability driven by electron and ion fluxes during neutral beam injection in tokamaks

Czech Academy of Sciences Publication Activity Database

Camilo de Souza, F.; Elfimov, A.; Galvão, R.M.O.; Krbec, Jaroslav; Seidl, Jakub; Stöckel, Jan; Hron, Martin; Havlíček, Josef; Mitošinková, Klára

2017-01-01

Roč. 381, č. 36 (2017), s. 3066-3070 ISSN 0375-9601 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 Institutional support: RVO:61389021 Keywords : Tokamak * Geodesic acoustic modes * Kinetic theory * Instability * Landau damping Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: 1.3 Physical sciences Impact factor: 1.772, year: 2016 http://www.sciencedirect.com/science/article/pii/S0375960117306989

Segmentation Using Symmetry Deviation

DEFF Research Database (Denmark)

Hollensen, Christian; Højgaard, L.; Specht, L.

2011-01-01

of the CT-scans into a single atlas. Afterwards the standard deviation of anatomical symmetry for the 20 normal patients was evaluated using non-rigid registration and registered onto the atlas to create an atlas for normal anatomical symmetry deviation. The same non-rigid registration was used on the 10...... hypopharyngeal cancer patients to find anatomical symmetry and evaluate it against the standard deviation of the normal patients to locate pathologic volumes. Combining the information with an absolute PET threshold of 3 Standard uptake value (SUV) a volume was automatically delineated. The overlap of automated....... The standard deviation of the anatomical symmetry, seen in figure for one patient along CT and PET, was extracted for normal patients and compared with the deviation from cancer patients giving a new way of determining cancer pathology location. Using the novel method an overlap concordance index...

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

Energy Technology Data Exchange (ETDEWEB)

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)

2016-11-15

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.

Circuital model for the spherical geodesic waveguide perfect drain

Science.gov (United States)

González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.

2012-08-01

The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.

Circuital model for the spherical geodesic waveguide perfect drain

International Nuclear Information System (INIS)

González, Juan C; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C

2012-01-01

The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000. (paper)

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

Energy Technology Data Exchange (ETDEWEB)

Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)

2016-11-25

We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

International Nuclear Information System (INIS)

Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.

2016-01-01

We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

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

Energy Technology Data Exchange (ETDEWEB)

Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich (Switzerland)

2017-06-01

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 it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument

Czech Academy of Sciences Publication Activity Database

Drábek, P.; Kufner, Alois; Kuliev, K.

2017-01-01

Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059

Shear-free axial model in massive Brans–Dicke gravity

Energy Technology Data Exchange (ETDEWEB)

Sharif, M., E-mail: msharif.math@pu.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782 (Pakistan)

2017-01-15

This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans–Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-free condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.

Generalized Fermat's principle and action for light rays in a curved spacetime

Science.gov (United States)

Frolov, Valeri P.

2013-09-01

We start with formulation of the generalized Fermat’s principle for light propagation in a curved spacetime. We apply Pontryagin’s minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.

Melting-pressure and density equations of 3He at temperatures from 0.001 to 30 K

International Nuclear Information System (INIS)

Huang Yonghua; Chen Guobang

2005-01-01

Nonsegmented equations for melting pressure and density at temperatures from 0.001 K to 30 K have been developed to fit the reference data. The maximum and average deviations between the melting pressure equation and the totaling 298 reference data are 2.17% and 0.218%, respectively. For the density equations, the average deviations are 0.236% for the liquid side and 0.218% for the solid side. Both the melting pressure curve and melting density curves predicted by the submitted equations approach their minimums at about 0.315 K

SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS

OpenAIRE

Kalpesh S. Tailor

2017-01-01

Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the c...

Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole

International Nuclear Information System (INIS)

Iftikhar, Sehrish; Sharif, M.

2015-01-01

We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole

Collapsing radiating stars with various equations of state

Science.gov (United States)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

48 CFR 2001.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2001... Individual deviations. In individual cases, deviations from either the FAR or the NRCAR will be authorized... deviations clearly in the best interest of the Government. Individual deviations must be authorized in...

Extreme super-resolution using the spherical geodesic waveguide

Science.gov (United States)

Miñano, Juan Carlos; González, Juan Carlos; Benítez, Pablo; Grabovičkić, Dejan

2012-06-01

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

48 CFR 801.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations. 801... Individual deviations. (a) Authority to authorize individual deviations from the FAR and VAAR is delegated to... nature of the deviation. (d) The DSPE may authorize individual deviations from the FAR and VAAR when an...

From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage

NARCIS (Netherlands)

Adams, S.; Dirr, N.; Peletier, M.A.; Zimmer, J.

2011-01-01

We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial

Liouville's equation and radiative acceleration in general relativity

International Nuclear Information System (INIS)

Keane, A.J.

1999-01-01

spacetimes. In the case of the Schwarzschild spacetime we find a solution of the Liouville equation which is invariant under the Killing vector symmetries and we adopt this as our model radiation field. Once a particular solution has been chosen the radiation field has been specified completely throughout the spacetime. In chapter 4 we investigate null and timelike geodesics in the Schwarzschild spacetime. Studying the null geodesics allows us to determine the viewing angles, that is, the (semi) angular size of the compact object as viewed by a stationary observer at an arbitrary point in the spacetime. The timelike geodesics are the trajectories of the (massive) test particles subject to no external radiation force and therefore constitute a limiting case of the radiative acceleration results. Given the radiation field one can calculate the radiation pressure force and because of special relativistic effects, the radiation pressure force experienced by the particle becomes velocity dependent. In chapter 5 we integrate the equations of motion for the case of purely radial motion in the Thomson limit. In this case we can obtain a tractable analytic expression for the solution in phase space, which can be compared with the high frequency case. In this chapter we consider a relativistic critical luminosity of a compact object, i.e. a relativistic Eddington luminosity. We also introduce and discuss terminal velocities and saturation velocities associated with a particular compact object. The terminal velocity of a radiation field is the 3-velocity required to annul the radiation pressure force on the test particle, neglecting the influence of any gravitational force on the particle. The saturation velocity is defined in the same way except the gravitational force is included. The saturation velocities are of course highly frequency dependent and provide important information about the dynamics of the system. In chapter 6 we discuss the Compton differential cross-section for

Detecting deviating behaviors without models

NARCIS (Netherlands)

Lu, X.; Fahland, D.; van den Biggelaar, F.J.H.M.; van der Aalst, W.M.P.; Reichert, M.; Reijers, H.A.

2016-01-01

Deviation detection is a set of techniques that identify deviations from normative processes in real process executions. These diagnostics are used to derive recommendations for improving business processes. Existing detection techniques identify deviations either only on the process instance level

Theory of phase-slip processes in thin and dirty current-carrying superconducting wires: Deviations from local equilibrium

International Nuclear Information System (INIS)

Kraehenbuehl, Y.

1983-01-01

Oscillatory phase-slip solution of a set of integrodifferential equations describing time-dependent processes in dirty superconductors in the Ginzburg-Landau regime are found numerically very near Tsub(c). Deviations from local equilibrium improve the agreement with observed V-I curves. (orig.)

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

Energy Technology Data Exchange (ETDEWEB)

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan, E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: jan.schee@fpf.slu.cz, E-mail: bobir.toshmatov@fpf.slu.cz, E-mail: jan.hladik@fpf.slu.cz, E-mail: jan.novotny@fpf.slu.cz [Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic)

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 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 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 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.

GEODESIC MONITORING OF VERTICAL MOVEMENT OF JSC «GRODNO AZOT» BUILDINGS USING DIGITAL DNA 03 LEVEL

Directory of Open Access Journals (Sweden)

V. I. Mikhailov

2010-01-01

Full Text Available The paper presents peculiar features and methodology pertaining to application of digital DNA 03 level for monitoring vertical movement of load-carrying structures in the workshops and foundations of various capacities, exhaust pipes and granulation towers having height from 100 to150 meters. The proposed methods presuppose usage of the results of engineering and geological investigations and highly accurate geodesic measurements considered in the process of hydro- and pneumatic tests of an isothermic storage of liquid ammonia and a production “Ammonia” shop taken as an example. 

Deviation from local thermodynamic equilibrium in a cesium-seeded argon plasma

International Nuclear Information System (INIS)

Stefanov, B.; Zarkova, L.

1985-11-01

The possibility of deviations from local thermodynamic equilibrium of a cesium seeded argon plasma has been analyzed. A four level model of cesium has been employed. Overpopulations of the ground state and the first excited state as well as the corresponding reduction of the electron density are calculated for cylindrical discharge structures by solving stationary rate equations. Numerical results are presented. These results indicate that in a large regime of plasma conditions the LTE assumption is valid for electron temperatures larger than 3000 K. (orig.)

Deviations of Lambert-Beer???s law affect corneal refractive parameters after refractive surgery

OpenAIRE

Jim??nez Cuesta, Jos?? Ram??n; Rodr??guez-Mar??n, Francisco; Gonz??lez Anera, Rosario; Jim??nez del Barco Jaldo, Luis Miguel

2006-01-01

We calculate whether deviations of Lambert-Beer???s law, which regulates depth ablation during corneal ablation, significantly influence corneal refractive parameters after refractive surgery and whether they influence visual performance. For this, we compute a point-to-point correction on the cornea while assuming a non-linear (including a quadratic term) fit for depth ablation. Post-surgical equations for refractive parameters using a non-linear fit show significant differences with respect...

Fokker-Planck equation in mirror research

International Nuclear Information System (INIS)

Post, R.F.

1983-01-01

Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror

The Gravity of Photons and the Necessary Rectification of Einstein Equation

Directory of Open Access Journals (Sweden)

Lo C. Y.

2006-01-01

Full Text Available It is pointed out that Special Relativity together with the principle of causality implies that the gravity of an electromagnetic wave is an accompanying gravitational wave propagating with the same speed. Since a gravitational wave carries energy-momentum, this accompanying wave would make the energy-stress tensor of the light to be different from the electromagnetic energy-stress tensor, and thus can produce a geodesic equation for the photons. Moreover, it is found that the appropriate Einstein equation must additionally have the photonic energy-stress tensor with the antigravity coupling in the source term. This would correct that, in disagreement with the calculations for the bending of light, existing solutions of gravity for an electromagnetic wave, is unbounded. This rectification is confirmed by calculating the gravity of electromagnetic plane-waves. The gravity of an electromagnetic wave is indeed an accompanying gravitational wave. Moreover, these calculations show the first time that Special Relativity and General Relativity are compatible because the physical meaning of coordinates has been clarified. The success of this rectification makes General Relativity standing out further among theories of gravity.

48 CFR 1501.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 1501.403 Section 1501.403 Federal Acquisition Regulations System ENVIRONMENTAL PROTECTION AGENCY GENERAL GENERAL Deviations 1501.403 Individual deviations. Requests for individual deviations from the FAR and the...

POSITIVE SOLUTIONS TO TWO TYPES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.

48 CFR 2401.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2401... DEVELOPMENT GENERAL FEDERAL ACQUISITION REGULATION SYSTEM Deviations 2401.403 Individual deviations. In individual cases, proposed deviations from the FAR or HUDAR shall be submitted to the Senior Procurement...

INDICATIVE MODEL OF DEVIATIONS IN PROJECT

Directory of Open Access Journals (Sweden)

Олена Борисівна ДАНЧЕНКО

2016-02-01

Full Text Available The article shows the process of constructing the project deviations indicator model. It based on a conceptual model of project deviations integrated management (PDIM. During the project different causes (such as risks, changes, problems, crises, conflicts, stress lead to deviations of integrated project indicators - time, cost, quality, and content. For a more detailed definition of where in the project deviations occur and how they are dangerous for the whole project, it needs to develop an indicative model of project deviations. It allows identifying the most dangerous deviations that require PDIM. As a basis for evaluation of project's success has been taken famous model IPMA Delta. During the evaluation, IPMA Delta estimated project management competence of organization in three modules: I-Module ("Individuals" - a self-assessment personnel, P-module ("Projects" - self-assessment of projects and/or programs, and O-module ("Organization" - used to conduct interviews with selected people during auditing company. In the process of building an indicative model of deviations in the project, the first step is the assessment of project management in the organization by IPMA Delta. In the future, built cognitive map and matrix of system interconnections of the project, which conducted simulations and built a scale of deviations for the selected project. They determined a size and place of deviations. To identify the detailed causes of deviations in the project management has been proposed to use the extended system of indicators, which is based on indicators of project management model Project Excellence. The proposed indicative model of deviations in projects allows to estimate the size of variation and more accurately identify the place of negative deviations in the project and provides the project manager information for operational decision making for the management of deviations in the implementation of the project

Large deviations and mixing for dissipative PDEs with unbounded random kicks

Science.gov (United States)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

48 CFR 1301.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations... DEPARTMENT OF COMMERCE ACQUISITION REGULATIONS SYSTEM Deviations From the FAR 1301.403 Individual deviations. The designee authorized to approve individual deviations from the FAR is set forth in CAM 1301.70. ...

48 CFR 301.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 301... ACQUISITION REGULATION SYSTEM Deviations From the FAR 301.403 Individual deviations. Contracting activities shall prepare requests for individual deviations to either the FAR or HHSAR in accordance with 301.470. ...

48 CFR 1201.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations... FEDERAL ACQUISITION REGULATIONS SYSTEM 70-Deviations From the FAR and TAR 1201.403 Individual deviations... Executive Service (SES) official or that of a Flag Officer, may authorize individual deviations (unless (FAR...

48 CFR 501.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 501... Individual deviations. (a) An individual deviation affects only one contract action. (1) The Head of the Contracting Activity (HCA) must approve an individual deviation to the FAR. The authority to grant an...

48 CFR 401.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 401... AGRICULTURE ACQUISITION REGULATION SYSTEM Deviations From the FAR and AGAR 401.403 Individual deviations. In individual cases, deviations from either the FAR or the AGAR will be authorized only when essential to effect...

48 CFR 2801.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2801... OF JUSTICE ACQUISITION REGULATIONS SYSTEM Deviations From the FAR and JAR 2801.403 Individual deviations. Individual deviations from the FAR or the JAR shall be approved by the head of the contracting...

Visualizing the Sample Standard Deviation

Science.gov (United States)

Sarkar, Jyotirmoy; Rashid, Mamunur

2017-01-01

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

Energy Technology Data Exchange (ETDEWEB)

Leitner, David M., E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557 (United States); Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Buchenberg, Sebastian; Brettel, Paul [Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany); Stock, Gerhard, E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany)

2015-02-21

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

International Nuclear Information System (INIS)

Leitner, David M.; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard

2015-01-01

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water

Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration

Directory of Open Access Journals (Sweden)

Petarpa Boonserm

2018-05-01

Full Text Available Geodesics (by definition have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates.

Light rays and the tidal gravitational pendulum

Science.gov (United States)

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

Complex Monge–Ampère equations and geodesics in the space of Kähler metrics

CERN Document Server

2012-01-01

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruc...

Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

Science.gov (United States)

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

Calculation of NARM's Equilibrium with Peng-Robinson Equation of State

Institute of Scientific and Technical Information of China (English)

LI Tingxun; GUO Kaihua; WANG Ruzhu; FAN Shuanshi

2001-01-01

The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR)equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with coreaction coefficient kij, the discrepancies of liquid molar volume data for R22+Rl14 and R22+R142b using PR equation are 7.7% and 8.1% , respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+Rl14 and R22+R142b.

Large deviation tail estimates and related limit laws for stochastic fixed point equations

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.

2013-01-01

We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE) of the form $V \\stackrel{d}{=} A\\max\\{V, D\\}+B$, where $(A, B, D) \\in (0, \\infty)\\times {\\mathbb R}^2$, for both the stationary and explosive cases. In the stationary case (when ${\\bf E} [\\log \\: A......] explosive case (when ${\\bf E} [\\log \\: A] > 0)$, we establish a central limit theorem for the forward recursion generated by the SFPE, namely the process $V_n= A_n \\max\\{V_{n-1...

The reinterpretation of standard deviation concept

OpenAIRE

Ye, Xiaoming

2017-01-01

Existing mathematical theory interprets the concept of standard deviation as the dispersion degree. Therefore, in measurement theory, both uncertainty concept and precision concept, which are expressed with standard deviation or times standard deviation, are also defined as the dispersion of measurement result, so that the concept logic is tangled. Through comparative analysis of the standard deviation concept and re-interpreting the measurement error evaluation principle, this paper points o...

Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction

International Nuclear Information System (INIS)

Peletier, Mark A.; Redig, Frank; Vafayi, Kiamars

2014-01-01

We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter m (BEP(m)), a Generalized Brownian Energy Process, and the Kipnis-Marchioro-Presutti (KMP) process. The hydrodynamic limit of each of these three processes is a parabolic equation, the linear heat equation in the case of the BEP(m) and the KMP, and a nonlinear heat equation for the Generalized Brownian Energy Process with parameter a (GBEP(a)). We prove the hydrodynamic limit rigorously for the BEP(m), and give a formal derivation for the GBEP(a). We then formally derive the pathwise large-deviation rate functional for the empirical measure of the three processes. These rate functionals imply gradient-flow structures for the limiting linear and nonlinear heat equations. We contrast these gradient-flow structures with those for processes describing the diffusion of mass, most importantly the class of Wasserstein gradient-flow systems. The linear and nonlinear heat-equation gradient-flow structures are each driven by entropy terms of the form −log ρ; they involve dissipation or mobility terms of order ρ 2 for the linear heat equation, and a nonlinear function of ρ for the nonlinear heat equation

Full-sky formulae for weak lensing power spectra from total angular momentum method

International Nuclear Information System (INIS)

Yamauchi, Daisuke; Taruya, Atsushi; Namikawa, Toshiya

2013-01-01

We systematically derive full-sky formulae for the weak lensing power spectra generated by scalar, vector and tensor perturbations from the total angular momentum (TAM) method. Based on both the geodesic and geodesic deviation equations, we first give the gauge-invariant expressions for the deflection angle and Jacobi map as observables of the CMB lensing and cosmic shear experiments. We then apply the TAM method, originally developed in the theoretical studies of CMB, to a systematic derivation of the angular power spectra. The TAM representation, which characterizes the total angular dependence of the spatial modes projected along a line-of-sight, can carry all the information of the lensing modes generated by scalar, vector, and tensor metric perturbations. This greatly simplifies the calculation, and we present a complete set of the full-sky formulae for angular power spectra in both the E-/B-mode cosmic shear and gradient-/curl-mode lensing potential of deflection angle. Based on the formulae, we give illustrative examples of non-vanishing B-mode cosmic shear and curl-mode of deflection angle in the presence of the vector and tensor perturbations, and explicitly compute the power spectra

48 CFR 3401.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Individual deviations. 3401.403 Section 3401.403 Federal Acquisition Regulations System DEPARTMENT OF EDUCATION ACQUISITION REGULATION GENERAL ED ACQUISITION REGULATION SYSTEM Deviations 3401.403 Individual deviations. An individual...

48 CFR 1.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Individual deviations. 1.403 Section 1.403 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION GENERAL FEDERAL ACQUISITION REGULATIONS SYSTEM Deviations from the FAR 1.403 Individual deviations. Individual...

48 CFR 2501.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 2501.403 Section 2501.403 Federal Acquisition Regulations System NATIONAL SCIENCE FOUNDATION GENERAL FEDERAL ACQUISITION REGULATIONS SYSTEM Deviations From the FAR 2501.403 Individual deviations. Individual...

Fidelity deviation in quantum teleportation

OpenAIRE

Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir

2018-01-01

We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel---we here consider the so-called Werner channel. To characterize our resu...

48 CFR 601.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Individual deviations. 601.403 Section 601.403 Federal Acquisition Regulations System DEPARTMENT OF STATE GENERAL DEPARTMENT OF STATE ACQUISITION REGULATIONS SYSTEM Deviations from the FAR 601.403 Individual deviations. The...

48 CFR 201.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 3 2010-10-01 2010-10-01 false Individual deviations. 201.403 Section 201.403 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM... Individual deviations. (1) Individual deviations, except those described in 201.402(1) and paragraph (2) of...

48 CFR 3001.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Individual deviations... from the FAR and HSAR 3001.403 Individual deviations. Unless precluded by law, executive order, or other regulation, the HCA is authorized to approve individual deviation (except with respect to (FAR) 48...

48 CFR 1901.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Individual deviations. 1901.403 Section 1901.403 Federal Acquisition Regulations System BROADCASTING BOARD OF GOVERNORS GENERAL... Individual deviations. Deviations from the IAAR or the FAR in individual cases shall be authorized by the...

Deviating From the Benchmarks

DEFF Research Database (Denmark)

Rocha, Vera; Van Praag, Mirjam; Carneiro, Anabela

This paper studies three related questions: To what extent otherwise similar startups employ different quantities and qualities of human capital at the moment of entry? How persistent are initial human capital choices over time? And how does deviating from human capital benchmarks influence firm......, founders human capital, and the ownership structure of startups (solo entrepreneurs versus entrepreneurial teams). We then study the survival implications of exogenous deviations from these benchmarks, based on spline models for survival data. Our results indicate that (especially negative) deviations from...... the benchmark can be substantial, are persistent over time, and hinder the survival of firms. The implications may, however, vary according to the sector and the ownership structure at entry. Given the stickiness of initial choices, wrong human capital decisions at entry turn out to be a close to irreversible...

Boundary driven Kawasaki process with long-range interaction: dynamical large deviations and steady states

International Nuclear Information System (INIS)

Mourragui, Mustapha; Orlandi, Enza

2013-01-01

A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long-range potential parametrized by β⩾0 and evolve according to an exclusion rule. It is shown that the empirical particle density under the diffusive scaling solves a quasilinear integro-differential evolution equation with Dirichlet boundary conditions. The associated dynamical large deviation principle is proved. Furthermore, when β is small enough, it is also demonstrated that the empirical particle density obeys a law of large numbers with respect to the stationary measures (hydrostatic). The macroscopic particle density solves a non-local, stationary, transport equation. (paper)

Computer generation of random deviates

International Nuclear Information System (INIS)

Cormack, John

1991-01-01

The need for random deviates arises in many scientific applications. In medical physics, Monte Carlo simulations have been used in radiology, radiation therapy and nuclear medicine. Specific instances include the modelling of x-ray scattering processes and the addition of random noise to images or curves in order to assess the effects of various processing procedures. Reliable sources of random deviates with statistical properties indistinguishable from true random deviates are a fundamental necessity for such tasks. This paper provides a review of computer algorithms which can be used to generate uniform random deviates and other distributions of interest to medical physicists, along with a few caveats relating to various problems and pitfalls which can occur. Source code listings for the generators discussed (in FORTRAN, Turbo-PASCAL and Data General ASSEMBLER) are available on request from the authors. 27 refs., 3 tabs., 5 figs

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

International Nuclear Information System (INIS)

Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi

2015-01-01

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. 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 3 , whereas it was 1719 cm 3 for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. 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

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

Science.gov (United States)

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

Coupling of linearized gravity to nonrelativistic test particles: Dynamics in the general laboratory frame

International Nuclear Information System (INIS)

Speliotopoulos, A.D.; Chiao, Raymond Y.

2004-01-01

The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of the couplings and the known results of tidal effects on test particles according to classical general relativity are pointed out. As a step towards resolving these inconsistencies, a general laboratory frame fixed on the worldline of an observer is constructed. In this frame, the dynamics of nonrelativistic test particles in the linearized gravity limit is studied, and their Hamiltonian dynamics is derived. It is shown that for stationary metrics this Hamiltonian reduces to the usual Hamiltonian for nonrelativistic particles undergoing geodesic motion. For nonstationary metrics with long-wavelength gravitational waves present (GWs), it reduces to the Hamiltonian for a nonrelativistic particle undergoing geodesic deviation motion. Arbitrary-wavelength GWs couple to the test particle through a vector-potential-like field N a , the net result of the tidal forces that the GW induces in the system, namely, a local velocity field on the system induced by tidal effects, as seen by an observer in the general laboratory frame. Effective electric and magnetic fields, which are related to the electric and magnetic parts of the Weyl tensor, are constructed from N a that obey equations of the same form as Maxwell's equations. A gedankin gravitational Aharonov-Bohm-type experiment using N a to measure the interference of quantum test particles is presented

Chaos in Kundt Type-III Spacetimes

International Nuclear Information System (INIS)

Sakalli, I.; Halilsoy, M.

2011-01-01

We consider geodesic motion in a particular Kundt type-III spacetime in which the Einstein-Yang-Mills equations admit the solutions. On a particular surface as constraint, we project the geodesics into the (x, y) plane and treat the problem as a two-dimensional one. Our numerical study shows that chaotic behavior emerges under reasonable conditions. (general)

Surgical Success Rates for Horizontal Concomitant Deviations According to the Type and Degree of Deviation

Directory of Open Access Journals (Sweden)

İhsan Çaça

2004-01-01

Full Text Available We evaluated the correlation with success rates and deviation type and degree inhorizontal concomitant deviations. 104 horizontal concomitan strabismus cases whowere operated in our clinic between January 1994 – December 2000 were included in thestudy. 56 cases undergone recession-resection procedure in the same eye 19 cases twomuscle recession and one muscle resection, 20 cases two muscle recession, 9 cases onlyone muscle recession. 10 ± prism diopter deviation in postoperative sixth monthexamination was accepted as surgical success.Surgical success rate was 90% and 89.3% in the cases with deviation angle of 15-30and 31-50 prism diopter respectively. Success rate was 78.9% if the angle was more than50 prism diopter. According to strabismus type when surgical success rate examined; inalternan esotropia 88.33%, in alternan exotropia 84.6%, in monocular esotropia 88%and in monocular exotropia 83.3% success was fixed. Statistically significant differencewas not found between strabismus type and surgical success rate. The binocular visiongaining rate was found as 51.8% after the treatment of cases.In strabismus surgery, preoperative deviation angle was found to be an effectivefactor on the success rate.

14 CFR 21.609 - Approval for deviation.

Science.gov (United States)

2010-01-01

... deviation. (a) Each manufacturer who requests approval to deviate from any performance standard of a TSO shall show that the standards from which a deviation is requested are compensated for by factors or... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Approval for deviation. 21.609 Section 21...

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

Science.gov (United States)

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Entanglement transitions induced by large deviations

Science.gov (United States)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Ambitwistor strings and the scattering equations at one loop

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim; Casali, Eduardo; Skinner, David [Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2014-04-15

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo-He-Yuan formulæ for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulæ in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang-Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non-separating and separating degenerations.

22 CFR 226.4 - Deviations.

Science.gov (United States)

2010-04-01

... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Deviations. 226.4 Section 226.4 Foreign Relations AGENCY FOR INTERNATIONAL DEVELOPMENT ADMINISTRATION OF ASSISTANCE AWARDS TO U.S. NON-GOVERNMENTAL ORGANIZATIONS General § 226.4 Deviations. The Office of Management and Budget (OMB) may grant exceptions for...

The Standard Deviation of Launch Vehicle Environments

Science.gov (United States)

Yunis, Isam

2005-01-01

Statistical analysis is used in the development of the launch vehicle environments of acoustics, vibrations, and shock. The standard deviation of these environments is critical to accurate statistical extrema. However, often very little data exists to define the standard deviation and it is better to use a typical standard deviation than one derived from a few measurements. This paper uses Space Shuttle and expendable launch vehicle flight data to define a typical standard deviation for acoustics and vibrations. The results suggest that 3dB is a conservative and reasonable standard deviation for the source environment and the payload environment.

New experimental proposals for testing Dirac equation

International Nuclear Information System (INIS)

Camacho, Abel; Macias, Alfredo

2004-01-01

The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by-product of this quest the possible modifications that some field equations, for instance, the motion equation of spin-1/2-particles, have already been considered. In the present Letter a modified Dirac equation, whose extra term embraces a second-order time derivative, is taken as mainstay, and three different experimental proposals to detect it are put forward. The novelty in these ideas is that two of them do not fall within the extant approaches in this context, to wit, red-shift, atomic interferometry, or Hughes-Drever type-like experiments

Deviations from thermal equilibrium in plasmas

International Nuclear Information System (INIS)

Burm, K.T.A.L.

2004-01-01

A plasma system in local thermal equilibrium can usually be described with only two parameters. To describe deviations from equilibrium two extra parameters are needed. However, it will be shown that deviations from temperature equilibrium and deviations from Saha equilibrium depend on one another. As a result, non-equilibrium plasmas can be described with three parameters. This reduction in parameter space will ease the plasma describing effort enormously

Deviating measurements in radiation protection. Legal assessment of deviations in radiation protection measurements

International Nuclear Information System (INIS)

Hoegl, A.

1996-01-01

This study investigates how, from a legal point of view, deviations in radiation protection measurements should be treated in comparisons between measured results and limits stipulated by nuclear legislation or goods transport regulations. A case-by-case distinction is proposed which is based on the legal concequences of the respective measurement. Commentaries on nuclear law contain no references to the legal assessment of deviating measurements in radiation protection. The examples quoted in legal commentaries on civil and criminal proceedings of the way in which errors made in measurements for speed control and determinations of the alcohol content in the blood are to be taken into account, and a commentary on ozone legislation, are examined for analogies with radiation protection measurements. Leading cases in the nuclear field are evaluated in the light of the requirements applying in case of deviations in measurements. The final section summarizes the most important findings and conclusions. (orig.) [de

The full integration of black hole solutions to symmetric supergravity theories

Energy Technology Data Exchange (ETDEWEB)

Chemissany, W., E-mail: wissam.chemissany@uleth.c [University of Lethbridge, Physics Department, Lethbridge Alberta, T1K 3M4 (Canada); Rosseel, J., E-mail: rosseel@to.infn.i [Dipartimento di Fisica Teorica, Universita di Torino and INFN-Sezione di Torino, Via P. Giuria 1, I-10125 Torino (Italy); Trigiante, M., E-mail: mario.trigiante@polito.i [Dipartimento di Fisica Politecnico di Torino, C.so Duca degli Abruzzi, 24, I-10129 Torino (Italy); Van Riet, T., E-mail: thomas.vanriet@fysast.uu.s [Institutionen foer Fysik och Astronomi, Box 803, SE-751 08 Uppsala (Sweden)

2010-05-11

We prove that all stationary and spherical symmetric black hole solutions to theories with symmetric target spaces are integrable and we provide an explicit integration method. This exact integration is based on the description of black hole solutions as geodesic curves on the moduli space of the theory when reduced over the time-like direction. These geodesic equations of motion can be rewritten as a specific Lax pair equation for which mathematicians have provided the integration algorithms when the initial conditions are described by a diagonalizable Lax matrix. On the other hand, solutions described by nilpotent Lax matrices, which originate from extremal regular (small) D=4 black holes can be obtained as suitable limits of solutions obtained in the diagonalizable case, as we show on the generating geodesic (i.e. most general geodesic modulo global symmetries of the D=3 model) corresponding to regular (and small) D=4 black holes. As a byproduct of our analysis we give the explicit form of the 'Wick rotation' connecting the orbits of BPS and non-BPS solutions in maximally supersymmetric supergravity and its STU truncation.

Geodesically complete BTZ-type solutions of 2  +  1 Born–Infeld gravity

International Nuclear Information System (INIS)

Bazeia, D; Losano, L; Olmo, Gonzalo J; Rubiera-Garcia, D

2017-01-01

We study Born–Infeld gravity coupled to a static, non-rotating electric field in 2  +  1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom. (paper)

9 CFR 318.308 - Deviations in processing.

Science.gov (United States)

2010-01-01

...) Deviations in processing (or process deviations) must be handled according to: (1)(i) A HACCP plan for canned...) of this section. (c) [Reserved] (d) Procedures for handling process deviations where the HACCP plan... accordance with the following procedures: (a) Emergency stops. (1) When retort jams or breakdowns occur...

ALLOMETRIC EQUATIONS FOR ESTIMATING ABOVEGROUND BIOMASS IN PAPUA TROPICAL FOREST

Directory of Open Access Journals (Sweden)

Sandhi Imam Maulana

2014-10-01

Full Text Available Allometric equations can be used to estimate biomass and carbon stock of  the forest. However, so far the allometric equations for commercial species in Papua tropical forests have not been appropriately developed. In this research, allometric equations are presented based on the genera of  commercial species. Few equations have been developed for the commercial species of  Intsia, Pometia, Palaquium and Vatica genera and an equation of  a mix of  these genera. The number of  trees sampled in this research was 49, with diameters (1.30 m above-ground or above buttresses ranging from 5 to 40 cm. Destructive sampling was used to collect the samples where Diameter at Breast Height (DBH and Wood Density (WD were used as predictors for dry weight of  Total Above-Ground Biomass (TAGB. Model comparison and selection were based on the values of  F-statistics, R-sq, R-sq (adj, and average deviation. Based on these statistical indicators, the most suitable model for Intsia, Pometia, Palaquium and Vatica genera respectively are Log(TAGB = -0.76 + 2.51Log(DBH, Log(TAGB = -0.84 + 2.57Log(DBH, Log(TAGB = -1.52 + 2.96Log(DBH, and Log(TAGB = -0.09 + 2.08Log(DBH. Additional explanatory variables such as Commercial Bole Height (CBH do not really increase the indicators’ goodness of  fit for the equation. An alternative model to incorporate wood density should  be considered for estimating the above-ground biomass for mixed genera. Comparing the presented mixed-genera equation; Log(TAGB = 0.205 + 2.08Log(DBH + 1.75Log(WD, R-sq: 97.0%, R-sq (adj: 96.9%, F statistics 750.67, average deviation: 3.5%; to previously published datashows that this local species specific equation differs substantially from previously published equations and this site-specific equation is  considered to give a better estimation of  biomass.

Density, viscosity, isothermal (vapour + liquid) equilibrium, excess molar volume, viscosity deviation, and their correlations for chloroform + methyl isobutyl ketone binary system

International Nuclear Information System (INIS)

Clara, Rene A.; Gomez Marigliano, Ana C.; Solimo, Horacio N.

