On the applicability of the geodesic deviation equation in General Relativity
Philipp, Dennis; Laemmerzahl, Claus
2016-01-01
Within the theory of General Relativity we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. The deviation equation is used to model satellite orbit constellations around the earth. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity. The deviation of nearby orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in Schwarzschild spacetime.
Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation
Lacquaniti, V; Vietri, F; 10.1007/s10714-009-0853-3
2009-01-01
In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $\\phi=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $\\phi$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.
A Brief Comment on Geodesic Deviation Equation in f(R) Gravity
Guarnizo, Alejandro; Tejeiro, Juan M
2014-01-01
In the context of metric $f(R)$ gravity, the Geodesic Deviation Equation (GDE) was first studied in arXiv:1010.5279v3, giving a general expression and studying a particular case, the FLRW universe. Recently, a new work appears arXiv:1312.2022v1 making a similar analysis. However, there is a discrepancy in the expressions for the null vector field case. Here we make explicit the contribution of the different operators in the GDE, finding the differences with our previous result.
On geodesic deviation in Schwarzschild spacetime
Philipp, Dennis; Laemmerzahl, Claus; Deshpande, Kaustubh
2015-01-01
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for...
Geodesics and Geodesic Deviation for Impulsive Gravitational Waves
Steinbauer, R
1998-01-01
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac delta distribution. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this problem we proceed by first regularizing the delta singularity, then solving the regularized equation within classical smooth functions and, finally, obtaining a distributional, regularization-idependent limit as solution to the original problem. We also treat the Jacobi equation which, despite being linear in the deviation vector field, involves even more delicate singular expressions, like the ``square'' of the delta distribution. Again the same regularization procedure provides us with a perfectly well behaved smooth regularization and a regularization-independent distributi...
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Geralico, Andrea; Jantzen, Robert T.
2011-04-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Jantzen, Robert T
2014-01-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Spin-geodesic deviations in the Kerr spacetime
Bini, D.; Geralico, A.
2011-11-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Spin-geodesic deviations in the Kerr spacetime
Bini, Donato
2014-01-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Interpreting spacetimes of any dimension using geodesic deviation
Podolsky, Jiri
2012-01-01
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corres...
Geodesic deviation in Kundt spacetimes of any dimension
Svarc, Robert
2012-01-01
Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type III, and type N purely transverse effects corresponding to gravitational waves with D(D-3)/2 independent polarization states. We explicitly study the most important examples, namely exact pp-waves, gyratons, and VSI spacetimes. This analysis helps us to clarify the geometrical and physical interpretation of the Kundt class of nonexpanding, nontwisting and shearfree geometries.
Relativistic and non-relativistic geodesic equations
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Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
Bini, Donato
2013-01-01
The deviation from geodesic motion of the world line of an extended body endowed with multipolar structure up to the mass quadrupole moment is studied in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The properties of the quadrupole tensor are clarified by identifying the relevant components which enter the equations of motion, leading to the definition of an effective quadrupole tensor sharing its own algebraic symmetries, but also obeying those implied by the Mathisson-Papapetrou-Dixon model itself. The equations of motion are then solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables in comparison with the one associated with the background curvature and under special assumptions on body's structure and motion. The resulting quasi-circular orbit is parametrized in a Keplerian-like form, so that temporal, radial and azimuthal eccentricities as well as semi-major axis, period and periastron advance are e...
Lie symmetries of the geodesic equations and projective collineations
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Tsamparlis, Michael; Paliathanasis, Andronikos, E-mail: mtsampa@phys.uoa.g, E-mail: paliathanasis@gmail.co [Department of Physics, Section Astrophysics Astronomy Mechanics, University of Athens, University of Athens, Zografos 15783, Athens (Greece)
2009-10-01
We study the Lie symmetries of the geodesic equations in a Riemannian space and show that they coincide with the projective symmetries of the Riemannian metric. We apply the result to the spaces of constant curvature.
Geodesic deviation in a nonlinear gravitational wave spacetime
Culetu, Hristu
2016-01-01
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\\xi^{v}$ and $\\xi^{u}$ of the separation vector behave as in flat space but the transversal components $\\xi^{x}$ and $\\xi^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
3+1 geodesic equation and images in numerical spacetimes
Vincent, Frederic H; Novak, Jérôme
2012-01-01
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.
About some diophantine equation and the resulting chaos in geodesics
Perrine, Serge
2001-06-01
We announce results about a complete Markoff theory for the diophantine equation: x2+y2+z2=3xyz+2x All its solutions can be computed. For positive integers, they are organized in two trees. With them, we build a new tree thanks to related continued fractions, and associated binary quadratic forms. In an infinite number of cases, the corresponding approximation and Markoff constants have the form: ((m-2)/√9m2-4 ) For other cases, we conjecture the expression of the constants. All of them converge towards (1/3) by lower values, similarly but differently from the classical Markoff theory. We conclude considering very briefly the link between such equations and geodesics on some Riemann surfaces.
Rational first integrals of geodesic equations and generalised hidden symmetries
Aoki, Arata; Tomoda, Kentaro
2016-01-01
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O'Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.
Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes
Flathmann, Kai
2016-01-01
In this article we derive the geodesic equations in the $\\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\\sigma$-function and in special cases in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.
Flathmann, Kai
2015-01-01
In this article we study the geodesic motion of test particles and light in the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types.
Exact solutions to the geodesic equations of linear dilaton black holes
Hamo, A H H
2015-01-01
In this paper, we analyze the geodesics of the 4-dimensional ($4D$) linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. LDBHs have non-asymptotically flat (NAF) geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange (EL) equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the WeierstrassP-function ($\\wp$-function), which is an elliptic-type special function.
On Non-commutative Geodesic Motion
Ulhoa, S C; Santos, A F
2013-01-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
On non-commutative geodesic motion
Ulhoa, S. C.; Amorim, R. G. G.; Santos, A. F.
2014-07-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
Kazempour, Sobhan; Soroushfar, Saheb
2016-01-01
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.
Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb
2017-03-01
A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.
Soroushfar, Saheb; Saffari, Reza; Sahami, Ehsan
2016-07-01
In this paper, we consider the timelike and null geodesics around the static (GMGHS, magnetically charged GMGHS, electrically charged GMGHS) and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained results we study astrophysical applications.
Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
Ren, Jiagang; Zhang, Xicheng
2008-01-01
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.
Hackmann, Eva
2015-01-01
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer Anomaly is addressed. The periastron shift and its post--Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space--times.
Soroushfar, Saheb; Kazempour, Sobhan; Grunau, Saskia; Kunz, Jutta
2016-01-01
We study the geodesic equations in the space time of a rotating charged black hole in $f(R)$ gravity. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\\wp$, $\\zeta$ and $\\sigma$ functions as well as the Kleinian $\\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types.
Nonrelativistic Geodesic Motion
Mangiarotti, L
1999-01-01
We show that any second order dynamic equation on a configuration space $X\\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.
Geodesic Motion in a Charged 2D Stringy Blackhole Spacetime
Uniyal, Rashmi; Purohit, K D
2014-01-01
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacetime.
Large Deviations for Multi-valued Stochastic Differential Equations
Ren, Jiagang; Zhang, Xicheng
2009-01-01
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
2005-01-18
equations are: 0212 2 = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ ∂ + z c d dz x c d dx t c d dt d dt cd td λλλλλ... td , (37) 0 2 2 2 =⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + dx dt z cc dx zd...calculation the sound-speed profile ( )CzKCzc /cosh)( 0= produces a space of constant positive curvature 0KK = . The deviation vector can be solved
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El-Nabulsi Rami Ahmad
2016-07-01
Full Text Available Starting with an extended complex backwardforward derivative operator in differential geometry which is motivated from non-local-in-time Lagrangian dynamics, higher-order geodesic equations are obtained within classical differential geometrical settings. We limit our analysis up to the 2nd-order derivative where some applications are discussed and a number of features are revealed accordingly.