2007-01-01

Density and viscosity measurements for pure chloroform and methyl isobutyl ketone at T = (283.15, 293.15, 303.15, and 313.15) K as well as for the binary system {x 1 chloroform + (1 - x 1 ) methyl isobutyl ketone} at the same temperatures were made over the whole concentration range. The experimental results were fitted to empirical equations, which permit the calculation of these properties over the whole concentration and temperature ranges studied. Data of the binary mixture were further used to calculate the excess molar volume and viscosity deviation. The (vapour + liquid) equilibrium (VLE) at T = 303.15 K for this binary system was also measured in order to calculate the activity coefficients and the excess molar Gibbs energy. This binary system shows no azeotrope and negative deviations from ideal behaviour. The excess or deviation properties were fitted to the Redlich-Kister polynomial relation to obtain their coefficients and standard deviations

Field lines of gravity, their curvature and torsion, the Lagrange and the Hamilton equations of the plumbline

Directory of Open Access Journals (Sweden)

E. W. Grafarend

1997-06-01

Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.

Beyond the geodesic approximation: Conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole

International Nuclear Information System (INIS)

Barack, Leor; Sago, Norichika

2011-01-01

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass μ is much smaller than the black hole mass M, and explore post-geodesic corrections of O(μ/M). Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the O(μ/M) conservative correction to the periastron advance of the orbit, as a function of the (gauge-dependent) semilatus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit ''redshift'' invariant. We compute the O(μ/M) conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak-field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

Weight of fitness deviation governs strict physical chaos in replicator dynamics

Science.gov (United States)

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Introducing the Mean Absolute Deviation "Effect" Size

Science.gov (United States)

Gorard, Stephen

2015-01-01

This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is easier to use and understand, and more tolerant of extreme…

Variability of glomerular filtration rate estimation equations in elderly Chinese patients with chronic kidney disease

Directory of Open Access Journals (Sweden)

Liu X

2012-10-01

Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the

Fidelity deviation in quantum teleportation

Science.gov (United States)

Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir

2018-04-01

We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.

Large deviations for noninteracting infinite-particle systems

International Nuclear Information System (INIS)

Donsker, M.D.; Varadhan, S.R.S.

1987-01-01

A large deviation property is established for noninteracting infinite particle systems. Previous large deviation results obtained by the authors involved a single I-function because the cases treated always involved a unique invariant measure for the process. In the context of this paper there is an infinite family of invariant measures and a corresponding infinite family of I-functions governing the large deviations

Sharp bounds for periodic solutions of Lipschitzian differential equations

International Nuclear Information System (INIS)

Zevin, A A

2009-01-01

A general system of Lipschitzian differential equations, containing simultaneously terms without delay and with arbitrary constant and time-varying delays, is considered. For the autonomous case, a lower bound for the period of nonconstant periodic solutions, expressed in the respective supremum Lipschitz constants, is found. For nonautonomous periodic equations, explicit upper bounds for the amplitudes and maximum derivatives of periodic solutions are obtained. For all n ≥ 2, the bounds do not depend on n and, in general, are different from that for n = 1. All the bounds are sharp; they are attained in linear differential equations with piece-wise constant deviating arguments. A relation between the obtained bounds and the sharp bounds in other metrics is established

48 CFR 1401.403 - Individual deviations.

Science.gov (United States)

2010-10-01

... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations. 1401.403 Section 1401.403 Federal Acquisition Regulations System DEPARTMENT OF THE INTERIOR GENERAL DEPARTMENT OF THE INTERIOR ACQUISITION REGULATION SYSTEM Deviations from the FAR and DIAR 1401.403 Individual...

TERMINOLOGY MANAGEMENT FRAMEWORK DEVIATIONS IN PROJECTS

Directory of Open Access Journals (Sweden)

Олена Борисівна ДАНЧЕНКО

2015-05-01

Full Text Available The article reviews new approaches to managing projects deviations (risks, changes, problems. By offering integrated control these parameters of the project and by analogy with medical terminological systems building a new system for managing terminological variations in the projects. With an improved method of triads system definitions are analyzed medical terms that make up terminological basis. Using the method of analogy proposed new definitions for managing deviations in projects. By using triad integrity built a new system triad in project management, which will subsequently also analogous to develop a new methodology of deviations in projects.

41 CFR 115-1.110 - Deviations.

Science.gov (United States)

2010-07-01

... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviations. 115-1.110 Section 115-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) ENVIRONMENTAL PROTECTION AGENCY 1-INTRODUCTION 1.1-Regulation System § 115-1.110 Deviations...

Excess molar volumes and deviation in viscosities of binary liquid mixtures of acrylic esters with hexane-1-ol at 303.15 and 313.15 K

Directory of Open Access Journals (Sweden)

Sujata S. Patil

2014-12-01

Full Text Available Densities and viscosities for the four binary liquid mixtures of methyl acrylate, ethyl acrylate, butyl acrylate and methyl methacrylate with hexane-1-ol at temperatures 303.15 and 313.15 K and at atmospheric pressure were measured over the entire composition range. These values were used to calculate excess molar volumes and deviation in viscosities which were fitted to Redlich–Kister polynomial equation. Recently proposed Jouyban Acree model was also used to correlate the experimental values of density and viscosity. The mixture viscosities were correlated by several semi-empirical approaches like Hind, Choudhary–Katti, Grunberg–Nissan, Tamura and Kurata, McAllister three and four body model equations. A graphical representation of excess molar volumes and deviation in isentropic compressibility shows positive nature whereas deviation in viscosity shows negative nature at both temperatures for all four binary liquid mixtures. Positive values of excess molar volumes show that volume expansion is taking place causing rupture of H-bonds in self associated alcohols. The results were discussed in terms of molecular interactions prevailing in the mixtures.

41 CFR 105-1.110 - Deviation.

Science.gov (United States)

2010-07-01

... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviation. 105-1.110 Section 105-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.110 Deviation. (a...

41 CFR 101-1.110 - Deviation.

Science.gov (United States)

2010-07-01

... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Deviation. 101-1.110 Section 101-1.110 Public Contracts and Property Management Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS GENERAL 1-INTRODUCTION 1.1-Regulation System § 101-1.110 Deviation...

Deviations from the Gutenberg–Richter law on account of a random distribution of block sizes

Energy Technology Data Exchange (ETDEWEB)

Sibiryakov, B. P., E-mail: sibiryakovbp@ipgg.sbras.ru [Trofimuk Institute of Oil and Gas Geology and Geophysics SB RAS, Novosibirsk, 630090 (Russian Federation); Novosibirsk State University, Novosibirsk, 630090 (Russian Federation)

2015-10-27

This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations are nonautomatically transformed into differential ones. It is impossible to consider an infinitesimal volume of a body, to which the major conservation laws could be applied, because the minimum representative volume of the body must contain at least a few elementary microstructures. The corresponding equations of motion are equations of infinite order, solutions of which include, along with usual sound waves, unusual waves with abnormally low velocities without a lower limit. It is shown that in such media weak perturbations can increase or decrease outside the limits. The number of complex roots of the corresponding dispersion equation, which can be interpreted as the number of unstable solutions, depends on the specific surface of cracks and is an almost linear dependence on a logarithmic scale, as in the seismological Gutenberg–Richter law. If the distance between one pore (crack) to another one is a random value with some distribution, we must write another dispersion equation and examine different scenarios depending on the statistical characteristics of the random distribution. In this case, there are sufficient deviations from the Gutenberg–Richter law and this theoretical result corresponds to some field and laboratory observations.

On the equivalence of inertial and gravitational mass of extended bodies in metric theories of gravity

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Chugreev, Yu.V.

1985-01-01

It is shown that in any metric theory of gravitation passessing conservation laws for energy-momentum of the substance and gravitational field taken together, the motion of centre of extended body mass occurs not according to the geodesic Riemann space-time. The centre of mass of the extended body during its motion about the orbit makes a vibrational movement in relation to supporting geodesic. Application of obtained general formulas to the Sun-Earth system and the use of experimental results on the Moon location with the regard of other experiments has shown with high accuracy of 10 -10 that the relation of gravitational passive Earth mass to its inert mass does not equal to 1 differing from it about 10 -8 . The Earth at its orbital motion makes a vibrational movement in relation to supporting geodesic with a period of 1 hour and amplitude not less than 10 -2 sm. the deviation of the Earth mass center motion from geodesic movement can be found in a corresponding experiment having a postnewton accuracy degree

A strategy to objectively evaluate the necessity of correcting detected target deviations in image guided radiotherapy

International Nuclear Information System (INIS)

Yue, Ning J.; Kim, Sung; Jabbour, Salma; Narra, Venkat; Haffty, Bruce G.

2007-01-01

verification and were used to determine potential target deviations. To derive the detected CTV geometry from the planning CTV based on the locations of the gold markers, the CTV was approximated with an elastic semirigid body model. The derived CTV geometry and shape were confirmed with CBCT imaging. The evaluation results and the related mathematical equations and computational algorithm are presented. It is concluded that the proposed strategy is potentially useful in establishing objective criteria for the necessity of correction of the target deviations

SU-F-R-05: Multidimensional Imaging Radiomics-Geodesics: A Novel Manifold Learning Based Automatic Feature Extraction Method for Diagnostic Prediction in Multiparametric Imaging

Energy Technology Data Exchange (ETDEWEB)

Parekh, V [The Johns Hopkins University, Computer Science. Baltimore, MD (United States); Jacobs, MA [The Johns Hopkins University School of Medicine, Dept of Radiology and Oncology. Baltimore, MD (United States)

2016-06-15

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) 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 MIRa

SU-F-R-05: Multidimensional Imaging Radiomics-Geodesics: A Novel Manifold Learning Based Automatic Feature Extraction Method for Diagnostic Prediction in Multiparametric Imaging

International Nuclear Information System (INIS)

Parekh, V; Jacobs, MA

2016-01-01

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) 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 MIRa

On the small time asymptotics of 3D stochastic primitive equations

OpenAIRE

Dong, Zhao; Zhang, Rangrang

2017-01-01

In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.

Comparing Standard Deviation Effects across Contexts

Science.gov (United States)

Ost, Ben; Gangopadhyaya, Anuj; Schiman, Jeffrey C.

2017-01-01

Studies using tests scores as the dependent variable often report point estimates in student standard deviation units. We note that a standard deviation is not a standard unit of measurement since the distribution of test scores can vary across contexts. As such, researchers should be cautious when interpreting differences in the numerical size of…

Transport Coefficients from Large Deviation Functions

Directory of Open Access Journals (Sweden)

Chloe Ya Gao

2017-10-01

Full Text Available We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green–Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.

Transport Coefficients from Large Deviation Functions

Science.gov (United States)

Gao, Chloe; Limmer, David

2017-10-01

We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.

Tidal stresses and energy gaps in microstate geometries

Science.gov (United States)

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.

41 CFR 109-1.110-50 - Deviation procedures.

Science.gov (United States)

2010-07-01

... best interest of the Government; (3) If applicable, the name of the contractor and identification of... background information which will contribute to a full understanding of the desired deviation. (b)(1... authorized to grant deviations to the DOE-PMR. (d) Requests for deviations from the FPMR will be coordinated...

Approaching nanometre accuracy in measurement of the profile deviation of a large plane mirror

International Nuclear Information System (INIS)

Müller, Andreas; Hofmann, Norbert; Manske, Eberhard

2012-01-01

The interferometric nanoprofilometer (INP), developed at the Institute of Process Measurement and Sensor Technology at the Ilmenau University of Technology, is a precision device for measuring the profile deviations of plane mirrors with a profile length of up to 250 mm at the nanometre scale. As its expanded uncertainty of U(l) = 7.8 nm at a confidence level of p = 95% (k = 2) was mainly influenced by the uncertainty of the straightness standard (3.6 nm) and the uncertainty caused by the signal and demodulation errors of the interferometer signals (1.2 nm), these two sources of uncertainty have been the subject of recent analyses and modifications. To measure the profile deviation of the standard mirror we performed a classic three-flat test using the INP. The three-flat test consists of a combination of measurements between three different test flats. The shape deviations of the three flats can then be determined by applying a least-squares solution of the resulting equation system. The results of this three-flat test showed surprisingly good consistency, enabling us to correct this systematic error in profile deviation measurements and reducing the uncertainty component of the standard mirror to 0.4 nm. Another area of research is the signal and demodulation error arising during the interpretation of the interferometer signals. In the case of the interferometric nanoprofilometer, the special challenge is that the maximum path length differences are too small during the scan of the entire profile deviation over perfectly aligned 250 mm long mirrors for proper interpolation and correction since they do not yet cover even half of an interference fringe. By applying a simple method of weighting to the interferometer data the common ellipse fitting could be performed successfully and the demodulation error was greatly reduced. The remaining uncertainty component is less than 0.5 nm. In summary we were successful in greatly reducing two major systematic errors. The

Assessing factors that influence deviations between measured and calculated reference evapotranspiration

Science.gov (United States)

Rodny, Marek; Nolz, Reinhard

2017-04-01

Evapotranspiration (ET) is a fundamental component of the hydrological cycle, but challenging to be quantified. Lysimeter facilities, for example, can be installed and operated to determine ET, but they are costly and represent only point measurements. Therefore, lysimeter data are traditionally used to develop, calibrate, and validate models that allow calculating reference evapotranspiration (ET0) based on meteorological data, which can be measured more easily. The standardized form of the well-known FAO Penman-Monteith equation (ASCE-EWRI) is recommended as a standard procedure for estimating ET0 and subsequently plant water requirements. Applied and validated under different climatic conditions, the Penman-Monteith equation is generally known to deliver proper results. On the other hand, several studies documented deviations between measured and calculated ET0 depending on environmental conditions. Potential reasons are, for example, differing or varying surface characteristics of the lysimeter and the location where the weather instruments are placed. Advection of sensible heat (transport of dry and hot air from surrounding areas) might be another reason for deviating ET-values. However, elaborating causal processes is complex and requires comprehensive data of high quality and specific analysis techniques. In order to assess influencing factors, we correlated differences between measured and calculated ET0 with pre-selected meteorological parameters and related system parameters. Basic data were hourly ET0-values from a weighing lysimeter (ET0_lys) with a surface area of 2.85 m2 (reference crop: frequently irrigated grass), weather data (air and soil temperature, relative humidity, air pressure, wind velocity, and solar radiation), and soil water content in different depths. ET0_ref was calculated in hourly time steps according to the standardized procedure after ASCE-EWRI (2005). Deviations between both datasets were calculated as ET0_lys-ET0_ref and

Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations

Directory of Open Access Journals (Sweden)

Shaikhet Leonid

2008-01-01

Full Text Available It is supposed that the fractional difference equation , has an equilibrium point and is exposed to additive stochastic perturbations type of that are directly proportional to the deviation of the system state from the equilibrium point . It is shown that known results in the theory of stability of stochastic difference equations that were obtained via V. Kolmanovskii and L. Shaikhet general method of Lyapunov functionals construction can be successfully used for getting of sufficient conditions for stability in probability of equilibrium points of the considered stochastic fractional difference equation. Numerous graphical illustrations of stability regions and trajectories of solutions are plotted.

The large deviation approach to statistical mechanics

International Nuclear Information System (INIS)

Touchette, Hugo

2009-01-01

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

The large deviation approach to statistical mechanics

Science.gov (United States)

Touchette, Hugo

2009-07-01

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

The Hubble law and the spiral structures of galaxies from equations of motion in general relativity

International Nuclear Information System (INIS)

Sachs, M.

1975-01-01

Fully exploiting the Lie group that characterizes the underlying symmetry of general relativity theory, Einstein's tensor formalism factorizes, yielding a generalized (16-component) quaternion field formalism. The associated generalized geodesic equation, taken as the equation of motion of a star, predicts the Hubble law from one approximation for the generally covariant equations of motion, and the spiral structure of galaxies from another approximation. These results depend on the imposition of appropriate boundary conditions. The Hubble law follows when the boundary conditions derive from the oscillating model cosmology, and not from the other cosmological models. The spiral structures of the galaxies follow from the same boundary conditions, but with a different time scale than for the whole universe. The solutions that imply the spiral motion are Fresnel integrals. These predict the star's motion to be along the 'Cornu Spiral'. The part of this spiral in the first quadrant is the imploding phase of the galaxy, corresponding to a motion with continually decreasing radii, approaching the galactic center as time increases. The part of the Cornu Spiral' in the third quadrant is the exploding phase, corresponding to continually increasing radii, as the star moves out from the hub. The spatial origin in the coordinate system of this curve is the inflection point, where the explosion changes to implosion. The two- (or many-) armed spiral galaxies are explained here in terms of two (or many) distinct explosions occurring at displaced times, in the domain of the rotating, planar galaxy. (author)

Transport Coefficients from Large Deviation Functions

OpenAIRE

Gao, Chloe Ya; Limmer, David T.

2017-01-01

We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate th...

Towards a large deviation theory for strongly correlated systems

International Nuclear Information System (INIS)

Ruiz, Guiomar; Tsallis, Constantino

2012-01-01

A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N→∞) limit yielding Gaussian distributions. The probability of n≠N/2 out of N throws is governed by e −Nr , r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q,γ) are studied, the (N→∞) limit yielding Q-Gaussians (Q→1 recovers a Gaussian). Its large deviations are governed by e q −Nr q (∝1/N 1/(q−1) , q>1), q=(Q−1)/(γ[3−Q])+1. This illustration opens the door towards a large-deviation foundation of nonextensive statistical mechanics. -- Highlights: ► We introduce the formalism of relative entropy for a single random binary variable and its q-generalization. ► We study a model of N strongly correlated binary random variables and their large-deviation probabilities. ► Large-deviation probability of strongly correlated model exhibits a q-exponential decay whose argument is proportional to N, as extensivity requires. ► Our results point to a q-generalized large deviation theory and suggest a large-deviation foundation of nonextensive statistical mechanics.

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.

Science.gov (United States)

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.

FINDING STANDARD DEVIATION OF A FUZZY NUMBER

OpenAIRE

Fokrul Alom Mazarbhuiya

2017-01-01

Two probability laws can be root of a possibility law. Considering two probability densities over two disjoint ranges, we can define the fuzzy standard deviation of a fuzzy variable with the help of the standard deviation two random variables in two disjoint spaces.

Geodesic Flow Kernel Support Vector Machine for Hyperspectral Image Classification by Unsupervised Subspace Feature Transfer

Directory of Open Access Journals (Sweden)

Alim Samat

2016-03-01

Full Text Available In order to deal with scenarios where the training data, used to deduce a model, and the validation data have different statistical distributions, we study the problem of transformed subspace feature transfer for domain adaptation (DA in the context of hyperspectral image classification via a geodesic Gaussian flow kernel based support vector machine (GFKSVM. To show the superior performance of the proposed approach, conventional support vector machines (SVMs and state-of-the-art DA algorithms, including information-theoretical learning of discriminative cluster for domain adaptation (ITLDC, joint distribution adaptation (JDA, and joint transfer matching (JTM, are also considered. Additionally, unsupervised linear and nonlinear subspace feature transfer techniques including principal component analysis (PCA, randomized nonlinear principal component analysis (rPCA, factor analysis (FA and non-negative matrix factorization (NNMF are investigated and compared. Experiments on two real hyperspectral images show the cross-image classification performances of the GFKSVM, confirming its effectiveness and suitability when applied to hyperspectral images.

Photon emission of extremal Kerr-Newman black holes

Energy Technology Data Exchange (ETDEWEB)

Wei, Shao-Wen; Gu, Bao-Min; Wang, Yong-Qiang; Liu, Yu-Xiao [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China)

2017-02-15

In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained. (orig.)

Constraints on deviations from ΛCDM within Horndeski gravity

Energy Technology Data Exchange (ETDEWEB)

Bellini, Emilio; Cuesta, Antonio J. [ICCUB, University of Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona (Spain); Jimenez, Raul; Verde, Licia, E-mail: emilio.bellini@icc.ub.edu, E-mail: ajcuesta@icc.ub.edu, E-mail: rauljimenez@g.harvard.edu, E-mail: liciaverde@icc.ub.edu [Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona (Spain)

2016-02-01

Recent anomalies found in cosmological datasets such as the low multipoles of the Cosmic Microwave Background or the low redshift amplitude and growth of clustering measured by e.g., abundance of galaxy clusters and redshift space distortions in galaxy surveys, have motivated explorations of models beyond standard ΛCDM. Of particular interest are models where general relativity (GR) is modified on large cosmological scales. Here we consider deviations from ΛCDM+GR within the context of Horndeski gravity, which is the most general theory of gravity with second derivatives in the equations of motion. We adopt a parametrization in which the four additional Horndeski functions of time α{sub i}(t) are proportional to the cosmological density of dark energy Ω{sub DE}(t). Constraints on this extended parameter space using a suite of state-of-the art cosmological observations are presented for the first time. Although the theory is able to accommodate the low multipoles of the Cosmic Microwave Background and the low amplitude of fluctuations from redshift space distortions, we find no significant tension with ΛCDM+GR when performing a global fit to recent cosmological data and thus there is no evidence against ΛCDM+GR from an analysis of the value of the Bayesian evidence ratio of the modified gravity models with respect to ΛCDM, despite introducing extra parameters. The posterior distribution of these extra parameters that we derive return strong constraints on any possible deviations from ΛCDM+GR in the context of Horndeski gravity. We illustrate how our results can be applied to a more general frameworks of modified gravity models.

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

Science.gov (United States)

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.

The large deviations theorem and ergodicity

International Nuclear Information System (INIS)

Gu Rongbao

2007-01-01

In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions

Large deviations

CERN Document Server

Deuschel, Jean-Dominique; Deuschel, Jean-Dominique

2001-01-01

This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allow

PoDMan: Policy Deviation Management

Directory of Open Access Journals (Sweden)

Aishwarya Bakshi

2017-07-01

Full Text Available Whenever an unexpected or exceptional situation occurs, complying with the existing policies may not be possible. The main objective of this work is to assist individuals and organizations to decide in the process of deviating from policies and performing a non-complying action. The paper proposes utilizing software agents as supportive tools to provide the best non-complying action while deviating from policies. The article also introduces a process in which the decision on the choice of non-complying action can be made. The work is motivated by a real scenario observed in a hospital in Norway and demonstrated through the same settings.

Geodesic paths and topological charges in quantum systems

Science.gov (United States)

Grangeiro Souza Barbosa Lima, Tiago Aecio

This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum

Quantum uncertainty relation based on the mean deviation

OpenAIRE

Sharma, Gautam; Mukhopadhyay, Chiranjib; Sazim, Sk; Pati, Arun Kumar

2018-01-01

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplica...

Effects of plasma current on nonlinear interactions of ITG turbulence, zonal flows and geodesic acoustic modes

International Nuclear Information System (INIS)

Angelino, P; Bottino, A; Hatzky, R; Jolliet, S; Sauter, O; Tran, T M; Villard, L

2006-01-01

The mutual interactions of ion temperature gradient (ITG) driven modes, zonal flows and geodesic acoustic modes (GAM) in tokamak plasmas are investigated using a global nonlinear gyrokinetic formulation with totally unconstrained evolution of temperature gradient and profile. A series of numerical simulations with the same initial temperature and density profile specifications is performed using a sequence of ideal MHD equilibria differing only in the value of the total plasma current, in particular with identical magnetic shear profiles and shapes of magnetic surfaces. On top of a bursty or quasi-steady state behaviour the zonal flows oscillate at the GAM frequency. The amplitude of these oscillations increases with the value of the safety factor q, resulting in a less effective suppression of ITG turbulence by zonal flows at a lower plasma current. The turbulence-driven volume-averaged radial heat transport is found to scale inversely with the total plasma current

Exploring Students' Conceptions of the Standard Deviation

Science.gov (United States)

delMas, Robert; Liu, Yan

2005-01-01

This study investigated introductory statistics students' conceptual understanding of the standard deviation. A computer environment was designed to promote students' ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an…

On the variational principle for the equations of perfect fluid dynamics

International Nuclear Information System (INIS)

Serre, D.

1993-01-01

One gives a new version of the variational principle δL = 0, L being the usual Lagrangian, for the perfect fluid mechanics. It is formally equivalent to the well-known principle but it gives the first rigorous derivation of the conservation laws (momentum and energy), including the discontinuous case (shock waves, contact discontinuities). Thanks to a new formulation of the constraints, we do not involve any Lagrange multiplier, which in previous works were neither physically relevant, since they do not appear in the Euler equations, nor mathematically relevant. We even give a variational interpretation of the entropy inequality when shock waves occur. Our method covers all aspects of the perfect fluids, including stationary and unstationary motion, compressible and incompressible fluids, axisymmetric case. When the velocity field admits a stream function, the variational principle gives rise to extremal points of the Lagrangian on various infinite dimensional manifolds. For a suitable choice of this manifold, the flow is itself periodic, that is all the fluid particles have a periodic motion with the same period. The flow describes a closed geodesic on some group of diffeomorphisms. (author). 10 refs

Gauge fields in a torsion field

International Nuclear Information System (INIS)

Rosu, Ion

2004-01-01

In this paper we analyse the motion and the field equations in a non-null curvature and torsion space. In this 4-n dimensional space, the connection coefficients are γ bc a = 1/2S bc a + 1/2T bc a, where S bc a is the symmetrical part and T bc a are the components of the torsion tensor. We will consider that all the fields depend on x = x α , α = 1,2,3,4 and do not depend on y = y k , k=1,2,...,n. The factor S bc a depends on the components of the metric tensor g αβ (x) and on the gauge fields A ν s 0 (x) and the components of the torsion depend only on the gauge fields A ν s 0 (x). We take into consideration the particular case for which the geodesic equations coincide with the motion equations in the presence of the gravitational and the gauge fields. In this case the field equations are Einstein equations in a 4-n dimensional space. We show that both the geodesic equations and the field equations can be obtained from a variational principle. (author)

Two examples of non strictly convex large deviations

OpenAIRE

De Marco, Stefano; Jacquier, Antoine; Roome, Patrick

2016-01-01

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.

A Visual Model for the Variance and Standard Deviation

Science.gov (United States)

Orris, J. B.

2011-01-01

This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.

Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type

International Nuclear Information System (INIS)

Bialy, Misha; Mironov, Andrey E

2011-01-01

In this paper, we deal with the classical question of the existence of polynomials in momenta integrals for geodesic flows on the 2-torus. For the quasilinear system on the coefficients of the polynomial integral, we investigate the region (so-called elliptic region) where two of the eigenvalues are complex conjugate. We show that for quartic integrals the other two eigenvalues are real and necessarily genuinely nonlinear. This observation, together with the property of the system to be rich (semi-Hamiltonian), enables us to classify elliptic regions completely. We prove that on these regions the integral is always reducible. The case of complex-conjugate eigenvalues for the system corresponding to the integral of degree 3 is done similarly. These results show that if new integrable examples exist, they can be found only within the region of hyperbolicity of the quasilinear system

New mathematical framework for spherical gravitational collapse

International Nuclear Information System (INIS)

Giambo, Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo

2003-01-01

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)

7 CFR 400.204 - Notification of deviation from standards.

Science.gov (United States)

2010-01-01

... 7 Agriculture 6 2010-01-01 2010-01-01 false Notification of deviation from standards. 400.204... Contract-Standards for Approval § 400.204 Notification of deviation from standards. A Contractor shall advise the Corporation immediately if the Contractor deviates from the requirements of these standards...

Flexible equation of state for a hard sphere and Lennard–Jones fluid ...

Indian Academy of Sciences (India)

Equation of state; Lennard–Jones potential; hard-sphere potential; liquid mixture; computer simulation. ... deviation than Barker–Henderson BH2 for LJ fluids, and results are much closer to molecular dynamics (MD) simulations than expectations and reproduce the existing simulation data and present EoS for LJ potential, ...

Non-linear neutron star oscillations viewed as deviations from an equilibrium state

International Nuclear Information System (INIS)

Sperhake, U

2002-01-01

A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)

21 CFR 330.11 - NDA deviations from applicable monograph.

Science.gov (United States)

2010-04-01

... 21 Food and Drugs 5 2010-04-01 2010-04-01 false NDA deviations from applicable monograph. 330.11... EFFECTIVE AND NOT MISBRANDED Administrative Procedures § 330.11 NDA deviations from applicable monograph. A new drug application requesting approval of an OTC drug deviating in any respect from a monograph that...

Adiabatic invariants of the extended KdV equation

Energy Technology Data Exchange (ETDEWEB)

Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)

2017-01-30

When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.

Modified Friedmann equation and inflation in a warped codimension-two braneworld

International Nuclear Information System (INIS)

Chen Fang; Cline, James M.; Kanno, Sugumi

2008-01-01

We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p θ =(α-1)ρ for the azimuthal pressure, is required to satisfy the junction conditions. For 1 5 the model is intrinsically stable, without the need for a GW field, and in this case we show that inflationary predictions can be modified by the nonstandard Friedmann equation; in particular, it is possible to get an upper limit on the spectral index, large deviations from the consistency condition between the tensor spectrum and ratio r, and large running of the spectral index even though the slow-roll parameters remain small.

Perception of midline deviations in smile esthetics by laypersons.

Science.gov (United States)

Ferreira, Jamille Barros; Silva, Licínio Esmeraldo da; Caetano, Márcia Tereza de Oliveira; Motta, Andrea Fonseca Jardim da; Cury-Saramago, Adriana de Alcantara; Mucha, José Nelson

2016-01-01

To evaluate the esthetic perception of upper dental midline deviation by laypersons and if adjacent structures influence their judgment. An album with 12 randomly distributed frontal view photographs of the smile of a woman with the midline digitally deviated was evaluated by 95 laypersons. The frontal view smiling photograph was modified to create from 1 mm to 5 mm deviations in the upper midline to the left side. The photographs were cropped in two different manners and divided into two groups of six photographs each: group LCN included the lips, chin, and two-thirds of the nose, and group L included the lips only. The laypersons performed the rate of each smile using a visual analog scale (VAS). Wilcoxon test, Student's t-test and Mann-Whitney test were applied, adopting a 5% level of significance. Laypersons were able to perceive midline deviations starting at 1 mm. Statistically significant results (p< 0.05) were found for all multiple comparisons of the values in photographs of group LCN and for almost all comparisons in photographs of group L. Comparisons between the photographs of groups LCN and L showed statistically significant values (p< 0.05) when the deviation was 1 mm. Laypersons were able to perceive the upper dental midline deviations of 1 mm, and above when the adjacent structures of the smiles were included. Deviations of 2 mm and above when the lips only were included. The visualization of structures adjacent to the smile demonstrated influence on the perception of midline deviation.

Positive nondecreasing solutions for a multi-term fractional-order functional differential equation with integral conditions

OpenAIRE

Ahmed M. A. El-Sayed; Ebtisam O. Bin-Taher

2011-01-01

In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.

Effect of nasal deviation on quality of life.

Science.gov (United States)

de Lima Ramos, Sueli; Hochman, Bernardo; Gomes, Heitor Carvalho; Abla, Luiz Eduardo Felipe; Veiga, Daniela Francescato; Juliano, Yara; Dini, Gal Moreira; Ferreira, Lydia Masako

2011-07-01

Nasal deviation is a common complaint in otorhinolaryngology and plastic surgery. This condition not only causes impairment of nasal function but also affects quality of life, leading to psychological distress. The subjective assessment of quality of life, as an important aspect of outcomes research, has received increasing attention in recent decades. Quality of life is measured using standardized questionnaires that have been tested for reliability, validity, and sensitivity. The aim of this study was to evaluate health-related quality of life, self-esteem, and depression in patients with nasal deviation. Sixty patients were selected for the study. Patients with nasal deviation (n = 32) were assigned to the study group, and patients without nasal deviation (n = 28) were assigned to the control group. The diagnosis of nasal deviation was made by digital photogrammetry. Quality of life was assessed using the Medical Outcomes Study 36-Item Short Form Health Survey questionnaire; the Rosenberg Self-Esteem/Federal University of São Paulo, Escola Paulista de Medicina Scale; and the 20-item Self-Report Questionnaire. There were significant differences between groups in the physical functioning and general health subscales of the Medical Outcomes Study 36-Item Short Form Health Survey (p < 0.05). Depression was detected in 11 patients (34.4 percent) in the study group and in two patients in the control group, with a significant difference between groups (p < 0.05). Nasal deviation is an aspect of rhinoplasty of which the surgeon should be aware so that proper psychological diagnosis can be made and suitable treatment can be planned because psychologically the patients with nasal deviation have significantly worse quality of life and are more prone to depression. Risk, II.(Figure is included in full-text article.).

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Directory of Open Access Journals (Sweden)

Claudio Cremaschini

2017-07-01

Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

A Multiparameter Thermal Conductivity Equation for 1,1-Difluoroethane (R152a) with an Optimized Functional Form

Science.gov (United States)

Scalabrin, G.; Marchi, P.; Finezzo, F.

2006-11-01

The application of an optimization technique to the available experimental data has led to the development of a new multiparameter equation λ = λ ( T,ρ ) for the representation of the thermal conductivity of 1,1-difluoroethane (R152a). The region of validity of the proposed equation covers the temperature range from 220 to 460 K and pressures up to 55 MPa, including the near-critical region. The average absolute deviation of the equation with respect to the selected 939 primary data points is 1.32%. The proposed equation represents therefore a significant improvement with respect to the literature conventional equation. The density value required by the equation is calculated at the chosen temperature and pressure conditions using a high accuracy equation of state for the fluid.

An empirical equation for the enthalpy of vaporization of quantum liquids

International Nuclear Information System (INIS)

Kuz, Victor A.; Meyra, Ariel G.; Zarragoicoechea, Guillermo J.

2004-01-01

An empirical equation for the enthalpy of vaporization of quantum fluids is presented. Dimensionless analysis is used to define enthalpy of vaporization as a function of temperature with a standard deviation of about 1%. Experimental data represented in these variables show two different behaviours and exhibit different maximum values of the enthalpy of vaporization, one corresponding to fluids with a triple point and the other to fluids having a lambda point. None of the existing empirical equations are able to describe this fact. Also enthalpy of vaporization of helium-3, n-deuterium and n-tritium are estimated

Association between septal deviation and sinonasal papilloma.