Ahangari, Fatemeh
2017-01-01
Scalar-field cosmology can be regarded as one of the significant fields of research in recent years. This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory. The mentioned string inspired Friedmann-Robertson-Lamai ^tre-Walker (FRLW) solution is one of the noteworthy solutions of Einstein field equations. For this purpose, first of all the Christoffel symbols and the corresponding system of geodesic equations are computed and then the associated Lie symmetries are totally analyzed. Moreover, the algebraic structure of the Lie algebra of local symmetries is briefly investigated and a complete classification of the symmetry subalgebras is presented. Besides by applying the resulted symmetry operators the invariant solutions of the system of geodesic equations are discussed. In addition, the Noether symmetries and the Killing vector fields of the geodesic Lagrangian are determined and the corresponding optimal system of one-dimensional subalgebras is constructed. Mainly, an entire set of local conservation laws is computed for our analyzed scalar-field cosmological solution. For this purpose, two distinct procedures are applied: the celebrated Noether's theorem and the direct method which is fundamentally based on a systematic application of Euler differential operators which annihilate any divergence expression identically.
Energy Technology Data Exchange (ETDEWEB)
Rowland, D R [Student Support Services, University of Queensland, Brisbane QLD 4072 (Australia)
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
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.
Oscillation in second order functional equations with deviating arguments
Bhagat Singh
1981-01-01
For the pair of functional equations (A)(r(t)y′(t))+p(t)h(h(g(t)))=f(t) and (B)(r(t)y′(t))−p(t)h(y(g(t)))=0 sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory. These conditions depend upon a positive solution of equation (B).
Moderate Deviation Principles for Stochastic Differential Equations with Jumps
2014-01-15
random measure and an in�nite dimensional Brownian motion) was derived. As in the Brownian motion case, the representation is motivated in part by...deviations of a smaller order than in large deviation theory . Consider for example an independent and identically distributed (iid) sequence fYigi1 of...8217") " E " 1 2 Z X[0;T ] ( ")21fj "jB"gdT + F G "("N " 1’") # " 1 2 3M 2(1); (3.6) where the last inequality follows from (3.5) on
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.
Nonlinear oscillations in disconjugate forced functional equations with deviating arguments
Bhagat Singh
1983-01-01
For the equation Lnv(t)+a(t)h(y(g(t)))=f(t) where Lny(t)=pn(t)(pn−1(t)(…(p1(t)(po(t)y(t))′)′…)′)′ sufficient conditions have been found for all of its solutions to be oscillatory. The conditions found also lead to growth estimates for tle nonoscillatory solutions.
Nonlinear oscillations in disconjugate forced functional equations with deviating arguments
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Bhagat Singh
1983-01-01
Full Text Available For the equation Lnv(t+a(th(y(g(t=f(t where Lny(t=pn(t(pn−1(t(…(p1(t(po(ty(t′′…′′ sufficient conditions have been found for all of its solutions to be oscillatory. The conditions found also lead to growth estimates for tle nonoscillatory solutions.
PERIODIC SOLUTIONS TO p-LAPLACIAN GENERALIZED LINARD EQUATION WITH DEVIATING ARGUMENTS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using the theory of coincidence degree,we study a kind of periodic solutions to p-Laplacian generalized Liénard equation with deviating arguments. A result on the existence of periodic solutions is obtained.
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
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
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.
Solutions to quasi-linear differential equations with iterated deviating arguments
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Rajib Haloi
2014-12-01
Full Text Available We establish sufficient conditions for the existence and uniqueness of solutions to quasi-linear differential equations with iterated deviating arguments, complex Banach space. The results are obtained by using the semigroup theory for parabolic equations and fixed point theorems. The main results are illustrated by an example.
On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument
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Došlá Z
2008-01-01
Full Text Available Abstract The half-linear difference equations with the deviating argument , are considered. We study the role of the deviating argument , especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover, the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation ( = 1. Some analogies or discrepancies on the growth of the nonoscillatory solutions for the delayed and advanced equations are presented; and the coexistence with different types of nonoscillatory solutions is studied.
Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure
Budhiraja, Amarjit; Dupuis, Paul
2012-01-01
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equations (PDE). A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative func...
Kardar-Parisi-Zhang Equation and Large Deviations for Random Walks in Weak Random Environments
Corwin, Ivan; Gu, Yu
2017-01-01
We consider the transition probabilities for random walks in 1+1 dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.
Directory of Open Access Journals (Sweden)
Pradeep Kumar
2013-10-01
Full Text Available The objective of this article is to prove the existence of piecewise continuous mild solutions to impulsive functional differential equation with iterated deviating arguments in a Banach space. The results are obtained by using the theory of analytic semigroups and fixed point theorems.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we study an even order neutral differential equation with deviating arguments, and obtain new oscillation results without the assumptions which were required for related results given before. Our results extend and improve many known oscillation criteria, based on the standard integral averaging technique.
On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument
Directory of Open Access Journals (Sweden)
M. Marini
2008-08-01
Full Text Available The half-linear difference equations with the deviating argument ÃŽÂ”(an|ÃŽÂ”xn|ÃŽÂ±sgnÃ¢Â€Â‰ÃŽÂ”xn+bn|xn+q|ÃŽÂ±sgnÃ¢Â€Â‰xn+q=0 , qÃ¢Â€Â‰Ã¢ÂˆÂˆÃ¢Â€Â‰Ã¢Â„Â¤ are considered. We study the role of the deviating argument q, especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover, the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation (q = 1. Some analogies or discrepancies on the growth of the nonoscillatory solutions for the delayed and advanced equations are presented; and the coexistence with different types of nonoscillatory solutions is studied.
Large deviations for a stochastic Landau-Lifshitz equation, extended version
Brzeźniak, Z; Jegaraj, T
2012-01-01
We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise; this could be a simple model of magnetization in a needle-shaped domain in magnetic media. After showing that a unique, regular solution exists, we obtain a large deviation principle for small noise asymptotics of solutions using the weak convergence method. We then apply the large deviation principle to show that small noise in the field can cause magnetization reversal and also to show the importance of the shape anisotropy parameter for reducing the disturbance of the magnetization caused by small noise in the field.
Universal Large-Deviation Function of the Kardar-Parisi-Zhang Equation in One Dimension
Derrida, B.; Appert, C.
1999-01-01
Using the Bethe ansatz, we calculate the whole large-deviation function of the displacement of particles in the asymmetric simple exclusion process (ASEP) on a ring. When the size of the ring is large, the central part of this large deviation function takes a scaling form independent of the density of particles. We suggest that this scaling function found for the ASEP is universal and should be characteristic of all the systems described by the Kardar-Parisi-Zhang equation in 1+1 dimension. Simulations done on two simple growth models are in reasonable agreement with this conjecture.
Hongchuan Yu; Zhang, Jian J.; Zheng Jiao
2014-01-01
We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solution...
On General Plane Fronted Waves. Geodesics
Candela, A M; Sánchez, M; Sanchez, Miguel
2003-01-01
A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = + 2 du dv + H(x,u) du^2$, with $(M_0, $ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity, causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of $H(x,u)$ with $x$ at infinity determines many properties of geodesics. Essentially, a subquadratic growth of $H$ ensures geodesic completeness and connectedness, while the critical situation appears when $H(x,u)$ behaves in some direction as $|x|^2$, as in the classical model of exact gravitational waves
A unified approach to the large deviations for small perturbations of random evolution equations
Institute of Scientific and Technical Information of China (English)
胡亦钧
1997-01-01
Let be the processes governed by the following stochastic differential equations:where v (t) is a random process independent of the Brownian motion B(·).Some large deviation (LD) properties of are proved.For a particular case,an explicit representation of the rate function is also given,which solves a problem posed by Eizenberg and Freidlin.In the meantime,an abstract LD theorem is obtained.
Institute of Scientific and Technical Information of China (English)
CHEN Wen-bin; GAO Fang; LU Shi-ping
2013-01-01
In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument (ϕp(x(t)-cx(t-σ))0)0+f(t, x0(t))+g(t, x(t-τ(t)))=e(t), some new results on the existence of periodic solutions is obtained.