Science.gov (United States)

Nomura, Kazuhiro; Ogawa, Takenori; Sugawara, Mitsuru; Honkura, Yohei; Oshima, Hidetoshi; Arakawa, Kazuya; Oshima, Takeshi; Katori, Yukio

2013-12-01

Sinonasal papilloma is a common benign epithelial tumor of the sinonasal tract and accounts for 0.5% to 4% of all nasal tumors. The etiology of sinonasal papilloma remains unclear, although human papilloma virus has been proposed as a major risk factor. Other etiological factors, such as anatomical variations of the nasal cavity, may be related to the pathogenesis of sinonasal papilloma, because deviated nasal septum is seen in patients with chronic rhinosinusitis. We, therefore, investigated the involvement of deviated nasal septum in the development of sinonasal papilloma. Preoperative computed tomography or magnetic resonance imaging findings of 83 patients with sinonasal papilloma were evaluated retrospectively. The side of papilloma and the direction of septal deviation showed a significant correlation. Septum deviated to the intact side in 51 of 83 patients (61.4%) and to the affected side in 18 of 83 patients (21.7%). Straight or S-shaped septum was observed in 14 of 83 patients (16.9%). Even after excluding 27 patients who underwent revision surgery and 15 patients in whom the papilloma touched the concave portion of the nasal septum, the concave side of septal deviation was associated with the development of sinonasal papilloma (p = 0.040). The high incidence of sinonasal papilloma in the concave side may reflect the consequences of the traumatic effects caused by wall shear stress of the high-velocity airflow and the increased chance of inhaling viruses and pollutants. The present study supports the causative role of human papilloma virus and toxic chemicals in the occurrence of sinonasal papilloma.

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

Science.gov (United States)

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 volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time.

Unification of Gravitation and Electromagnetism in a Relativistic ...

African Journals Online (AJOL)

A theory of gravitation is considered in a relativistic version of Finslerian geometry. It is found that both the geodesic equations and the Finslerian analogue of the Einstein\\'s field equations have terms that involve the electromagnetic field tensor, thereby pointing out to the geometrization of electrodynamics and hence to a ...

Hearing protector performance and standard deviation.

Science.gov (United States)

Williams, W; Dillon, H

2005-01-01

The attenuation performance of a hearing protector is used to estimate the protected exposure level of the user. The aim is to reduce the exposed level to an acceptable value. Users should expect the attenuation to fall within a reasonable range of values around a norm. However, an analysis of extensive test data indicates that there is a negative relationship between attenuation performance and the standard deviation. This result is deduced using a variation in the method of calculating a single number rating of attenuation that is more amenable to drawing statistical inferences. As performance is typically specified as a function of the mean attenuation minus one or two standard deviations from the mean to ensure that greater than 50% of the wearer population are well protected, the implication of increasing standard deviation with decreasing attenuation found in this study means that a significant number of users are, in fact, experiencing over-protection. These users may be disinclined to use their hearing protectors because of an increased feeling of acoustic isolation. This problem is exacerbated in areas with lower noise levels.

Top Yukawa deviation in extra dimension

International Nuclear Information System (INIS)

Haba, Naoyuki; Oda, Kin-ya; Takahashi, Ryo

2009-01-01

We suggest a simple one-Higgs-doublet model living in the bulk of five-dimensional spacetime compactified on S 1 /Z 2 , in which the top Yukawa coupling can be smaller than the naive standard-model expectation, i.e. the top quark mass divided by the Higgs vacuum expectation value. If we find only single Higgs particle at the LHC and also observe the top Yukawa deviation, our scenario becomes a realistic candidate beyond the standard model. The Yukawa deviation comes from the fact that the wave function profile of the free physical Higgs field can become different from that of the vacuum expectation value, due to the presence of the brane-localized Higgs potentials. In the Brane-Localized Fermion scenario, we find sizable top Yukawa deviation, which could be checked at the LHC experiment, with a dominant Higgs production channel being the WW fusion. We also study the Bulk Fermion scenario with brane-localized Higgs potential, which resembles the Universal Extra Dimension model with a stable dark matter candidate. We show that both scenarios are consistent with the current electroweak precision measurements.

Spacetime completeness of non-singular black holes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)

2017-05-01

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 types 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.

Linear and nonlinear properties of numerical methods for the rotating shallow water equations

Science.gov (United States)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal

Positive nondecreasing solutions for a multi-term fractional-order functional differential equation with integral conditions

Directory of Open Access Journals (Sweden)

Ahmed M. A. El-Sayed

2011-12-01

Full Text Available In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.

On the Calculation of Quantum Mechanical Ground States from Classical Geodesic Motion on Certain Spaces of Constant Negative Curvature

CERN Document Server

Tomaschitz, R

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.

Prosthodontic management of mandibular deviation using palatal ramp appliance

Directory of Open Access Journals (Sweden)

Prince Kumar

2012-08-01

Full Text Available Segmental resection of the mandible generally results in deviation of the mandible to the defective side. This loss of continuity of the mandible destroys the balance of the lower face and leads to decreased mandibular function by deviation of the residual segment toward the surgical site. Prosthetic methods advocated to reduce or eliminate mandibular deviation include intermaxillary fixation, removable mandibular guide flange, palatal ramp, implant-supported prosthesis and palatal guidance restorations which may be useful in reducing mandibular deviation and improving masticatory performance and efficiency. These methods and restorations would be combined with a well organized mandibular exercise regimen. This clinical report describes the rehabilitation following segmental mandibulectomy using palatal ramp prosthesis.

An analysis of the 'semi-dissipative' terms in the plasma-dynamical equations

Energy Technology Data Exchange (ETDEWEB)

Story, L

1979-01-01

Consideration is given to the terms arising from collision corrections to the pressures and convective energy flows in the equation of state for the total and electrokinetic pressures and the convective part of the total and relative energy flows obtained by applying hydrodynamical projection techniques to a weakly coupled collisionless plasma near equilibrium. It is shown that the unusual semidissipative contributions to the total pressure deviation from equilibrium and to the convective portion of the total and relative energy flows are zero. The semidissipative contributions in the electrokinetic pressure deviation from equilibrium still remain, however, due to the inclusion of terms usually appearing in the friction vector.

Scaphoid and lunate movement in different ranges of carpal radioulnar deviation.

Science.gov (United States)

Tang, Jin Bo; Xu, Jing; Xie, Ren Guo

2011-01-01

We aimed to investigate scaphoid and lunate movement in radial deviation and in slight and moderate ulnar deviation ranges in vivo. We obtained computed tomography scans of the right wrists from 20° radial deviation to 40° ulnar deviation in 20° increments in 6 volunteers. The 3-dimensional bony structures of the wrist, including the distal radius and ulna, were reconstructed with customized software. The changes in position of the scaphoid and lunate along flexion-extension motion (FEM), radioulnar deviation (RUD), and supination-pronation axes in 3 parts--radial deviation and slight and moderate ulnar deviation--of the carpal RUD were calculated and analyzed. During carpal RUD, scaphoid and lunate motion along 3 axes--FEM, RUD, and supination-pronation--were the greatest in the middle third of the measured RUD (from neutral position to 20° ulnar deviation) and the smallest in radial deviation. Scaphoid motion along the FEM, RUD, and supination-pronation axes in the middle third was about half that in the entire motion range. In the middle motion range, lunate movement along the FEM and RUD axes was also the greatest. During carpal RUD, the greatest scaphoid and lunate movement occurs in the middle of the arc--slight ulnar deviation--which the wrist frequently adopts to accomplish major hand actions. At radial deviation, scaphoid and lunate motion is the smallest. Copyright © 2011 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.

An absolute deviation approach to assessing correlation.

OpenAIRE

Gorard, S.

2015-01-01

This paper describes two possible alternatives to the more traditional Pearson’s R correlation coefficient, both based on using the mean absolute deviation, rather than the standard deviation, as a measure of dispersion. Pearson’s R is well-established and has many advantages. However, these newer variants also have several advantages, including greater simplicity and ease of computation, and perhaps greater tolerance of underlying assumptions (such as the need for linearity). The first alter...

State: Soave-Redlich-Kwong Equation of State

Directory of Open Access Journals (Sweden)

M H. Joshipura

2000-01-01

for Soave Redlich Kwong (SRK Equations of State (EOS, available in literature have been compared. 313 compounds, compromising of 29 different classes of families, have been selected for the study. The reduced temperatures were studied in three regions; (i Tr=0.7 and (iii entire range from freezing point to critical point. It was observed that all the models compared here show the acceptable behavior except model proposed by Soave (Soave, 1992. Some families showed very high deviation in AAD, which can be attributed to more than one factor like polarity, acentricity, and association.

38 CFR 36.4304 - Deviations; changes of identity.

Science.gov (United States)

2010-07-01

... identity. 36.4304 Section 36.4304 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS... Deviations; changes of identity. A deviation of more than 5 percent between the estimates upon which a... change in the identity of the property upon which the original appraisal was based, will invalidate the...

Moderate deviations principles for the kernel estimator of ...

African Journals Online (AJOL)

Abstract. The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of condence regions for the regression function. Resume. L'objectif de ...

48 CFR 1352.219-71 - Notification to delay performance (Deviation).

Science.gov (United States)

2010-10-01

... performance (Deviation). 1352.219-71 Section 1352.219-71 Federal Acquisition Regulations System DEPARTMENT OF....219-71 Notification to delay performance (Deviation). As prescribed in 48 CFR 1319.811-3(b), insert the following clause: Notification To Delay Performance (Deviation) (APR 2010) The contractor shall...

Stability study of pre-stack seismic inversion based on the full Zoeppritz equation

Science.gov (United States)

Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao

2017-10-01

Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most

Integrable Hamiltonian systems and spectral theory

CERN Document Server

Moser, J

1981-01-01

Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.

Cosmology as relativistic particle mechanics: from big crunch to big bang

Energy Technology Data Exchange (ETDEWEB)

Russo, J G [Institucio Catalana de Recerca i Estudis Avancats, Departament ECM, Facultat de FIsica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain); Townsend, P K [Institucio Catalana de Recerca i Estudis Avancats, Departament ECM, Facultat de FIsica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)

2005-02-21

Cosmology can be viewed as geodesic motion in an appropriate metric on an 'augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved) cosmologies for models with N scalar fields taking values in a hyperbolic target space for which the augmented target space is a Milne universe. The singularities of these cosmologies correspond to points at which the particle trajectory crosses the Milne horizon, suggesting a novel resolution of them, which we explore via the Wheeler-DeWitt equation.

7 CFR 400.174 - Notification of deviation from financial standards.

Science.gov (United States)

2010-01-01

... 7 Agriculture 6 2010-01-01 2010-01-01 false Notification of deviation from financial standards... Agreement-Standards for Approval; Regulations for the 1997 and Subsequent Reinsurance Years § 400.174 Notification of deviation from financial standards. An insurer must immediately advise FCIC if it deviates from...

Exergy analysis on throttle reduction efficiency based on real gas equations

International Nuclear Information System (INIS)

Luo, Yuxi; Wang, Xuanyin

2010-01-01

This paper proposes an approach to calculate the efficiency of throttling in which the exergy (available energy) is used to evaluate the energy conversion processes. In the exergy calculation for real gases, a difficult part of integration can be removed by judiciously advised thermodynamic paths; the compressibility factor is calculated by using Peng-Robinson (P-R) equation. It is found that the largest deviation between the exergies calculated by the real gas equation and ideal gas assumption is about 1%. Because the exergy is a function of the pressure and temperature, the Joule-Thomson coefficients are used to calculate the temperature changes of throttling, based on the compressibility factors of the Soave-Redlich-Kwong (S-R-K) and P-R equations, and the temperature decreases are compared with those calculated by empirical formula. The result shows that the heat exergy contributes very little in throttling. The simple equation of ideal gas is suggested to calculate the efficiency of throttling for air at atmospheric temperatures.

Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements

OpenAIRE

Ming-Hung Chiu; Jia-Ze Shen; Jian-Ming Huang

2016-01-01

We proposed heterodyne angle deviation interferometry (HADI) for angle deviation measurements. The phase shift of an angular sensor (which can be a metal film or a surface plasmon resonance (SPR) prism) is proportional to the deviation angle of the test beam. The method has been demonstrated in bubble and speaker’s vibration measurements in this paper. In the speaker’s vibration measurement, the voltage from the phase channel of a lock-in amplifier includes the vibration level and frequency. ...

Unification of Electromagnetism and Gravitation in the Framework of General Geometry

OpenAIRE

Shahverdiyev, Shervgi

2005-01-01

A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. It is shown that equation of motion for a particle interacting with electromagnetic field coincides exactly with equation for geodesics of geometry underlying Electromag...

IMPROVEMENT OF THE REDLICH-KWONG EQUATION OF STATE BY MODIFICATION OF CO-VOLUME PARAMETER

Directory of Open Access Journals (Sweden)

Ratnawati Ratnawati

2012-02-01

Full Text Available Cubic equations of state are widely used in phase-equilibrium calculations because of their simplicity and accuracy. Most equations of states are not accurate enough for predicting density of liquid and dense gas. A modification on the Redlich-Kwong (RK equation of state is developed. Parameter b is modified by introducing a new parameter,b, which is a function of molecular weight and temperature. The modification gives a significant improvement over the original RK equation for predicting density. For 6538 data points of 27 compounds, the proposed equation gives only 2.8% of average absolute deviation (AAD, while the original RK and the Soave-Redlich-Kwong (SRK equations give 11.4% and 11.7%, respectively. The proposed modification improves the performance of the RK equation for predicting vapor pressure as well. For 2829 data points of 94 compounds, the proposed modification lowers the AAD of the RK equation from 1460% down to 30.8%. It is comparable to the famous SRK equation, which give 5.8% of AAD. The advantage of the proposed equation is that it uses only critical pressure and temperature as other equations of states do, and molecular weight, which is easily calculated. Another advantage is that the proposed equation simpler than the SRK equation of state.

[The crooked nose: correction of dorsal and caudal septal deviations].

Science.gov (United States)

Foda, H M T

2010-09-01

The deviated nose represents a complex cosmetic and functional problem. Septal surgery plays a central role in the successful management of the externally deviated nose. This study included 800 patients seeking rhinoplasty to correct external nasal deviations; 71% of these suffered from variable degrees of nasal obstruction. Septal surgery was necessary in 736 (92%) patients, not only to improve breathing, but also to achieve a straight, symmetric external nose. A graduated surgical approach was adopted to allow correction of the dorsal and caudal deviations of the nasal septum without weakening its structural support to the nasal dorsum or nasal tip. The approach depended on full mobilization of deviated cartilage, followed by straightening of the cartilage and its fixation in the corrected position by using bony splinting grafts through an external rhinoplasty approach.

Some applications on tangent bundle with Kaluza-Klein metric

Directory of Open Access Journals (Sweden)

Murat Altunbaş

2017-01-01

Full Text Available In this paper, differential equations of geodesics; parallelism, incompressibility and closeness conditions of the horizontal and complete lift of the vector fields are investigated with respect to Kaluza-Klein metric on tangent bundle.

A new preprocessing parameter estimation based on geodesic active contour model for automatic vestibular neuritis diagnosis.

Science.gov (United States)

Ben Slama, Amine; Mouelhi, Aymen; Sahli, Hanene; Manoubi, Sondes; Mbarek, Chiraz; Trabelsi, Hedi; Fnaiech, Farhat; Sayadi, Mounir

2017-07-01

The diagnostic of the vestibular neuritis (VN) presents many difficulties to traditional assessment methods This paper deals with a fully automatic VN diagnostic system based on nystagmus parameter estimation using a pupil detection algorithm. A geodesic active contour model is implemented to find an accurate segmentation region of the pupil. Hence, the novelty of the proposed algorithm is to speed up the standard segmentation by using a specific mask located on the region of interest. This allows a drastically computing time reduction and a great performance and accuracy of the obtained results. After using this fast segmentation algorithm, the obtained estimated parameters are represented in temporal and frequency settings. A useful principal component analysis (PCA) selection procedure is then applied to obtain a reduced number of estimated parameters which are used to train a multi neural network (MNN). Experimental results on 90 eye movement videos show the effectiveness and the accuracy of the proposed estimation algorithm versus previous work. Copyright © 2017 Elsevier B.V. All rights reserved.

Computer-aided measurement of liver volumes in CT by means of geodesic active contour segmentation coupled with level-set algorithms

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)

2010-05-15

Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F{<=}f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less

Computer-aided measurement of liver volumes in CT by means of geodesic active contour segmentation coupled with level-set algorithms

International Nuclear Information System (INIS)

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

2010-01-01

Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F≤f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less completion time

On the calculation of quantum mechanical ground states from classical geodesic motion on certain spaces of constant negative curvature

International Nuclear Information System (INIS)

Tomaschitz, R.