Directory of Open Access Journals (Sweden)
A. A. Adepoju
2009-01-01
Full Text Available Problem statement: All simultaneous equation estimation methods have some desirable asymptotic properties and these properties become effective in large samples. This study is relevant since samples available to researchers are mostly small in practice and are often plagued with the problem of mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The objective of this research was to study the small sample properties of these estimators when the errors are correlated to determine if the properties will still hold when available samples are relatively small and the errors were correlated. Approach: Most of the evidence on the small sample properties of the simultaneous equation estimators was studied from sampling (or Monte Carlo experiments. It is important to rank estimators on the merit they have when applied to small samples. This study examined the performances of five simultaneous estimation techniques using some of the basic characteristics of the sampling distributions rather than their full description. The characteristics considered here are the mean, the total absolute bias and the root mean square error. Results: The result revealed that the ranking of the five estimators in respect of the Average Total Absolute Bias (ATAB is invariant to the choice of the upper (P1 or lower (P2 triangular matrix. The result of the FIML using RMSE of estimates was outstandingly best in the open-ended intervals and outstandingly poor in the closed interval (-0.051 and P2 we re-combined. Conclusion: (i The ranking of the various simultaneous estimation methods considered based on their small sample properties differs according to the correlation status of the error term, the identifiability status of the equation and the assumed triangular matrix. (ii The nature of the relationship under study also determined which of the criteria for judging the
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
Dryuma, V S
1998-01-01
The law of transformation of affine connection for n-dimensional manifolds as the system of nonlinear equations on local coordinates of manifold is considered. The extension of the Darboux-Lame system of equations to the spaces of constant negative curvature is demonstrated. Geodesic deviation equation as well as the equations of geodesics are presented in the form of the matrix Darboux-Lame system of equations.
Geodesically Complete Universe
Bars, Itzhak
2011-01-01
This talk is about solving cosmological equations analytically without approximations, and discovering new phenomena that could not be noticed with approximate solutions. We found all the solutions of the Friedmann equations for a specific model, including all the zero-size-bounce solutions that do not violate the null energy condition, as well as all the finite-size-bounce solutions, and then discovered model independent phenomena. Among them is the notion of geodesic completeness for the geometry of the universe. From this we learned a few new general lessons for cosmology. Among them is that anisotropy provides a model independent attractor mechanism to some specific initial values for cosmological fields, and that there is a period of antigravity in the history of the universe. The results are obtained only at the classical gravity level. Effects of quantum gravity or string theory are unknown, they are not even formulated, so there are new theoretical challenges.
Multimode geodesic branching components
Schulz, D.; Voges, E.
1983-01-01
Geodesic branching components are investigated for multimode guided wave optics. Geodesic structures with particular properties, e.g. focussing star couplers, are derived by a synthesis technique based on a theorem of Toraldo di Francia. Experimentally, the geodesic surfaces are printed on acrylic glass and are spin-coated with organic film waveguides.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.
Equation of Motion of a Spinning Test Particle in Gravitational Field
Institute of Scientific and Technical Information of China (English)
LIU Chang-Yong; WU Ning
2008-01-01
Based on the coupling between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetie field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.
2016-01-01
We study geodesics on surfaces in the setting of classical differential geometry. We define the curvature of curves and surfaces in three-space and use the fundamental forms of a surface to measure lengths, angles, and areas. We follow Riemann and adopt a more abstract approach, and use tensor notation to discuss Gaussian curvature, Gauss's Theorema Egregium, geodesic curves, and the Gauss-Bonnet theorem. Properties of geodesics are proven by variational methods, showing the connection betwee...
Geodesics of simultaneity in Schwarzschild
Paiva, F M
2010-01-01
Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\\mu}\\dd x^\\mu=0$). These geodesics are studied in the exterior region of \\Sch's metric.
Separable geodesic action slicing in stationary spacetimes
Bini, Donato; Jantzen, Robert T
2014-01-01
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlev\\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.
Estakhr, Ahmad Reza
2016-10-01
DJ̲μ/Dτ =J̲ν ∂νU̲μ + ∂νT̲μν +Γαβμ J̲αU̲β ︷ Steady Component + ∂νRμν +Γαβμ Rαβ ︷ Perturbations EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows. The EAMG equations are used to describe Relativistic Jet.
Stability of Geodesically Complete Cosmologies
Creminelli, Paolo; Santoni, Luca; Trincherini, Enrico
2016-01-01
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} \\delta N~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Indian Academy of Sciences (India)
D B Lortan; S D Maharaj; N K Dadhich
2001-06-01
We investigate the propagation equations for the expansion, vorticity and shear for perfect ﬂuid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that ﬂuid ﬂow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic ﬂows: there exist no proper conformal Killing vectors ( ≠ 0) for perfect ﬂuids except for Robertson–Walker space-times. For a nonhomothetic vector ﬁeld the propagation of the quantity ln () along the integral curves of the symmetry vector is homogeneous.
Stability of geodesically complete cosmologies
Energy Technology Data Exchange (ETDEWEB)
Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Pirtskhalava, David [Institute of Physics, École Polytechnique Fédérale de Lausanne,Lausanne, CH-1015 (Switzerland); Santoni, Luca; Trincherini, Enrico [Scuola Normale Superiore,Piazza dei Cavalieri 7, Pisa, 56126 (Italy); INFN - Sezione di Pisa,Largo B. Pontecorvo 3, Pisa, 56100 (Italy)
2016-11-22
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator {sup (3)} RδN is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Focusing of geodesic congruences in an accelerated expanding Universe
Albareti, F D; de la Cruz-Dombriz, A
2012-01-01
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from...
A Large Deviation, Hamilton-Jacobi Equation Approach to a Statistical Theory for Turbulence
2012-09-03
and its associated compressible Euler equations, Comptes Rendus Mathematique , (09 2011): 973. doi: 10.1016/j.crma.2011.08.013 2012/09/03 14:17:15 6...Hamilton-Jacobi PDE is shown to be well-posed. (joint work with T Nguyen, Journal de Mathematique Pures et Appliquees). Future works focusing on large time behavior for such equations is currently under its way. Technology Transfer
Energy Technology Data Exchange (ETDEWEB)
Geethanjali, H.S. [Department of Physics, Bangalore Institute of Technology, Bangalore 560004, Karnataka (India); Nagaraja, D., E-mail: nagarajdd86@gmail.com [Department of Physics, Bangalore Institute of Technology, Bangalore 560004, Karnataka (India); Melavanki, R.M., E-mail: melavanki73@gmail.com [Department of Physics, M S Ramaiah Institute of Technology, Bangalore 560054, Karnataka (India); Kusanur, R.A. [Department of Chemistry, R.V. College of Engineering, Bangalore 560059, Karnataka (India)
2015-11-15
The fluorescence quenching study of two boronic acid derivatives 5-chloro-2-methoxy phenyl boronic acid (5CMPBA) and 4-fluoro-2-methoxyphenyl boronic acid (4FMPBA) in alcohols of varying viscosities is carried out at room temperature by steady state fluorescence measurements. Aniline is used as quencher. The negative deviation in the Stern–Volmer (S–V) plots has been observed for both the molecules with moderate quencher concentration. The downward curvature in the S–V plot is interpreted in terms of existence of different conformers of the solutes in the ground state. The formation of intermolecular and intramolecular hydrogen bonding in alcohol environments is taken to be responsible for the conformational changes in the ground state of the solutes. The modified Stern–Volmer equation or Lehrer equation is used to calculate Stern–Volmer constant (K{sub SV}) and it is found to be above 100 for most of the solvents used. - Highlights: • Fluorescence quenching of two boronic acid derivatives by aniline in alcohols is carried out at room temperature. • A negative deviation is observed in Stern-Volmer(S-V) plots and it is explained using S-V kinetics and Lehrer equation. • The negative deviation observed in the S–V plot is explained in terms of intramolecular and intermolecular hydrogen bond formations.
Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
Directory of Open Access Journals (Sweden)
Zaihong Wang
2013-01-01
Full Text Available We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ=p(t, where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x=g(±∞ exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.
Symmetries of geodesic motion in Gödel-type spacetimes
Energy Technology Data Exchange (ETDEWEB)
Camci, U., E-mail: ucamci@akdeniz.edu.tr [Department of Physics, Akdeniz University, 07058 Antalya (Turkey)
2014-07-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Gödel-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for t-dot , r-dot ,φ-dot and ż of each classes I-IV which depends essentially on two independent parameters m and w, we explicitly integrated the geodesic equations of motion for the corresponding Gödel-type spacetimes.
A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies
Nilsson, Ulf S.; Uggla, Claes; Wainwright, John
2000-10-01
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of space-time anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.
Geodesic congruences in warped spacetimes
Ghosh, Suman; Kar, Sayan
2010-01-01
In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. We begin our investigations with the simplest case, namely geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes. Analytical expressions for the expansion scalar are obtained and the effect of including one or more thin branes (i.e. a background which is a slice of AdS spacetime) on its evolution, is pointed out. Subsequently, we move on to studying such congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using the analytical expressions for the velocity field components, we interpret the expansion, shear and rotation (ESR) along the flows. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in the ba...
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2002-04-01
Full Text Available We study the oscillation of solutions to the differential equation $$ dot{x}(t +a_1(tx[r(t]+a_2(tx[p(t]=0, quad tgeq t_0 $$ which has a retarded argument $r(t$ and an advanced argument $p(t$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results.
Boundedness of solutions for a Lienard equation with multiple deviating arguments
Directory of Open Access Journals (Sweden)
Changhong Zhao
2009-01-01
Full Text Available We consider the Lienard equation $$ x''(t+f_1 (x(t (x'(t^{2}+f_2 (x(t x'(t+g_0(x(t +sum_{j=1}^{m} g_{j}(x(t-au_{j}(t=p(t, $$ where $f_1$, $f_2$, $g_1 $ and $g_2$ are continuous functions, the delays $au_j(tgeq 0$ are bounded continuous, and $p(t$ is a bounded continuous function. We obtain sufficient conditions for all solutions and their derivatives to be bounded.
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.
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
}, D_n\\} +B_n$, where $\\{ (A_n,B_n,D_n): n \\in \\pintegers \\}$ is an i.i.d.\\ sequence of random variables. Next, we consider recursions where the driving sequence of vectors, $\\{(A_n, B_n, D_n): n \\in \\pintegers \\}$, is modulated by a Markov chain in general state space. We demonstrate an asymmetry......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 ${\\bf E} [\\log \\: A......] 0)$, 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...
Closed timelike geodesics in a gas of cosmic strings
Grøn, Ø; Gron, Oyvind; Johannesen, Steinar
2007-01-01
We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.
Spherical geodesic mesh generation
Energy Technology Data Exchange (ETDEWEB)
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Energy Technology Data Exchange (ETDEWEB)
Townsend, Paul K [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Wohlfarth, Mattias N R [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2004-12-07
For gravity coupled to N scalar fields, with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N + 1)-dimensional 'augmented' target space of Lorentzian signature (1, N), timelike if V > 0, null if V = 0 and spacelike if V < 0. Accelerating cosmologies correspond to timelike geodesics that lie within an 'acceleration subcone' of the 'lightcone'. Non-flat (k = {+-}1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N + 2, of signature (1, N + 1) for k = -1 and signature (2, N) for k = +1. This formalism is illustrated by cosmological solutions of models with an exponential potential, which are comprehensively analysed; the late-time behaviour for other potentials of current interest is deduced by comparison.
Townsend, P K; Townsend, Paul K.; Wohlfarth, Mattias N.R.
2004-01-01
For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `extended target space' of Lorentzian signature (1,N), timelike if V>0 and spacelike if V<0. Accelerating cosmologies correspond to timelike geodesics that lie within an `acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N+2, of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. We illustrate these results for various potentials of current interest, including exponential and inverse power potentials.
Geodesics in the (anti-)de Sitter spacetime
Tho, Nguyen Phuc Ky
2016-01-01
A class of exact solutions of the geodesic equations in (anti-)de Sitter spacetimes is presented. The geodesics for test particles in $AdS_4$ and $dS_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. The world lines of test particles are not dependent on their energy as noted. Spontaneous symmetry breaking of $AdS_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in the vacuum. Interestingly, the energy of a pair and the time its particles moving along their geodesics can be related by a relation similar to Heisenberg uncertainty one pertaining quantum vacuum fluctuations. The sinusoidal geodesics of $AdS_4$ spacetime can describe the world lines of the virtual particles and antiparticles. The hyperbolic sine geodesics of $dS_4$ spacetime can explain why galaxies move apart with positive accelerations.
A Perspicuous Description of the Schwarzschild Black Hole Geodesics
Arik, Metin
2016-01-01
Schwarzschild black hole is the simplest black hole that is studied most in detail. Its behavior is best understood by looking at the geodesics of the particles under the influence of its gravitational field. In this paper, the focus of attention is giving a perspicuous description of the Schwarzschild geodesics by using analogue potential approach. Specifically we discuss geodesics of light and of a massive particle in the case that their angular momentum is non zero in the Schwarzschild spacetime. This discussion is done by defining analogue potentials out of geodesic equations and defining relevant dimensionless conserved quantities. Then, we designate how geodesics change in response to the change of these quantities. Our results indicate the relation between the particles' motion near black hole horizon and their angular momentum. Furthermore, we make a comparison between Newtonian Physics (NP) and General Relativity (GR) in the language of the analogue potential approach.
Aichholzer, Oswin; Korman Cozzetti, Matías; Pilz, Alexander; Vogtenhuber, Birgit
2014-01-01
The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset of at least four...
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro; Tamaoka, Kotaro
2017-05-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using a conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show that our construction agrees with the known result of the conformal partial waves.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro
2016-01-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construction agrees with the known result of the conformal partial waves.
Geodesic curvature driven surface microdomain formation.
Adkins, Melissa R; Zhou, Y C
2017-09-15
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Geodesic curvature driven surface microdomain formation
Adkins, Melissa R.; Zhou, Y. C.
2017-09-01
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
On the Geodesic Nature of Wegner's Flow
Itto, Yuichi; Abe, Sumiyoshi
2008-01-01
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is...
On Properties of Geodesic -Preinvex Functions
Directory of Open Access Journals (Sweden)
I. Ahmad
2009-01-01
Full Text Available The present paper deals with the properties of geodesic -preinvex functions and their relationships with -invex functions and strictly geodesic -preinvex functions. The geodesic -pre-pseudo-invex and geodesic -pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.
Geodesic motion on closed spaces: Two numerical examples
Energy Technology Data Exchange (ETDEWEB)
Müller, Daniel, E-mail: muller@fis.unb.br [Universidade de Brasília, Instituto de Física, Cxp 04455, Asa Norte, 70919-900, Brasília, DF (Brazil)
2012-01-09
The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy–momentum tensor in Universes with non-trivial topology. The purpose of this work is to provide concrete numerical examples of geodesic flows. Two manifolds with genus g=0 are given. In one the chaotic regions, form sets of negligible or zero measure. In the second example the geodesic flow shows the presence of measurable chaotic regions. The approach is “experimental”, numerical, and there is no attempt to an analytical calculation. -- Highlights: ► Elementary differential geometry of surfaces and the Gauss–Bonnet theorem. ► The geodesic equation is numerically solved for two metrics on the sphere. ► With the Poincare surface, chaotic and regular regions are identified. ► Chaotic regions increase as the curvature fluctuation of the manifold increases.
Deployable geodesic truss structure
Mikulas, Martin M., Jr. (Inventor); Rhodes, Marvin D. (Inventor); Simonton, J. Wayne (Inventor)
1987-01-01
A deployable geodesic truss structure which can be deployed from a stowed state to an erected state is described. The truss structure includes a series of bays, each bay having sets of battens connected by longitudinal cross members which give the bay its axial and torsional stiffness. The cross members are hinged at their mid point by a joint so that the cross members are foldable for deployment or collapsing. The bays are deployed and stabilized by actuator means connected between the mid point joints of the cross members. Hinged longerons may be provided to also connect the sets of battens and to collapse for stowing with the rest of the truss structure.
Horndeski black hole geodesics
Tretyakova, D A
2016-01-01
We examine geodesics for the scalar-tensor black holes in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits may not be present within some model parameters range. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations. We also present a new (although very similar to those previously known) solution, which contains the orbits we expect from a compact object, admits regular scalar field at the horizon and and can fit into the known stability criteria.
Symmetries of geodesic motion in G\\"{o}del-type spacetimes
Camci, U
2014-01-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for $\\dot{t}, \\dot{r}, \\dot{\\phi}$ and $\\dot{z}$ of each classes I-IV which depends essentially on two independent parameters $m$ and $w$, we explicitly integrated the geodesic equations of motion for the corresponding G\\"{o}del-type spacetimes.
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.
Large Deviations for 2-D Stochastic Navier-Stokes Equations with Jumps%二维带跳Navier-Stokes方程解的大偏差原理
Institute of Scientific and Technical Information of China (English)
赵辉艳
2012-01-01
在带泊松跳二维随机Navier-Stokes方程解的解的存在唯一性的基础上,利用弱收敛的方法证明了带泊松跳二维随机Navier-Stokes方程解的Freidlin-Wentzell型的大偏差原理.%In this paper,under the existence and uniqueness of the solution of stochastic 2-D Navier-Stokes equation,we prove Freidlin-Wentzell＇s large deviation principle for 2-D Stochastic Navier-Stokes Equation driven by multiplicative noise with Poisson jumps by using weak convergence approach.