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)

Complexity analysis based on generalized deviation for financial markets

Science.gov (United States)

Li, Chao; Shang, Pengjian

2018-03-01

In this paper, a new modified method is proposed as a measure to investigate the correlation between past price and future volatility for financial time series, known as the complexity analysis based on generalized deviation. In comparison with the former retarded volatility model, the new approach is both simple and computationally efficient. The method based on the generalized deviation function presents us an exhaustive way showing the quantization of the financial market rules. Robustness of this method is verified by numerical experiments with both artificial and financial time series. Results show that the generalized deviation complexity analysis method not only identifies the volatility of financial time series, but provides a comprehensive way distinguishing the different characteristics between stock indices and individual stocks. Exponential functions can be used to successfully fit the volatility curves and quantify the changes of complexity for stock market data. Then we study the influence for negative domain of deviation coefficient and differences during the volatile periods and calm periods. after the data analysis of the experimental model, we found that the generalized deviation model has definite advantages in exploring the relationship between the historical returns and future volatility.

Influence of asymmetrical drawing radius deviation in micro deep drawing

Science.gov (United States)

Heinrich, L.; Kobayashi, H.; Shimizu, T.; Yang, M.; Vollertsen, F.

2017-09-01

Nowadays, an increasing demand for small metal parts in electronic and automotive industries can be observed. Deep drawing is a well-suited technology for the production of such parts due to its excellent qualities for mass production. However, the downscaling of the forming process leads to new challenges in tooling and process design, such as high relative deviation of tool geometry or blank displacement compared to the macro scale. FEM simulation has been a widely-used tool to investigate the influence of symmetrical process deviations as for instance a global variance of the drawing radius. This study shows a different approach that allows to determine the impact of asymmetrical process deviations on micro deep drawing. In this particular case the impact of an asymmetrical drawing radius deviation and blank displacement on cup geometry deviation was investigated for different drawing ratios by experiments and FEM simulation. It was found that both variations result in an increasing cup height deviation. Nevertheless, with increasing drawing ratio a constant drawing radius deviation has an increasing impact, while blank displacement results in a decreasing offset of the cups geometry. This is explained by different mechanisms that result in an uneven cup geometry. While blank displacement leads to material surplus on one side of the cup, an unsymmetrical radius deviation on the other hand generates uneven stretching of the cups wall. This is intensified for higher drawing ratios. It can be concluded that the effect of uneven radius geometry proves to be of major importance for the production of accurately shaped micro cups and cannot be compensated by intentional blank displacement.

Limiting values of large deviation probabilities of quadratic statistics

NARCIS (Netherlands)

Jeurnink, Gerardus A.M.; Kallenberg, W.C.M.

1990-01-01

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation

Refraction in Terms of the Deviation of the Light.

Science.gov (United States)

Goldberg, Fred M.

1985-01-01

Discusses refraction in terms of the deviation of light. Points out that in physics courses where very little mathematics is used, it might be more suitable to describe refraction entirely in terms of the deviation, rather than by introducing Snell's law. (DH)

Mean-deviation analysis in the theory of choice.

Science.gov (United States)

Grechuk, Bogdan; Molyboha, Anton; Zabarankin, Michael

2012-08-01

Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered. © 2012 Society for Risk Analysis.

Illusory shadow person causing paradoxical gaze deviations during temporal lobe seizures

NARCIS (Netherlands)

Zijlmans, M.; van Eijsden, P.; Ferrier, C. H.; Kho, K. H.; van Rijen, P. C.; Leijten, F. S. S.

Generally, activation of the frontal eye field during seizures can cause versive (forced) gaze deviation, while non-versive head deviation is hypothesised to result from ictal neglect after inactivation of the ipsilateral temporoparietal area. Almost all non-versive head deviations occurring during

Geometry of the isotropic oscillator driven by the conformal mode

Energy Technology Data Exchange (ETDEWEB)

Galajinsky, Anton [Tomsk Polytechnic University, School of Physics, Tomsk (Russian Federation)

2018-01-15

Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. The conventional methods include the Jacobi metric and the Eisenhart lift. In this work, a modification of the Eisenhart lift is proposed which describes the isotropic oscillator in arbitrary dimension driven by the one-dimensional conformal mode. (orig.)

Equation of state and jamming density for equivalent bi- and polydisperse, smooth, hard sphere systems.

NARCIS (Netherlands)

Ogarko, V.; Luding, Stefan

2012-01-01

We study bi- and polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid

Deviations from Newton's law in supersymmetric large extra dimensions

International Nuclear Information System (INIS)

Callin, P.; Burgess, C.P.

2006-01-01

Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case

Performance of Phonatory Deviation Diagrams in Synthesized Voice Analysis.

Science.gov (United States)

Lopes, Leonardo Wanderley; da Silva, Karoline Evangelista; da Silva Evangelista, Deyverson; Almeida, Anna Alice; Silva, Priscila Oliveira Costa; Lucero, Jorge; Behlau, Mara

2018-05-02

To analyze the performance of a phonatory deviation diagram (PDD) in discriminating the presence and severity of voice deviation and the predominant voice quality of synthesized voices. A speech-language pathologist performed the auditory-perceptual analysis of the synthesized voice (n = 871). The PDD distribution of voice signals was analyzed according to area, quadrant, shape, and density. Differences in signal distribution regarding the PDD area and quadrant were detected when differentiating the signals with and without voice deviation and with different predominant voice quality. Differences in signal distribution were found in all PDD parameters as a function of the severity of voice disorder. The PDD area and quadrant can differentiate normal voices from deviant synthesized voices. There are differences in signal distribution in PDD area and quadrant as a function of the severity of voice disorder and the predominant voice quality. However, the PDD area and quadrant do not differentiate the signals as a function of severity of voice disorder and differentiated only the breathy and rough voices from the normal and strained voices. PDD density is able to differentiate only signals with moderate and severe deviation. PDD shape shows differences between signals with different severities of voice deviation. © 2018 S. Karger AG, Basel.

Detection of geodesic acoustic mode oscillations, using multiple signal classification analysis of Doppler backscattering signal on Tore Supra

International Nuclear Information System (INIS)

Vermare, L.; Hennequin, P.; Gürcan, Ö.D.

2012-01-01

This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the additional heating power is varied, the frequency is found to scale with C s /R. The MUltiple SIgnal Classification (MUSIC) algorithm is employed to access the temporal evolution of the perpendicular velocity of density fluctuations. The method is presented in some detail, and is validated and compared against standard methods, such as the conventional fast Fourier transform method, using a synthetic signal. It stands out as a powerful data analysis method to follow the Doppler frequency with a high temporal resolution, which is important in order to extract the dynamics of GAMs. (paper)

Generation of deviation parameters for amino acid singlets, doublets ...

Indian Academy of Sciences (India)

We present a new method, secondary structure prediction by deviation parameter (SSPDP) for predicting the secondary structure of proteins from amino acid sequence. Deviation parameters (DP) for amino acid singlets, doublets and triplets were computed with respect to secondary structural elements of proteins based on ...

VAR Portfolio Optimal: Perbandingan Antara Metode Markowitz dan Mean Absolute Deviation

Directory of Open Access Journals (Sweden)

R. Agus Sartono

2009-05-01

Full Text Available Portfolio selection method which have been introduced by Harry Markowitz (1952 used variance or deviation standard as a measure of risk. Kanno and Yamazaki (1991 introduced another method and used mean absolute deviation as a measure of risk instead of variance. The Value-at Risk (VaR is a relatively new method to capitalized risk that been used by financial institutions. The aim of this research is compare between mean variance and mean absolute deviation of two portfolios. Next, we attempt to assess the VaR of two portfolios using delta normal method and historical simulation. We use the secondary data from the Jakarta Stock Exchange – LQ45 during 2003. We find that there is a weak-positive correlation between deviation standard and return in both portfolios. The VaR nolmal delta based on mean absolute deviation method eventually is higher than the VaR normal delta based on mean variance method. However, based on the historical simulation the VaR of two methods is statistically insignificant. Thus, the deviation standard is sufficient measures of portfolio risk.Keywords: optimalisasi portofolio, mean-variance, mean-absolute deviation, value-at-risk, metode delta normal, metode simulasi historis

Importance sampling large deviations in nonequilibrium steady states. I

Science.gov (United States)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2018-03-01

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Importance sampling large deviations in nonequilibrium steady states. I.

Science.gov (United States)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T

2018-03-28

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

General relativity

International Nuclear Information System (INIS)

Gourgoulhon, Eric

2013-01-01

The author proposes a course on general relativity. He first presents a geometrical framework by addressing, presenting and discussion the following notions: the relativistic space-time, the metric tensor, Universe lines, observers, principle of equivalence and geodesics. In the next part, he addresses gravitational fields with spherical symmetry: presentation of the Schwarzschild metrics, radial light geodesics, gravitational spectral shift (Einstein effect), orbitals of material objects, photon trajectories. The next parts address the Einstein equation, black holes, gravitational waves, and cosmological solutions. Appendices propose a discussion of the relationship between relativity and GPS, some problems and their solutions, and Sage codes

Some geometric properties of magneto-fluid flows

OpenAIRE

Gangwar, S. S.; Babu, Ram

1982-01-01

By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non-dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.

Stochastic models with power-law tails the equation X = AX + B

CERN Document Server

Buraczewski, Dariusz; Mikosch, Thomas

2016-01-01

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...

Implicit methods for equation-free analysis: convergence results and analysis of emergent waves in microscopic traffic models

DEFF Research Database (Denmark)

Marschler, Christian; Sieber, Jan; Berkemer, Rainer

2014-01-01

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold...... against the direction of traffic. Equation-free analysis enables us to investigate the behavior of the microscopic traffic model on a macroscopic level. The standard deviation of cars' headways is chosen as the macroscopic measure of the underlying dynamics such that traveling wave solutions correspond...... to equilibria on the macroscopic level in the equation-free setup. The collapse of the traffic jam to the free flow then corresponds to a saddle-node bifurcation of this macroscopic equilibrium. We continue this bifurcation in two parameters using equation-free analysis....

Energy, momentum and angular momentum conservations in de Sitter gravity

International Nuclear Information System (INIS)

Lu, Jia-An

2016-01-01

In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle’s world line from a geodesic. All the results are compared to the ordinary Lorentz gravity. (paper)

Dark matter as a dynamic effect due to a non-minimal gravitational coupling with matter (I): Analytical results

International Nuclear Information System (INIS)

Bertolami, O; Paramos, J

2010-01-01

In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically generated effect derived from this modification to General Relativity. Two possibilities are discussed: firstly, that the observed discrepancy between the measured rotation velocity and the classical prediction is due to a deviation from geodesic motion, due to a non-(covariant) conservation of the energy-momentum tensor; secondly, that even if the principle of energy conservation holds, the dynamical effects arising due to the non-trivial terms in the Einstein equations of motion can give rise to an extra density contribution that may be interpreted as dark matter. In this work, The mechanism of the latter alternative is detailed; a numerical session ascertaining the order of magnitude of the relevant parameters is undertaken in another contribution to this volume, with possible cosmological implications discussed.

Standard Deviation for Small Samples

Science.gov (United States)

Joarder, Anwar H.; Latif, Raja M.

2006-01-01

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…

The deviation matrix of a continuous-time Markov chain

NARCIS (Netherlands)

Coolen-Schrijner, P.; van Doorn, E.A.

2001-01-01

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a

The deviation matrix of a continuous-time Markov chain

NARCIS (Netherlands)

Coolen-Schrijner, Pauline; van Doorn, Erik A.

2002-01-01

he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a

Relativistic three-particle dynamical equations: II. Application to the trinucleon system

International Nuclear Information System (INIS)

Adhikari, S.K.; Tomio, L.

1993-11-01

The contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy is calculated employing five sets tri nucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (author)

Nucleon Mass from a Covariant Three-Quark Faddeev Equation

International Nuclear Information System (INIS)

Eichmann, G.; Alkofer, R.; Krassnigg, A.; Nicmorus, D.

2010-01-01

We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.

45 CFR 63.19 - Budget revisions and minor deviations.

Science.gov (United States)

2010-10-01

... 45 Public Welfare 1 2010-10-01 2010-10-01 false Budget revisions and minor deviations. 63.19 Section 63.19 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION GRANT PROGRAMS... Budget revisions and minor deviations. Pursuant to § 74.102(d) of this title, paragraphs (b)(3) and (b)(4...

The role of septal surgery in management of the deviated nose.

Science.gov (United States)

Foda, Hossam M T

2005-02-01

The deviated nose represents a complex cosmetic and functional problem. Septal surgery plays a central role in the successful management of the externally deviated nose. This study included 260 patients seeking rhinoplasty to correct external nasal deviations; 75 percent of them had various degrees of nasal obstruction. Septal surgery was necessary in 232 patients (89 percent), not only to improve breathing but also to achieve a straight, symmetrical, external nose as well. A graduated surgical approach was adopted to allow correction of the dorsal and caudal deviations of the nasal septum without weakening its structural support to the dorsum or nasal tip. The approach depended on full mobilization of deviated cartilage, followed by straightening of the cartilage and its fixation in the corrected position by using bony splinting grafts through an external rhinoplasty approach.

Note onset deviations as musical piece signatures.

Science.gov (United States)

Serrà, Joan; Özaslan, Tan Hakan; Arcos, Josep Lluis

2013-01-01

A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.

Note onset deviations as musical piece signatures.

Directory of Open Access Journals (Sweden)

Joan Serrà

Full Text Available A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.

Killing vectors in algebraically special space-times

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1984-01-01

The form of the isometric, homothetic, and conformal Killing vectors for algebraically special metrics which admit a shear-free congruence of null geodesics is obtained by considering their complexification, using the existence of a congruence of null strings. The Killing equations are partially integrated and the reasons which permit this reduction are exhibited. In the case where the congruence of null strings has a vanishing expansion, the Killing equations are reduced to a single master equation

An Analysis of the Linguistic Deviation in Chapter X of Oliver Twist

Institute of Scientific and Technical Information of China (English)

刘聪

2013-01-01

Charles Dickens is one of the greatest critical realist writers of the Victorian Age. In language, he is often compared with William Shakespeare for his adeptness with the vernacular and large vocabulary. Charles Dickens achieved a recognizable place among English writers through the use of the stylistic features in his fictional language. Oliver Twist is the best representative of Charles Dickens’style, which makes it the most appropriate choice for the present stylistic study on Charles Dickens. No one who has ever read the dehumanizing workhouse scenes of Oliver Twist and the dark, criminal underworld life can forget them. This thesis attempts to investigate Oliver Twist through the approach of modern stylistics, particularly the theory of linguistic devia-tion. This thesis consists of an introduction, the main body and a conclusion. The introduction offers a brief summary of the com-ments on Charles Dickens and Chapter X of Oliver Twist, introduces the newly rising linguistic deviation theories, and brings about the theories on which this thesis settles. The main body explores the deviation effects produced from four aspects: lexical deviation, grammatical deviation, graphological deviation, and semantic deviation. It endeavors to show Dickens ’manipulating language and the effects achieved through this manipulation. The conclusion mainly sums up the previous analysis, and reveals the theme of the novel, positive effect of linguistic deviation and significance of deviation application.

Fluid observers and tilting cosmology

International Nuclear Information System (INIS)

Coley, A A; Hervik, S; Lim, W C

2006-01-01

We study perfect fluid cosmological models with a constant equation of state parameter γ in which there are two naturally defined timelike congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding spatially homogeneous tilted perfect fluid models, with an emphasis on future evolution with extreme tilt. We show that for ultra-radiative equations of state (i.e. γ > 4/3), generically the tilt becomes extreme at late times and the fluid observers will reach infinite expansion within a finite proper time and experience a singularity similar to that of the big rip. In addition, we show that for sub-radiative equations of state (i.e. γ < 4/3), the tilt can become extreme at late times and give rise to an effective quintessential equation of state. To establish the connection with phantom cosmology and quintessence, we calculate the effective equation of state in the models under consideration and we determine the future asymptotic behaviour of the tilting models in the fluid frame variables using the boost formulae. We also discuss spatially inhomogeneous models and tilting spatially homogeneous models with a cosmological constant

Cross-code gyrokinetic verification and benchmark on the linear collisionless dynamics of the geodesic acoustic mode

Science.gov (United States)

Biancalani, A.; Bottino, A.; Ehrlacher, C.; Grandgirard, V.; Merlo, G.; Novikau, I.; Qiu, Z.; Sonnendrücker, E.; Garbet, X.; Görler, T.; Leerink, S.; Palermo, F.; Zarzoso, D.

2017-06-01

The linear properties of the geodesic acoustic modes (GAMs) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, and safety factor), electro-magnetic effects, collisions, and the presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the Lagrangian (particle-in-cell) code ORB5, the Eulerian code GENE, and semi-Lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.

Decreasing the amplitude deviation of Guassian filter in surface roughness measurements

Science.gov (United States)

Liu, Bo; Wang, Yu

2008-12-01

A new approach for decreasing the amplitude characteristic deviation of Guassian filter in surface roughness measurements is presented in this paper. According to Central Limit Theorem, many different Guassian approximation filters could be constructed. By using first-order Butterworth filter and moving average filter to approximate Guassian filter, their directions of amplitude deviation are opposite, and their locations of extreme value are close. So the linear combination of them could reduce the amplitude deviation greatly. The maximum amplitude deviation is only about 0.11% through paralleling them. The algorithm of this new method is simple and its efficiency is high.

Non-relativistic spinning particle in a Newton-Cartan background

Science.gov (United States)

Barducci, Andrea; Casalbuoni, Roberto; Gomis, Joaquim

2018-01-01

We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.

Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function

International Nuclear Information System (INIS)

Mao, G.; Li, Z.; Zhuo, Y.

1996-01-01

We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society

Some geometric properties of magneto-fluid flows

Directory of Open Access Journals (Sweden)

S. S. Gangwar

1982-01-01

Full Text Available By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non-dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.

Minimizing Hexapod Robot Foot Deviations Using Multilayer Perceptron

Directory of Open Access Journals (Sweden)

Vytautas Valaitis

2015-12-01

Full Text Available Rough-terrain traversability is one of the most valuable characteristics of walking robots. Even despite their slower speeds and more complex control algorithms, walking robots have far wider usability than wheeled or tracked robots. However, efficient movement over irregular surfaces can only be achieved by eliminating all possible difficulties, which in many cases are caused by a high number of degrees of freedom, feet slippage, frictions and inertias between different robot parts or even badly developed inverse kinematics (IK. In this paper we address the hexapod robot-foot deviation problem. We compare the foot-positioning accuracy of unconfigured inverse kinematics and Multilayer Perceptron-based (MLP methods via theory, computer modelling and experiments on a physical robot. Using MLP-based methods, we were able to significantly decrease deviations while reaching desired positions with the hexapod's foot. Furthermore, this method is able to compensate for deviations of the robot arising from any possible reason.

The Impact of Advanced Technologies on Treatment Deviations in Radiation Treatment Delivery

International Nuclear Information System (INIS)

Marks, Lawrence B.; Light, Kim L.; Hubbs, Jessica L.; Georgas, Debra L.; Jones, Ellen L.; Wright, Melanie C.; Willett, Christopher G.; Yin Fangfang

2007-01-01

Purpose: To assess the impact of new technologies on deviation rates in radiation therapy (RT). Methods and Materials: Treatment delivery deviations in RT were prospectively monitored during a time of technology upgrade. In January 2003, our department had three accelerators, none with 'modern' technologies (e.g., without multileaf collimators [MLC]). In 2003 to 2004, we upgraded to five new accelerators, four with MLC, and associated advanced capabilities. The deviation rates among patients treated on 'high-technology' versus 'low-technology' machines (defined as those with vs. without MLC) were compared over time using the two-tailed Fisher's exact test. Results: In 2003, there was no significant difference between the deviation rate in the 'high-technology' versus 'low-technology' groups (0.16% vs. 0.11%, p = 0.45). In 2005 to 2006, the deviation rate for the 'high-technology' groups was lower than the 'low-technology' (0.083% vs. 0.21%, p = 0.009). This difference was caused by a decline in deviations on the 'high-technology' machines over time (p = 0.053), as well as an unexpected trend toward an increase in deviations over time on the 'low-technology' machines (p = 0.15). Conclusions: Advances in RT delivery systems appear to reduce the rate of treatment deviations. Deviation rates on 'high-technology' machines with MLC decline over time, suggesting a learning curve after the introduction of new technologies. Associated with the adoption of 'high-technology' was an unexpected increase in the deviation rate with 'low-technology' approaches, which may reflect an over-reliance on tools inherent to 'high-technology' machines. With the introduction of new technologies, continued diligence is needed to ensure that staff remain proficient with 'low-technology' approaches

Interactive visualization of a thin disc around a Schwarzschild black hole

International Nuclear Information System (INIS)

Müller, Thomas; Frauendiener, Jörg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a Schwarzschild black hole can be determined interactively by means of an analytic solution to the geodesic equation processed on current high-performance graphical processing units. This approach can, in principle, be customized for any other thin disc in a spacetime with geodesics given in closed form. The interactive visualization discussed here can be used either in a first course in general relativity for demonstration purposes only or as a thesis for an enthusiastic student in an advanced course with some basic knowledge of OpenGL and a programming language. (paper)

Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes

Directory of Open Access Journals (Sweden)

Junichi Hirukawa

2012-01-01

Full Text Available This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes.

Science.gov (United States)

Cafaro, Carlo; Alsing, Paul M

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

Science.gov (United States)

Cafaro, Carlo; Alsing, Paul M.

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Introduction to general relativity

CERN Document Server

Parthasarthy, R

2016-01-01

INTRODUCTION TO GENERAL RELATIVITY begins with a description of the geometry of curved space, explaining geodesics, parallel transport, covariant differentiation, geodesic deviation and spacetime symmetry by killing vectors. It then introduces Einstein's theory of gravitation followed by Schwarzschild solution with its relevance to Positive Mass theorem. The three tests for Einstein's gravity are explained. Other exact solutions such as Vaidya, Kerr and Reisner - Nordstrom metric are included. In the Chapter on cosmological solutions, a detailed description of Godel metric is provided. It then introduces five dimensional spacetime of Kaluza showing the unification of gravity with electromagnetism. This is extended to include non-Abelian gauge theory by invoking compact extra dimensions. Explicit expressions in this case for Christoffel connections and ricci tensor are derived and the higher dimensional gravity action is shown to compactification are given.

A robust standard deviation control chart

NARCIS (Netherlands)

Schoonhoven, M.; Does, R.J.M.M.

2012-01-01

This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse

3D early embryogenesis image filtering by nonlinear partial differential equations.

Science.gov (United States)

Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

2010-08-01

We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which

Deviation from Covered Interest Rate Parity in Korea

Directory of Open Access Journals (Sweden)

Seungho Lee

2003-06-01

Full Text Available This paper tested the factors which cause deviation from covered interest rate parity (CIRP in Korea, using regression and VAR models. The empirical evidence indicates that the difference between the swap rate and interest rate differential exists and is greatly affected by variables which represent the currency liquidity situation of foreign exchange banks. In other words, the deviation from CIRP can easily occur due to the lack of foreign exchange liquidity of banks in a thin market, despite few capital constraints, small transaction costs, and trivial default risk in Korea.

A perturbed Lennard-Jones chain equation of state for liquid metals

Energy Technology Data Exchange (ETDEWEB)

Mousazadeh, M H; Marageh, M Ghanadi [AEOI, JIH Research Laboratory, 11365/8486, Tehran (Iran, Islamic Republic of)

2006-05-24

The perturbed Lennard-Jones chain (PLJC) equation of state is formulated based on first-order variational perturbation theory. The model uses two parameters for a monatomic system, segment size, {sigma}, and segment energy, {epsilon}/k. In this work, we employed the PLJC equation to calculate the liquid density of 26 metals, including alkali and alkali earth metals, iron, cobalt, nickel, copper, silver, gold, zinc, cadmium, mercury, aluminium, gallium, indium, thallium, tin, lead, antimony, and bismuth, for which accurate experimental data exist in the literature. The calculations cover a broad range of temperatures ranging from the melting point to close to the critical point and pressures ranging from the vapour-pressure curve up to pressures as high as 2000 bar. The average absolute deviation in the liquid density predicted by the PLJC equation of state in the saturation line compared with experimental data is 1.26%. Also, using the normal melting temperature and liquid density at melting point (T{sub m}, {rho}{sub m}) as input data for the estimation of the equation of state parameters provides a good correlation of liquid density at saturated and compressed pressures.

Dynamics of stringy congruence in the early universe

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2011-01-01

We study twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and shear in terms of the expansion of the Universe. We observe in this higher dimensional cosmology that, as the early universe evolves with expansion rate, the twist of the stringy congruence decreases exponentially and the initial twist value should be large enough to sustain the rotations of the ensuing universe, while the effects of the shear are negligible to produce the isotropic and homogeneous universe. We also investigate the twist and shear of the geodesic surface congruence of the null strings.

Neutrino oscillations in the Kerr-Newman spacetime

International Nuclear Information System (INIS)

Ren Jun; Zhang Chengmin

2010-01-01

The mass neutrino oscillation in the Kerr-Newman (K-N) spacetime is studied in the plane θ = θ 0 , and general equations of the oscillation phases are given. The effect of the rotation and electric charge on the phase is presented. Then, we consider three special cases. (1) The neutrinos travel along the geodesics with angular momentum L = aE in the equatorial plane. (2) The neutrinos travel along the geodesics with L = 0 in the equatorial plane. (3) The neutrinos travel along the radial geodesics in the direction θ = 0. Finally, we calculate the proper oscillation length in the K-N spacetime. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. When the neutrino travels out of the gravitational field, a blue shift of the oscillation length takes place. We discuss the variation of the oscillation length influenced by the gravitational field strength, the rotation a 2 and charge Q.

Geometry of Hamiltonian chaos

DEFF Research Database (Denmark)

Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

2007-01-01

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

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

Science.gov (United States)

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.

Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation

Science.gov (United States)

Wasserman, Nicholas H.; Casey, Stephanie; Champion, Joe; Huey, Maryann

2017-01-01

This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator--not just a descriptive statistic for the variation (spread) in data--is related to teachers' instruction regarding standard deviation, particularly…

A better norm-referenced grading using the standard deviation criterion.

Science.gov (United States)

Chan, Wing-shing

2014-01-01

The commonly used norm-referenced grading assigns grades to rank-ordered students in fixed percentiles. It has the disadvantage of ignoring the actual distance of scores among students. A simple norm-referenced grading via standard deviation is suggested for routine educational grading. The number of standard deviation of a student's score from the class mean was used as the common yardstick to measure achievement level. Cumulative probability of a normal distribution was referenced to help decide the amount of students included within a grade. RESULTS of the foremost 12 students from a medical examination were used for illustrating this grading method. Grading by standard deviation seemed to produce better cutoffs in allocating an appropriate grade to students more according to their differential achievements and had less chance in creating arbitrary cutoffs in between two similarly scored students than grading by fixed percentile. Grading by standard deviation has more advantages and is more flexible than grading by fixed percentile for norm-referenced grading.

A novel solution to the Klein–Gordon equation in the presence of a strong rotating electric field

Energy Technology Data Exchange (ETDEWEB)

Raicher, E., E-mail: erez.raicher@mail.huji.ac.il [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Eliezer, S. [Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Nuclear Fusion Institute, Polytechnic University of Madrid, Madrid (Spain); Zigler, A. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)

2015-11-12

The Klein–Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects) the emission processes and the particle motion in Quantum Electrodynamics (QED) cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised.

Measurement and analysis of the thoracic patient setup deviations in routine radiotherapy

International Nuclear Information System (INIS)

Jia Mingxuan; Zou Huawei; Wu Rong; Sun Jian; Dong Xiaoqi

2003-01-01

Objective: To determine the magnitude of the setup deviations of the thoracic patients in routine radiotherapy. Methods: Altogether 408 films for 21 thoracic patients were recorded using the electronic portal imaging device (EPID), and comparison with reference CT simulator digitally-reconstructed radiograph (DRR) for anterior-posterior fields was performed. The deviation of setup for 21 patients in the left-right (RL), superior-inferior (SI) directions and rotation about the anterior-posterior (AP) axis were measured and analyzed. Results: Without immobilization device, the mean translational and rotational setup deviations were (0.7±3.1) mm and (1.5±4.1) mm in the RL and SI directions, respectively, and (0.3±2.4) degree about AP axis. With immobilization device, the mean translational and rotational setup deviations were (0.5±2.4) mm and (0.8±2.7) mm in the RL and SI directions respectively, and (0.2±1.6) degree about AP axis. Conclusion: The setup deviations in thoracic patients irradiation may be reduced with the use of the immobilization device. The setup deviation in the SI direction is greater than that in the RL direction. The setup deviations are mainly random errors

Sea Surface Height Deviation, Aviso, 0.25 degrees, Global, Science Quality

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — Aviso Sea Surface Height Deviation is the deviation from the mean geoid as measured from 1993 - 1995. This is Science Quality data.

48 CFR 201.404 - Class deviations.

Science.gov (United States)

2010-10-01

..., and the Defense Logistics Agency, may approve any class deviation, other than those described in 201...) Diminish any preference given small business concerns by the FAR or DFARS; or (D) Extend to requirements imposed by statute or by regulations of other agencies such as the Small Business Administration and the...

Large deviations in the presence of cooperativity and slow dynamics

Science.gov (United States)

Whitelam, Stephen

2018-06-01

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative or when its basic time scale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change in shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition but do not necessarily do so.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

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

2000-01-01

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

The phonatory deviation diagram: a novel objective measurement of vocal function.

Science.gov (United States)

Madazio, Glaucya; Leão, Sylvia; Behlau, Mara

2011-01-01

To identify the discriminative characteristics of the phonatory deviation diagram (PDD) in rough, breathy and tense voices. One hundred and ninety-six samples of normal and dysphonic voices from adults were submitted to perceptual auditory evaluation, focusing on the predominant vocal quality and the degree of deviation. Acoustic analysis was performed with the VoxMetria (CTS Informatica). Significant differences were observed between the dysphonic and normal groups (p < 0.001), and also between the breathy and rough samples (p = 0.044) and the breathy and tense samples (p < 0.001). All normal voices were positioned in the inferior left quadrant, 45% of the rough voices in the inferior right quadrant, 52.6% of the breathy voices in the superior right quadrant and 54.3% of the tense voices in the inferior left quadrant of the PDD. In the inferior left quadrant, 93.8% of voices with no deviation were located and 72.7% of voices with mild deviation; voices with moderate deviation were distributed in the inferior and superior right quadrants, the latter ones containing the most deviant voices and 80% of voices with severe deviation. The PDD was able to discriminate normal from dysphonic voices, and the distribution was related to the type and degree of voice alteration. Copyright © 2011 S. Karger AG, Basel.

Statistical properties of the deviations of f 0 F 2 from monthly medians

Directory of Open Access Journals (Sweden)

Y. Tulunay

2002-06-01

Full Text Available The deviations of hourly f 0 F 2 from monthly medians for 20 stations in Europe during the period 1958-1998 are studied. Spectral analysis is used to show that, both for original data (for each hour and for the deviations from monthly medians, the deterministic components are the harmonics of 11 years (solar cycle, 1 year and its harmonics, 27 days and 12 h 50.49 m (2nd harmonic of lunar rotation period L 2 periodicities. Using histograms for one year samples, it is shown that the deviations from monthly medians are nearly zero mean (mean < 0.5 and approximately Gaussian (relative difference range between %10 to %20 and their standard deviations are larger for daylight hours (in the range 5-7. It is shown that the amplitude distribution of the positive and negative deviations is nearly symmetrical at night hours, but asymmetrical for day hours. The positive and negative deviations are then studied separately and it is observed that the positive deviations are nearly independent of R12 except for high latitudes, but negative deviations are modulated by R12 . The 90% confidence interval for negative deviations for each station and each hour is computed as a linear model in terms of R12. After correction for local time, it is shown that for all hours the confidence intervals increase with latitude but decrease above 60N. Long-term trend analysis showed that there is an increase in the amplitude of positive deviations from monthly means irrespective of the solar conditions. Using spectral analysis it is also shown that the seasonal dependency of negative deviations is more accentuated than the seasonal dependency of positive deviations especially at low latitudes. In certain stations, it is also observed that the 4th harmonic of 1 year corresponding to a periodicity of 3 months, which is missing in f 0 F 2 data, appears in the spectra of negative variations.

VAR Portfolio Optimal: Perbandingan Antara Metode Markowitz Dan Mean Absolute Deviation

OpenAIRE

Sartono, R. Agus; Setiawan, Arie Andika

2006-01-01

Portfolio selection method which have been introduced by Harry Markowitz (1952) used variance or deviation standard as a measure of risk. Kanno and Yamazaki (1991) introduced another method and used mean absolute deviation as a measure of risk instead of variance. The Value-at Risk (VaR) is a relatively new method to capitalized risk that been used by financial institutions. The aim of this research is compare between mean variance and mean absolute deviation of two portfolios. Next, we attem...

Black holes in brane worlds

Indian Academy of Sciences (India)

Abstract. A Kerr metric describing a rotating black hole is obtained on the three brane in a five-dimensional Randall-Sundrum brane world by considering a rotating five-dimensional black string in the bulk. We examine the causal structure of this space-time through the geodesic equations.

Excess molar volumes and deviation in viscosities of binary liquid mixtures of acrylic esters with hexane-1-ol at 303.15 and 313.15K

OpenAIRE

Patil, Sujata S.; Mirgane, Sunil R.; Arbad, Balasaheb R.

2014-01-01

Densities and viscosities for the four binary liquid mixtures of methyl acrylate, ethyl acrylate, butyl acrylate and methyl methacrylate with hexane-1-ol at temperatures 303.15 and 313.15 K and at atmospheric pressure were measured over the entire composition range. These values were used to calculate excess molar volumes and deviation in viscosities which were fitted to Redlich–Kister polynomial equation. Recently proposed Jouyban Acree model was also used to correlate the experimental value...

Large deviation function for a driven underdamped particle in a periodic potential

Science.gov (United States)

Fischer, Lukas P.; Pietzonka, Patrick; Seifert, Udo

2018-02-01

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.