Institute of Scientific and Technical Information of China (English)
XIANG; Kainan
2001-01-01
［1］ Cruzeiro, A. B., Malliavin, P., Renormalized differential geometry on path spaces: Structural equation, curvature, J. Funct. Anal., 1996, 139: 119-181.［2］ Stroock, D. W., Some thoughts about Riemannian structures on path spaces, preprint, 1996.［3］ Driver, B., A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal., 1992, 109: 272-376.［4］ Enchev, O., Stroock, D. W., Towards a Riemannian geometry on the path space over a Riemannian manifold, J. Funct. Anal., 1995, 134: 392-416.［5］ Hsu, E., Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal., 1995, 134: 417-450.［6］ Lyons, T. J., Qian, Z. M., A class of vector fields on path space, J.Funct. Anal., 1997, 145: 205-223.［7］ Li, X. D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal., to be published.［8］ Driver, B., Towards calculus and geometry on path spaces, in Proc. Symp. Pure and Appl. Math. 57 (ed. Cranston, M., Pinsky, M.), Cornell: AMS, 1993, 1995.
Geodesics and Newton's Law in Brane Backgrounds
Mück, W; Volovich, I V
2000-01-01
In brane world models our universe is considered as a brane imbedded into ahigher dimensional space. We discuss the behaviour of geodesics in theRandall-Sundrum background and point out that free massive particles cannotmove along the brane only. The brane is repulsive, and matter will be expelledfrom the brane into the extra dimension. This is rather undesirable, and hencewe study an alternative model with a non-compact extra dimension, but with anattractive brane embedded into the higher dimensional space. We study thelinearized gravity equations and show that Newton's gravitational law is validon the brane also in the alternative background.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
On the regularity of geodesic rays associated to test configurations
Phong, D. H.; Sturm, Jacob
2007-01-01
Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation. Geometrically, this is accomplished by the use a positive line bundle on the resolution which is trivial outside of the exceptional divisor.
Geodesics in the space of K\\"ahler cone metrics
Calama, Simone
2012-01-01
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\\"ahler cone metrics.
Analytical solutions for geodesics in black hole spacetimes
Hackmann, Eva
2015-01-01
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general timelike and lightlike motion is also presented.
An Efficient Geodesic Path Solution for Prolate Spheroids
1979-07-01
unit tangent vector is determinr 4, the other relevant parameter in the ray analysis , namely, the unit binprmal vector 6 can readily be obtained via...geodesic shown in Fig. S . Recall that the unit tangent vectors for the geodesic are given by Equations (1l)-(15). Assuming at a particular point (e )on the...Aeronautics and Space Adi&inistration, ’,,ashington, D.C. 20546. [3] M.M. Lipschutz, Theory and Problems of Di-fferentia-l_(eni ret-rv, Schaums Outline
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
National Research Council Canada - National Science Library
Huang, Wei-Xian; Wu, Hua-Jing-Ling; Wang, Guo-Jin
2013-01-01
In order to explore a new approach to construct surfaces bounded by geodesics or lines of curvature, a method of surface modeling based on fourth-order partial differential equations (PDEs) is presented...
Integrable vs Nonintegrable Geodesic Soliton Behavior
Fringer, O B
1999-01-01
We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler-Poincare equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program for ideal fluids, but where the kinetic energy metric is different from the L2 norm of the velocity. These pde possess a finite-dimensional invariant manifold of particle-like (measure-valued) solutions we call ``pulsons.'' We solve the particle dynamics of the two-pulson interaction analytically as a canonical Hamiltonian system for geodesic motion with two degrees of freedom and a conserved momentum. The result of this two-pulson interaction for rear-end collisions is elastic scattering with a phase shift, as occurs with solitons. In contrast, head-on antisymmetric collisons of pulsons tend to form singularities.
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.
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of g...
Geodesic components for guided wave optics
Chang, W. L.; Voges, E.
1980-10-01
Geodesic elements for beam displacement, beam deflection, beam splitting, and imaging are derived for passive optical devices. The elements are suitable in particular for multimode devices, and a complex performance is achievable by the combined action of different geodesic structures on a common substrate. A general theorem of Toraldo di Francia (1957) on the geodesics of rotational surfaces is used to develop geodesic components for beam deflection and multiple beam splitting in a prescribed manner.
Hollander, Frank den
2008-01-01
This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve
Geodesic motion in the space-time of a non-compact boson star
Eilers, Keno; Kagramanova, Valeria; Schaffer, Isabell; Toma, Catalin
2013-01-01
We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -- depending on the scalar field's mass -- can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular, can -- however -- only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particle's energy and angular momentum. The space-time of a boson star approaches the Schwarzschild space-time asymptotically, however deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions ...
Geodesic models generated by Lie symmetries
Abebe, G Z; Govinder, K S
2014-01-01
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
On the Morris - Thorne wormhole geodesics
Culetu, Hristu
2014-01-01
The properties of a particular Misner - Thorne wormhole are investigated. The "exotic stress-energy" needed to maintain the wormhole open corresponds to a massless scalar field whose Lagrangean density contains a negative kinetic term. While the Komar energy of the spacetime is vanishing due to the negative energy density and radial pressure, the ADM energy is (minus) the Planck energy. The timelike geodesics are hyperbolae and any static observer is inertial. The null radial trajectories are also hyperbolae and Lorentz invariant as Coleman- de Luccia expanding bubble or Ipser-Sikivie domain wall. Using a different equation of state for the fluid on the dynamic wormhole throat of Redmount and Suen, we reached an equation of motion for the throat (a hyperbola) that leads to a negative surface energy density and the throat expands with the same acceleration $2\\pi |\\sigma|$ as the Ipser-Sikivie domain wall.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li.
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of geodesic acoustic mode activity. Phenomenologically a radial propagation of zonal modes shows some characteristics of a classical analogon to second sound in quantum condensates.
Thermodynamic Geodesics of a Reissner Nordstr\\"om Black Hole
Farrugia, Christine
2016-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordstr\\"om black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems. It can be deduced that the relation which the geodesics establish between the entropy $S$ and electric charge $Q$ of the black hole extremises changes in the black hole's mass. Indeed, at any given point along a geodesic, the value of $\\text{d}S/\\text{d}Q$ is of the same order of magnitude as the rate at which entropy changes with charge during a constant-mass perturbation. Our claim is further justified by the fact that the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation.
A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole
Soroushfar, Saheb; Jafari, Afsaneh
2015-01-01
This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.
MHD modeling on geodesic grids
Florinski, V; Balsara, D S; Meyer, C
2013-01-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional "Cartesian" frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a sim...
Do electromagnetic waves always propagate along null geodesics?
Asenjo, Felipe A
2016-01-01
We find exact solutions to Maxwell equations written in terms of four-vector potentials in non--rotating, as well as in G\\"odel and Kerr spacetimes. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non--rotating spherical symmetric spacetimes, electromagnetic plane waves travel along null geodesics. However, electromagnetic plane waves on G\\"odel and Kerr spacetimes do not exhibit that behavior.
Landau damping of geodesic acoustic mode in toroidally rotating tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment, The Collaborative Innovation Center for Advanced Fusion Energy and Plasma Science, and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Cao, Jintao [Bejing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-06-15
Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary toroidal Mach number is analytically derived. The effects of toroidal rotation on the GAM frequency and damping rate do not depend on the orientation of equilibrium flow. It is shown that the toroidal Mach number M increases the GAM frequency and dramatically decreases the Landau damping rate.