On the geodesic incompleteness of spacetimes containing marginally (outer) trapped surfaces

International Nuclear Information System (INIS)

Costa e Silva, I P

2012-01-01

In a recent paper, Eichmair et al (2012 arXiv:1204.0278v1) have proved a Gannon–Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. A natural question is whether the corresponding incomplete geodesics could still be complete in a possible non-globally hyperbolic extension of spacetime. In this paper, some variants of their result are given with weaker causality assumptions, thus suggesting that the answer is generically negative, at least if the putative extension has no closed timelike curves. We consider first marginally trapped surfaces (MTS) in chronological spacetimes, introducing the natural notion of a generic MTS, a notion also applicable to MOTS. In particular, a Hawking–Penrose-type singularity theorem is proven in chronological spacetimes with dimension n ⩾ 3 containing a generic MTS. Such surfaces naturally arise as cross-sections of quasi-local generalizations of black hole horizons, such as dynamical and trapping horizons, and we discuss some natural conditions which ensure the existence of MTS in initial data sets. Nevertheless, much of the more recent literature has focused on MOTS rather than MTS as quasi-local substitutes for the description of black holes, as they are arguably more natural and easier to handle in a number of situations. It is therefore pertinent to ask to what extent one can deduce the existence of singularities in the presence of MOTS alone. We address this issue and show that singularities indeed arise in the presence of generic MOTS, but under slightly stronger causal conditions than those in the case of MTS (specifically, for causally simple spacetimes). On the other hand, we show that with additional conditions on the MOTS itself, namely that it is either the boundary of a compact spatial region, or strictly stable in a suitable sense, a Penrose–Hawking-type singularity theorem can still be established for

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

International Nuclear Information System (INIS)

Cohl, H S; Kalnins, E G

2012-01-01

Due to the isotropy of d-dimensional hyperbolic space, there exists a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hyperboloid model of hyperbolic geometry with R > 0 represents a Riemannian manifold with negative-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the hyperbolic sine, finite summation expressions over hyperbolic functions, Gauss hypergeometric functions and in terms of the associated Legendre function of the second kind with order and degree given by d/2 − 1 with real argument greater than unity. We also demonstrate uniqueness for a fundamental solution of Laplace’s equation on this manifold in terms of a vanishing decay at infinity. In rotationally invariant coordinate systems, we compute the azimuthal Fourier coefficients for a fundamental solution of Laplace’s equation on the R-radius hyperboloid. For d ⩾ 2, we compute the Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace’s equation on this negative-constant curvature Riemannian manifold. In three dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace’s equation is obtained through comparison with its corresponding Gegenbauer expansion. (paper)

Evolutionary implications of genetic code deviations

International Nuclear Information System (INIS)

Chela Flores, J.

1986-07-01

By extending the standard genetic code into a temperature dependent regime, we propose a train of molecular events leading to alternative coding. The first few examples of these deviations have already been reported in some ciliated protozoans and Gram positive bacteria. A possible range of further alternative coding, still within the context of universality, is pointed out. (author)

A novel solution to the Klein–Gordon equation in the presence of a strong rotating electric field

Directory of Open Access Journals (Sweden)

E. Raicher

2015-11-01

Full Text Available The Klein–Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects the emission processes and the particle motion in Quantum Electrodynamics (QED cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised.

The role of conformal symmetry in gravity and the standard model

NARCIS (Netherlands)

Lucat, Stefano; Prokopec, Tomislav

2016-01-01

In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a symmetry of both the geodesic equation and the Riemann tensor. We

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating ...

Enterprise Analysis of Strategic Airlift to Obtain Competitive Advantage Through Fuel Efficiency

Science.gov (United States)

2014-09-18

case risk scenarios. Ruan, Zhang, Miao and Shen (2011) combined the vehicle loading and capacitated VRP. Their hybrid approach utilized honey bee ...Scott AFB, IL: HQ AMC/A3V. Vincenty, T. (1975). Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations. FE

Full-field transmission-type angle-deviation optical microscope with reflectivity-height transformation.

Science.gov (United States)

Chiu, Ming-Hung; Tan, Chen-Tai; Tsai, Ming-Hung; Yang, Ya-Hsin

2015-10-01

This full-field transmission-type three-dimensional (3D) optical microscope is constructed based on the angle deviation method (ADM) and the algorithm of reflectivity-height transformation (RHT). The surface height is proportional to the deviation angle of light passing through the object. The angle deviation and surface height can be measured based on the reflectivity closed to the critical angle using a parallelogram prism and two CCDs.

A course on large deviations with an introduction to Gibbs measures

CERN Document Server

Rassoul-Agha, Firas

2015-01-01

This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the ...

Isothermal equation of state of a lithium fluoride single crystal

Energy Technology Data Exchange (ETDEWEB)

Kim, K.Y.

1975-01-01

An isothermal equation of state of a LiF single crystal was determined from length change measurements of the specimen as a function of hydrostatic pressure up to approximately 7 kbars at 28 to 41/sup 0/C. The length change was measured with an accuracy of approximately 500 A by using a Fabry Perot type He--Ne laser interferometer for a 1-m long specimen at temperatures constant to less than 0.002/sup 0/C. Several two- and three-parameter equations of state were used in analyzing the measured pressure-volume data. The computer fit for each equation of state determines not only the value of its parameters but also the standard deviations associated with them and one dependent variable, either pressure or volume. With the parameters determined, the equations of state are extrapolated to approximately 5 megabars in order to see discrepancies. Using the Born model of ionic solids, two equations of state were derived both from a power law potential and from an exponential form for the repulsive energy of alkali metal halides and used to fit the pressure-volume data of a LiF single crystal. They are also extrapolated to approximately 5 megabars. The Birch's two-parameter equation and the Grover, Getting, and Kennedy equation are indistinguishable from the two equations of state derived from the Born model for pressures approximately equal to or less than 800 kbars within +-20 kbars. The above four equations of state also fit closely the Pagannone and Drickamer static compression data, the Christian shock wave data, and the Kormer et al. shock wave data. The isothermal bulk modulus and its first pressure derivative at atmospheric pressure and 28.83/sup 0/C are 664.5 +- 0.5 kbars and 5.40 +- 0.18, respectively, in close agreement with those values ultrasonically measured by R. A. Miller and C. S. Smith. (auth)

Governing equations for a seriated continuum: an unequal velocity model for two-phase flow

International Nuclear Information System (INIS)

Solbrig, C.W.; Hughes, E.D.

1975-05-01

The description of the flow of two-phase fluids is important in many engineering devices. Unexpected transient conditions which occur in these devices cannot, in general, be treated with single-component momentum equations. Instead, the use of momentum equations for each phase is necessary in order to describe the varied transient situations which can occur. These transient conditions can include phases moving in the opposite directions, such as steam moving upward and liquid moving downward, as well as phases moving in the same direction. The derivation of continuity and momentum equations for each phase and an overall energy equation for the mixture are presented. Terms describing interphase forces are described. A seriated (series of) continuum is distinguished from an interpenetrating medium by the representation of interphase friction with velocity differences in the former and velocity gradients in the latter. The seriated continuum also considers imbedded stationary solid surfaces such as occur in nuclear reactor cores. These stationary surfaces are taken into account with source terms. Sufficient constitutive equations are presented to form a complete set of equations. Methods are presented to show that all these coefficients are determinable from microscopic models and well known experimental results. Comparison of the present deviation with previous work is also given. The equations derived here may also be employed in certain multiphase, multicomponent flow applications. (U.S.)

Constraints on the nature of inertial motion arising from the universality of free fall and the conformal causal structure of space-time

International Nuclear Information System (INIS)

Coleman, R.A.; Korte, H.

1984-01-01

According to the principle of the universality of free fall, the motions of all neutral monopole particles are governed by one common path structure. This principle does not, however, require the path structure to be geodesic; that is, the path structure need not be a projective structure. It is shown that any equation of motion structure (either a curve or a path structure) that has sufficient microisotropy to be compatible with the conformal causal structure of space-time must be geodesic and must be unique. Hence, the empirically well-supported principles of conformal causality and of the universality of free fall together require the existence of a unique Weyl structure on space-time

The parameter of the dark energy equation of state for high redshifts

International Nuclear Information System (INIS)

Montiel, Ariadna; Breton, Nora

2011-01-01

We study the behavior of the parameter w(z) of the dark-energy equation of state, P x = w(z)ρ x , as function of the redshift data from GRBs, to check its deviations from its most accepted value of -1. To this end we first find a reasonable calibration for the GRB in order to extract the luminosity distance d L as a function of the redshift. Then we proceed to calculate the Hubble function H(z) and w(z).

Analysis of form deviation in non-isothermal glass molding

Science.gov (United States)

Kreilkamp, H.; Grunwald, T.; Dambon, O.; Klocke, F.

2018-02-01

Especially in the market of sensors, LED lighting and medical technologies, there is a growing demand for precise yet low-cost glass optics. This demand poses a major challenge for glass manufacturers who are confronted with the challenge arising from the trend towards ever-higher levels of precision combined with immense pressure on market prices. Since current manufacturing technologies especially grinding and polishing as well as Precision Glass Molding (PGM) are not able to achieve the desired production costs, glass manufacturers are looking for alternative technologies. Non-isothermal Glass Molding (NGM) has been shown to have a big potential for low-cost mass manufacturing of complex glass optics. However, the biggest drawback of this technology at the moment is the limited accuracy of the manufactured glass optics. This research is addressing the specific challenges of non-isothermal glass molding with respect to form deviation of molded glass optics. Based on empirical models, the influencing factors on form deviation in particular form accuracy, waviness and surface roughness will be discussed. A comparison with traditional isothermal glass molding processes (PGM) will point out the specific challenges of non-isothermal process conditions. Furthermore, the underlying physical principle leading to the formation of form deviations will be analyzed in detail with the help of numerical simulation. In this way, this research contributes to a better understanding of form deviations in non-isothermal glass molding and is an important step towards new applications demanding precise yet low-cost glass optics.

Incorporating assumption deviation risk in quantitative risk assessments: A semi-quantitative approach

International Nuclear Information System (INIS)

Khorsandi, Jahon; Aven, Terje

2017-01-01

Quantitative risk assessments (QRAs) of complex engineering systems are based on numerous assumptions and expert judgments, as there is limited information available for supporting the analysis. In addition to sensitivity analyses, the concept of assumption deviation risk has been suggested as a means for explicitly considering the risk related to inaccuracies and deviations in the assumptions, which can significantly impact the results of the QRAs. However, challenges remain for its practical implementation, considering the number of assumptions and magnitude of deviations to be considered. This paper presents an approach for integrating an assumption deviation risk analysis as part of QRAs. The approach begins with identifying the safety objectives for which the QRA aims to support, and then identifies critical assumptions with respect to ensuring the objectives are met. Key issues addressed include the deviations required to violate the safety objectives, the uncertainties related to the occurrence of such events, and the strength of knowledge supporting the assessments. Three levels of assumptions are considered, which include assumptions related to the system's structural and operational characteristics, the effectiveness of the established barriers, as well as the consequence analysis process. The approach is illustrated for the case of an offshore installation. - Highlights: • An approach for assessing the risk of deviations in QRA assumptions is presented. • Critical deviations and uncertainties related to their occurrence are addressed. • The analysis promotes critical thinking about the foundation and results of QRAs. • The approach is illustrated for the case of an offshore installation.

A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

International Nuclear Information System (INIS)

Davis, Paul

2006-01-01

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable

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

Science.gov (United States)

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

Does standard deviation matter? Using "standard deviation" to quantify security of multistage testing.

Science.gov (United States)

Wang, Chun; Zheng, Yi; Chang, Hua-Hua

2014-01-01

With the advent of web-based technology, online testing is becoming a mainstream mode in large-scale educational assessments. Most online tests are administered continuously in a testing window, which may post test security problems because examinees who take the test earlier may share information with those who take the test later. Researchers have proposed various statistical indices to assess the test security, and one most often used index is the average test-overlap rate, which was further generalized to the item pooling index (Chang & Zhang, 2002, 2003). These indices, however, are all defined as the means (that is, the expected proportion of common items among examinees) and they were originally proposed for computerized adaptive testing (CAT). Recently, multistage testing (MST) has become a popular alternative to CAT. The unique features of MST make it important to report not only the mean, but also the standard deviation (SD) of test overlap rate, as we advocate in this paper. The standard deviation of test overlap rate adds important information to the test security profile, because for the same mean, a large SD reflects that certain groups of examinees share more common items than other groups. In this study, we analytically derived the lower bounds of the SD under MST, with the results under CAT as a benchmark. It is shown that when the mean overlap rate is the same between MST and CAT, the SD of test overlap tends to be larger in MST. A simulation study was conducted to provide empirical evidence. We also compared the security of MST under the single-pool versus the multiple-pool designs; both analytical and simulation studies show that the non-overlapping multiple-pool design will slightly increase the security risk.

FITTING AND TESTING ALLOMETRIC EQUATIONS FOR MEXICO’S SINALOAN TROPICAL DRY TREES AND FOREST INVENTORY PLOTS

Directory of Open Access Journals (Sweden)

Jose de Jesus Navar Chaidez

2016-05-01

Full Text Available Aboveground tree biomass (bole, branches and foliage, M, plays a key role in the conventional and sustainable management of forest communities. The standard approach to assess tree or plot M is harvesting trees, developing and fitting allometric equations to trees or forest inventory plot data. In the absence of local tree allometry, it is usually recommended to fit off site allometric equations to evaluate tree or plot M. This research aims: (a to develop an updated on site allometric equation (b to fit available off site allometric equations to destructively harvested trees and (c to fit available allometric equations to plot M of Mexico’s Sinaloan tropical dry forests to understand sources of inherent tree and plot M variability. Results showed that: (a the improved on site allometric equation increases precision in contrast to the conventional biomass equation previously reported as well as to off site tree M equations, (b off site allometry projects tree and plot M deviates by close to one order of magnitude. Two tested and recommended approaches to increase tree and plot M precision when fitting off site equations are: (i to use all available tree allometric functions to come up with a mean equation or (ii to calibrate off site equations by fitting new, local parameters that can be calculated using statistical programs.These options would eventually increase tree and plot M precision in regional evaluations.

Precision analysis for standard deviation measurements of immobile single fluorescent molecule images.

Science.gov (United States)

DeSantis, Michael C; DeCenzo, Shawn H; Li, Je-Luen; Wang, Y M

2010-03-29

Standard deviation measurements of intensity profiles of stationary single fluorescent molecules are useful for studying axial localization, molecular orientation, and a fluorescence imaging system's spatial resolution. Here we report on the analysis of the precision of standard deviation measurements of intensity profiles of single fluorescent molecules imaged using an EMCCD camera.We have developed an analytical expression for the standard deviation measurement error of a single image which is a function of the total number of detected photons, the background photon noise, and the camera pixel size. The theoretical results agree well with the experimental, simulation, and numerical integration results. Using this expression, we show that single-molecule standard deviation measurements offer nanometer precision for a large range of experimental parameters.

Features of a relativistic space-time with seven isometries

International Nuclear Information System (INIS)

Reboucas, M.J.; Teixeira, A.F.F.

1986-01-01

Previous works on the Reboucas-Tiomno spacetime are extended. It is shown that the RT model is Petrov type 0 and exhibit its conformally flat form. The geodesic equations are fully integrated and corresponding motions are discussed at lenght. Confrontation with other rare solutions possessing seven isometries is made. (Author) [pt

A correlational study of scoliosis and trunk balance in adult patients with mandibular deviation.

Directory of Open Access Journals (Sweden)

Shuncheng Zhou

Full Text Available Previous studies have confirmed that patients with mandibular deviation often have abnormal morphology of their cervical vertebrae. However, the relationship between mandibular deviation, scoliosis, and trunk balance has not been studied. Currently, mandibular deviation is usually treated as a single pathology, which leads to poor clinical efficiency. We investigated the relationship of spine coronal morphology and trunk balance in adult patients with mandibular deviation, and compared the finding to those in healthy volunteers. 35 adult patients with skeletal mandibular deviation and 10 healthy volunteers underwent anterior X-ray films of the head and posteroanterior X-ray films of the spine. Landmarks and lines were drawn and measured on these films. The axis distance method was used to measure the degree of scoliosis and the balance angle method was used to measure trunk balance. The relationship of mandibular deviation, spine coronal morphology and trunk balance was evaluated with the Pearson correlation method. The spine coronal morphology of patients with mandibular deviation demonstrated an "S" type curve, while a straight line parallel with the gravity line was found in the control group (significant difference, p1°, while the control group had a normal trunk balance (imbalance angle <1°. There was a significant difference between the two groups (p<0.01. The degree of scoliosis and shoulder imbalance correlated with the degree of mandibular deviation, and presented a linear trend. The direction of mandibular deviation was the same as that of the lateral bending of thoracolumbar vertebrae, which was opposite to the direction of lateral bending of cervical vertebrae. Our study shows the degree of mandibular deviation has a high correlation with the degree of scoliosis and trunk imbalance, all the three deformities should be clinically evaluated in the management of mandibular deviation.