A Continuum Mechanical Approach to Geodesics in Shape Space
2010-01-01
A CONTINUUM MECHANICAL APPROACH TO GEODESICS IN SHAPE SPACE By Benedikt Wirth Leah Bar Martin Rumpf and Guillermo Sapiro IMA Preprint Series # 2295...Benedikt Wirth† Leah Bar‡ Martin Rumpf† Guillermo Sapiro‡ †Institute for Numerical Simulation, University of Bonn, Germany ‡Department of Electrical and...mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto
Smith, Gary
2015-01-01
Did you know that having a messy room will make you racist? Or that human beings possess the ability to postpone death until after important ceremonial occasions? Or that people live three to five years longer if they have positive initials, like ACE? All of these facts' have been argued with a straight face by researchers and backed up with reams of data and convincing statistics.As Nobel Prize-winning economist Ronald Coase once cynically observed, If you torture data long enough, it will confess.' Lying with statistics is a time-honoured con. In Standard Deviations, ec
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
LIU; Chungen
2002-01-01
［1］Klingenberg, W., Riemannian Geometry, Berlin: Walter de Gruyter, 1982.［2］Morse, M., The Calculus of Variations in the Large, Vol. 18,New York: Colloquium Publ., 1934.［3］Long, Y., Bott formula of the Maslov_type index theory, Pacific J. Math., 1999, 187: 113-149.［4］Hingston, N., On the lengths of closed geodesics on a two_sphere, Proc. Amer. Math. Soc., 1997, 125(10): 3099-3106.［5］Hingston, N., On the growth of the number of closed geodesics on the two_sphere, Inter. Math. Res. Notices, 1993, 9: 253-262.［6］Ballmann, W., Thorberrgsson, G., Ziller, W., Closed geodesics on positively curved manifolds, Annals of Math., 1982, 116: 213-247.［7］Bott, R., On the iteration of closed geodesics and the Sturm intersection theory, Commun. Pure Appl. Math., 1956, 9: 171-206.［8］Yakubovich, V., Starzhinskii, V., Linear Differential Equations with Periodic Ceofficients, New York: John Wiley & Sons, 1975.［9］Long, Y., Zhu, C., Closed characteristics on compact convex hypersurfaces in R2n, Nankai Inst. of Math., Preprint Series, No. 1999_M_002, Revised Dec. 2000.［10］Rademacher, H. _B., On the average indices of closed geodesics, J. Diff. Geom., 1989, 29: 65-83.［11］Liu, C., Long, Y., Iteration inequalities of the Maslov_type index theory with applications, J. Diff. Equa., 2000, 165: 355-376.［12］Liu, C., Long, Y., An optimal increasing estimate of the iterated Maslov_type indices, Chinese Science Bulletin, 1997, 42: 2275-2277.［13］Long, Y., Precise iteration formula of the Maslov_type index theory and ellipticity of closed characteristics,Advances in Math., 2000, 154: 76-131.［14］Bangert, V., On the existence of closed geodesics on two_spheres, Inter. J. of Math., 1993, 4: 1-10.［15］Bao, D., Chern, S. S., Shen, Z., An Introduction to Riemann_Finsler Geometry, New York: Springer_Verlag, 2000.［16］Bott, R., Lectures on More theory, old and new, Bull. Amer. Math. Soc., 1982, 7(2): 331-358.［17］Franks, J., Geodesics on S2 and
Constrained Geodesic Centers of a Simple Polygon
Oh, Eunjin; Son, Wanbin; Ahn, Hee-Kap
2016-01-01
For any two points in a simple polygon P, the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regions. In this paper, we show how to compute the geodesic centers constrained to a set of line segment...
Geodesics and Acceleration in Influence Theory
Walsh, James; Knuth, Kevin
Influence theory is concerned with a foundational approach where it is assumed that particles influence one another in a discrete one-to-one fashion. This results in a partially ordered set of influence events, called the influence network, where particles are represented by totally ordered chains of events. Information physics considers physical laws to result from consistent quantification of physical phenomena. Knuth and Bahreyni (2014) demonstrated that the mathematics of spacetime emerges from consistent quantification of influence events by embedded coordinated observers. Knuth (2014) showed that in 1 +1 dimensions observer-based predictions about a free (uninfluenced) particle result in the Dirac equation. Here, we show that when a particle in 1 +1 dimensions is influenced, it is uniquely and consistently described in terms of relativistic acceleration for constant rate of influence and in general obeys equations of the form of the geodesic equations of general relativity. This suggests that Influence Theory can also account for forces (like gravity), which give rise to well-known relativistic effects such as time dilation.
Thermodynamic geodesics of a Reissner Nordström black hole
Farrugia, Christine; Sultana, Joseph
2017-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordström black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems (Phys Rev D 41:1142-1151, 1990). It can be deduced that the relation which the geodesics establish between the entropy S and electric charge Q of the black hole extremises changes in the black hole's mass. Indeed, the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation. We also find that in certain cases, the geodesics describe the evolution brought about by the constant emission of Hawking radiation and charged-particle pairs.
Quantum frictionless trajectories versus geodesics
Barbado, Luis C; Garay, Luis J
2015-01-01
Moving particles outside a star will generally experience quantum friction caused by Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring back-scattering). They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
A Dynamical Systems Approach to Schwarzschild Null Geodesics
Belbruno, Edward
2011-01-01
The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular m...
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
Geodesic acoustic modes with poloidal mode couplings ad infinitum
Singh, Rameswar; Garbet, X; Hennequin, P; Vermare, L; Morel, P; Singh, R
2015-01-01
Geodesic acoustic modes (GAMs) are studied, for the first time, including all poloidal mode $(m)$ couplings using drift reduced fluid equations. The nearest neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number $k_{r}$. The infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fractions. Convergence study of linear GAM dispersion with respect to $k_{r}$ and the $m$-spectra confirms that high m couplings become increasingly important with $k_{r}$. The radially sorted roots overlap with experimentally measured GAM frequency profile in low collisionality shots in Tore Supra thus explaining the reduced frequency of GAM in Tore Supra.
Embedding spacetime via a geodesically equivalent metric of Euclidean signature
Jonsson, Rickard
2001-01-01
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent, or dual, metric can be embedded in ordinary Euclidean space. On the embedded surface freely falling particles move on the shortest path. Thus one can visualize how acceleration in a gravitational field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature, even the weak gravity of our Earth. This may provide a nice pedagogical tool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions. In an addendum I extend the analysis concerning the shape of an embedding of the dual spacetime of a line through a planet of constant proper density.
Geodesic flows and their deformations in Bertrand spacetimes
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
In this article we will discuss some features of a particular spacetime called Bertrand space-time of Type II (BST-II). This spacetime is associated with multiple real parameters. The various energy conditions and geodesic equations of BST-II are used to find the limits of these parameters which can result in a meaningful and physical space-time. It will be shown that in certain circumstances where the weak and strong energy conditions hold BST-II can be thought of as a physically interesting spacetime. Further, the talk discusses about the ESR parameters in this spacetime. The properties of these parameters are nemerically analyzed keeping an eye on the focussing property of radial timelike and radial null geodesics.
Polyaffine parametrization of image registration based on geodesic flows
DEFF Research Database (Denmark)
Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.
2012-01-01
Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....... is very similar to existing methods, we show that we can find an analytical solution. This solution converges exponentially to the true solution, and the gradients may be determined similarly. We compare to existing prominent methods; the log-euclidean polyaffine framework, and the DARTEL implementation...
A Note on Geodesically Bounded -Trees
Directory of Open Access Journals (Sweden)
Kirk WA
2010-01-01
Full Text Available It is proved that a complete geodesically bounded -tree is the closed convex hull of the set of its extreme points. It is also noted that if is a closed convex geodesically bounded subset of a complete -tree and if a nonexpansive mapping satisfies then has a fixed point. The latter result fails if is only continuous.
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
The Poincar\\'e reduction problem for geodesics on deformed spheres
Sinitsyn, D O
2011-01-01
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation theory with the view of obtaining a topological classification of the set of geodesics on a manifold. To that end we use the X-ray transform familiar in the integral geometry, and obtain the system of averaged equations of motion, which turns out to be a Hamiltonian one. The system serves an asymptotic reduction of the initial exact system of 2n-2 equations to that of 2n-4 equations on the Grassmann manifold G(2,n). The Poisson brackets of the reduction system are determined by the Lie algebra of the group SO(n). In the important cases of two-dimensional and a range of three-dimensional hypersurfaces it allows a topological classification of the set of geodesics.
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
2016-01-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
2017-05-01
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Quantum frictionless trajectories versus geodesics
Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.
2015-10-01
Moving particles outside a star will generally experience quantum friction caused by the Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring backscattering). Along these trajectories, observers perceive just stellar emission, without further contribution from the Unruh effect. They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that it could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
Null Geodesics in Brane World Scenarios
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Feng; ZHANG Yuan-Zhong
2004-01-01
We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z2 symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate thc Z2 symmetry.
Line graphs and $2$-geodesic transitivity
Devillers, Alice; Jin, Wei; Li, Cai Heng; Praeger, Cheryl E.
2012-01-01
For a graph $\\Gamma$, a positive integer $s$ and a subgroup $G\\leq \\Aut(\\Gamma)$, we prove that $G$ is transitive on the set of $s$-arcs of $\\Gamma$ if and only if $\\Gamma$ has girth at least $2(s-1)$ and $G$ is transitive on the set of $(s-1)$-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic $2$-geodesic transitive graphs are the complete multipartite graph $K_{3[2]}$ and the icosahedron. Secondly we classify 2-geodesic transitive graphs ...
Multichannel image regularization using anisotropic geodesic filtering
Energy Technology Data Exchange (ETDEWEB)
Grazzini, Jacopo A [Los Alamos National Laboratory
2010-01-01
This paper extends a recent image-dependent regularization approach introduced in aiming at edge-preserving smoothing. For that purpose, geodesic distances equipped with a Riemannian metric need to be estimated in local neighbourhoods. By deriving an appropriate metric from the gradient structure tensor, the associated geodesic paths are constrained to follow salient features in images. Following, we design a generalized anisotropic geodesic filter; incorporating not only a measure of the edge strength, like in the original method, but also further directional information about the image structures. The proposed filter is particularly efficient at smoothing heterogeneous areas while preserving relevant structures in multichannel images.
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.)
Large deviations and idempotent probability
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...
Ramified optimal transportation in geodesic metric spaces
Xia, Qinglan
2009-01-01
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimen...
Dissertation: Geodesics of Random Riemannian Metrics
LaGatta, Tom
2011-01-01
We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on $\\mathbb R^d$. We are motivated in our study by the random geometry of first-passage percolation (FPP), a lattice model which was developed to model fluid flow through porous media. By adapting techniques from standard FPP, we prove a shape theorem for our model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one. In differential geometry, geodesics are curves which locally minimize length. They need not do so globally: consider great circles on a sphere. For lattice models of FPP, there are many open questions related to minimizing geodesics; similarly, it is interesting from a geometric perspective when geodesics are globally minimizing. In the present study, we show that for any fixed st...
On superintegrable systems closed to geodesic motion
Tsiganov, A V
1997-01-01
In this work we consider superintegrable systems in the classical $r$-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational potentials from geodesic motion on $R^{2n}$.
Geodesics in the static Mallett spacetime
Olum, Ken D
2010-01-01
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Characterization of Null Geodesics on Kerr Spacetimes
Paganini, Claudio F; Oancea, Marius A
2016-01-01
We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore we show that from the point of view of any timelike observer outside of a black hole, trapping can be understood as a smooth set of spacelike directions on the observers' celestial sphere.
On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
Ortiz, Néstor; Zannias, Thomas
2015-01-01
Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.
Photon Geodesics in FRW Cosmologies
Bikwa, Ojeh; Shevchuk, Andrew
2011-01-01
The Hubble radius is a particular manifestation of the Universe's gravitational horizon, R_h(t_0)=c/H_0, the distance beyond which physical processes remain unobservable to us at the present epoch. Based on recent observations of the cosmic microwave background (CMB) with WMAP, and ground-based and HST searches for Type Ia supernovae, we now know that R_h(t_0)~13.5 Glyr. This coincides with the maximum distance (ct_0~13.7 Glyr) light could have traveled since the big bang. However, the physical meaning of R_h is still not universally understood or accepted, though the minimalist view holds that it is merely the proper distance at which the rate of cosmic recession reaches the speed of light c. Even so, it is sometimes argued that we can see light from sources beyond R_h, the claim being that R_h lies at a redshift of only ~2, whereas the CMB was produced at a much greater redshift (~1100). In this paper, we build on recent developments with the gravitational radius by actually calculating null geodesics for a...
Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections
Institute of Scientific and Technical Information of China (English)
SHI Bing-Ren; LI Ji-Quan; DONG Jia-Qi
2005-01-01
@@ The geodesic acoustic mode in general toroidally axisymmetric plasmas such as Tokamak and spherical torus is studied in detail. The mode structure is found and the dispersion equation is derived and solved for arbitrary toroidally axi-symmetric plasmas. Besides the finite aspect ratio, effects of elongation and triangularity on this mode are clarified.
On Geodesic Flows and Their Deformations in Bertrand Space-times
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
We study the energy conditions and geodesic equations of Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the parameter space where the weak and strong energy conditions hold. We further compute the ESR parameters for a class of such space-times and analyze them numerically.
Geodesic Structures of Lifshitz Black Holes in 2+1 Dimensions
Cruz, Norman; Villanueva, J R
2013-01-01
We present an study of the geodesic equations of a black hole spacetime which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev.{\\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non radial geodesics are given in terms of the Weierstrass elliptic $\\wp$, $\\sigma$, and $\\zeta$ functions.
Craniofacial Reconstruction Evaluation by Geodesic Network
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, various precise iteration equalities and inequalities of Morse indices for the closed geodesics are established. As applications of these formulae, multiplicity results of closed geodesics on some Riemannian manifolds are proved.
Orbifold Riemann surfaces and geodesic algebras
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L O [Steklov Mathematical Institute, Moscow (Russian Federation)], E-mail: chekhov@mi.ras.ru
2009-07-31
We study the Teichmueller theory of Riemann surfaces with orbifold points of order 2 using the fat graph technique. The previously developed technique of quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebras of geodesic functions is applicable to the surfaces with orbifold points. We describe classical and quantum braid group relations for particular sets of geodesic functions corresponding to A{sub n} and D{sub n} algebras and describe their central elements for the Poisson and quantum algebras.
'Proper acceleration' of a null geodesic in curved spacetime
Tian Gui Hua; Liang Can Bin
2002-01-01
Given a null geodesic in Minkowski spacetime, there exists a one-parameter family of observers in 'hyperbolic' motion which approaches the null geodesic as the parameter x sub 0 approaches zero. It is well known that the proper acceleration of the observers in the family approaches infinity as their world line approaches the null geodesic. The main purpose of this paper is to generalize this result to future-complete null geodesics in curved spacetimes.
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.
A Conformal Extension Theorem based on Null Conformal Geodesics
Lübbe, Christian
2008-01-01
In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and Luebbe.
Black-Box Optimization Using Geodesics in Statistical Manifolds
Directory of Open Access Journals (Sweden)
Jérémy Bensadon
2015-01-01
Full Text Available Information geometric optimization (IGO is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a Riemannian manifold, defining a parametrization-invariant first order differential equation and, thus, yielding an approximately parametrization-invariant algorithm (up to second order in the step size. We define the geodesic IGO update, a fully parametrization-invariant algorithm using the Riemannian structure, and we compute it for the manifold of Gaussians, thanks to Noether’s theorem. However, in similar algorithms, such as CMA-ES (Covariance Matrix Adaptation - Evolution Strategy and xNES (exponential Natural Evolution Strategy, the time steps for the mean and the covariance are decoupled. We suggest two ways of doing so: twisted geodesic IGO (GIGO and blockwise GIGO. Finally, we show that while the xNES algorithm is not GIGO, it is an instance of blockwise GIGO applied to the mean and covariance matrix separately. Therefore, xNES has an almost parametrization-invariant description.
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of...
Energy Technology Data Exchange (ETDEWEB)
Saito, Ryo [APC, (CNRS-Université Paris 7), 10 rue Alice Domon et Léonie Duquet, 75205 Paris (France); Naruko, Atsushi [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan); Hiramatsu, Takashi; Sasaki, Misao, E-mail: rsaito@apc.univ-paris7.fr, E-mail: naruko@th.phys.titech.ac.jp, E-mail: hiramatz@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-10-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.
Saito, Ryo; Hiramatsu, Takashi; Sasaki, Misao
2014-01-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Geodesic Acoustic Propagation and Ballooning Mode Formalism
Li, M. B.; Diamond, P. H.; Young, G. G.; Arakawa, M.
2005-10-01
Relevance of ballooning formalism (BMF) in nonlinear interaction of toroidal electromagnetic drift waves in the presence of zonal flows and Geodesic Acoustic Oscillation (GAO) is critically examined from a physical argument of radial propagation of wave packets. To achieve the quasi-translational invariance of poloidal harmonics which is necessary for the BMF, the geodesic curvature induced transfer [1] of fluctuation energy in radial direction should occur faster than the time scale of physical interest. Of course, this does not happen necessarily in drift-Alfven (DALF) turbulence simulations [2]. This observation casts considerable doubts on the applicability of various codes based on the BMF concept to nonlinear electromagnetic problems. [1] B. Scott, Phys. Letters A 320 (2003) 53. [2] B. Scott, New J. Phys 7 (2005) 92.
Free of centrifugal acceleration spacetime - Geodesics
Culetu, Hristu
2013-01-01
A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $\\rho = -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. We found that the Tolman-Komar gravitational energy is finite everywhere. The timelike and null geodesics of the spacetime are examined.
Analytical time-like geodesics
Kostic, Uros
2012-01-01
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r=r(\\lambda), t=t(\\chi), and \\tau=\\tau(\\chi), where \\lambda\\ is the true anomaly and \\chi\\ is a parameter along the orbit. A very simple relation between \\lambda\\ and \\chi\\ is also shown. These solutions are very useful for modeling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.
On the determination of shifting operators along geodesics on a surface
Directory of Open Access Journals (Sweden)
Drašković Zoran
2013-01-01
Full Text Available A procedure to obtain a closed form of the shifting operators along a known geodesic line on a surface as a solution of a system of linear algebraic equations is proposed. Its correctness is numerically demonstrated in the case of a helicoid surface and a spherical one. The future use of these operators in finite element approximations of tensor fields in non-Euclidean spaces is announced.
Space-time Geodesics of the 5D Schwarzschild field and its deformation retract
Ahmed, Nasr
2014-01-01
In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.
Dissociated Vertical Deviation
... Frequently Asked Questions Español Condiciones Chinese Conditions Dissociated Vertical Deviation En Español Read in Chinese What is Dissociated Vertical Deviation (DVD)? DVD is a condition in which ...
Studying null and time-like geodesics in the classroom
Müller, Thomas; 10.1088/0143-0807/32/3/011
2011-01-01
In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have some explicit examples available which show the different behaviour of geodesics. In this paper we present the GeodesicViewer, an interactive tool for studying the behaviour of geodesics in many different space-times. The geodesics can be represented in several ways, depending on the space-time in question. The use of a local reference frame and 'Cartesian-like' coordinates helps the students to develop some intuition in various situations. We present the various features of the GeodesicViewer in the form of readily formulated exercises for the students.
Geometric Structures and Field Equations of Dirac-Lu Space
Institute of Scientific and Technical Information of China (English)
REN Xin-An; ZHANG Li-You
2008-01-01
In this paper, a -invariant Lorentz metric on the Dirac-Lu space is given, and then the geodesic equation is investigated. Finally, we discuss the field equations and find their solutions by the method of separating variables.
Focal properties of geodesic waveguide lenses
Verber, C. M.; Vahey, D. W.; Wood, V. E.
1976-01-01
The focal properties of uncorrected geodesic lenses in ion-exchanged glass waveguides are reported. A 13.8-mm-focal-length lens resolved beams with an angular separation of 27.6 mrad, while a 28-mm-focal-length lens resolved beams with an angular separation of only 3.3 mrad. Intensity profiles of the focal region of the former lens revealed a 40-micron spot size when the input aperture was 5 mm, and a spot size of 7.7 microns when the aperture was reduced to 1 mm. This value is close to the diffraction-limited spot size of 5.7 microns.
Light geodesics near an evaporating black hole
Energy Technology Data Exchange (ETDEWEB)
Guerreiro, Thiago, E-mail: thiago.barbosa@unige.ch; Monteiro, Fernando, E-mail: fernando.monteiro@unige.ch
2015-10-16
Quantum effects imply that an infalling observer cannot cross the event horizon of an evaporating black hole, even in her proper time. The Penrose diagram of an evaporating black hole is different from the one usually reported in the literature. We show that before the observer can cross the horizon the black hole disappears. Possible observational consequences are discussed. - Highlights: • We calculate the in-falling light geodesics in an evaporating black hole. • For our calculation we use a non-static metric called Vaydia metric. • We show that in-falling light cannot cross the event horizon. • In this case there is no information paradox.
Geodesic least squares regression on information manifolds
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2014-12-05
We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply this to scaling laws in magnetic confinement fusion.
Black Hole Decay as Geodesic Motion
Sen-Gupta, K; Gupta, Kumar S.; Sen, Siddhartha
2003-01-01
We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The decay rate is shown to be correctly described by geodesic motion in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. We also show that the near-horizon conformal symmetry predicts a precise correction term to the usual expression for the decay rate of black holes. The results obtained here are a consequence of the holographic nature of the system.
A triangulation-invariant method for anisotropic geodesic map computation on surface meshes.
Yoo, Sang Wook; Seong, Joon-Kyung; Sung, Min-Hyuk; Shin, Sung Yo; Cohen, Elaine
2012-10-01
This paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner.
Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime
Müller, Thomas
2011-01-01
The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first course in general relativity to give them a deeper inside in the calculation of non-affinely parametrized null and time-like geodesics and a straightforward approach to determine the gravitational lensing effect due to curved spacetime by means of the Jacobi equation. Both topics are necessary for a thorough discussion of the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. The visual effects of the traveller can be reproduced with an interactive Java application.
Vacuum non-expanding horizons and shear-free null geodesic congruences
Adamo, T M
2009-01-01
We investigate the geometry of a particular class of null surfaces in space-time called vacuum Non-Expanding Horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex world-line in a complex four dimensional space, each such choice induces a CR structure on the horizon, and a particular world-line (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.
Models of rotating boson stars and geodesics around them: New type of orbits
Grandclément, Philippe; Somé, Claire; Gourgoulhon, Eric
2014-07-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number k=3 and k=4, as well as the first determination of the maximum mass of free-field boson stars with k=2. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for k=1, 2 and 3. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbit: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
Ortaggio, M
2007-01-01
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.
Models of rotating boson stars and geodesics around them: new type of orbits
Grandclement, Philippe; Gourgoulhon, Eric
2014-01-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, $2$ and $3$. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbits: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi; Sasaki, Misao
2014-01-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a per...
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of FEGC to the radial flow. The reason for the reduction of damping rate is that when the effect of FEGC counts, the new resonant velocity becomes much larger than ions thermal velocity with equilibrium distribution obeying Maxwellian distribution, compared with unmodified Landau resonant velocity. Especially, FEGC changes the characters of the frequency and damping rate of low-frequency GAM as functions of safety factor $q$ .
An Algorithm for Constructing Principal Geodesics in Phylogenetic Treespace.
Nye, Tom M W
2014-01-01
Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks, clustering and multidimensional scaling have been developed and applied to tree samples. This paper describes a stochastic algorithm for constructing a principal geodesic or line through treespace which is analogous to the first principal component in standard principal components analysis. A principal geodesic summarizes the most variable features of a sample of trees, in terms of both tree topology and branch lengths, and it can be visualized as an animation of smoothly changing trees. The algorithm performs a stochastic search through parameter space for a geodesic which minimizes the sum of squared projected distances of the data points. This procedure aims to identify the globally optimal principal geodesic, though convergence to locally optimal geodesics is possible. The methodology is illustrated by constructing principal geodesics for experimental and simulated data sets, demonstrating the insight into samples of trees that can be gained and how the method improves on a previously published approach. A java package called GeoPhytter for constructing and visualizing principal geodesics is freely available from www.ncl.ac.uk/ ntmwn/geophytter.
On large deviations for ensembles of distributions
Khrychev, D. A.
2013-11-01
The paper is concerned with the large deviations problem in the Freidlin-Wentzell formulation without the assumption of the uniqueness of the solution to the equation involving white noise. In other words, it is assumed that for each \\varepsilon>0 the nonempty set \\mathscr P_\\varepsilon of weak solutions is not necessarily a singleton. Analogues of a number of concepts in the theory of large deviations are introduced for the set \\{\\mathscr P_\\varepsilon,\\,\\varepsilon>0\\}, hereafter referred to as an ensemble of distributions. The ensembles of weak solutions of an n-dimensional stochastic Navier-Stokes system and stochastic wave equation with power-law nonlinearity are shown to be uniformly exponentially tight. An idempotent Wiener process in a Hilbert space and idempotent partial differential equations are defined. The accumulation points in the sense of large deviations of the ensembles in question are shown to be weak solutions of the corresponding idempotent equations. Bibliography: 14 titles.
Geodesics of McVittie Spacetime with a Phantom Cosmological Background
Antoniou, Ioannis
2016-01-01
We investigate the geodesics of a Schwarzschild spacetime embedded in an isotropic expanding cosmological background (McVittie metric). We focus on bound particle geodesics in a background including matter and phantom dark energy with constant dark energy equation of state parameter $w<-1$ involving a future Big Rip singularity at a time $t_{\\ast}$. Such geodesics have been previously studied in the Newtonian approximation and found to lead to dissociation of bound systems at a time $t_{rip}
Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows
Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch
2017-09-01
Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.
A geodesic model in conformal superspace
Gomes, Henrique de A
2016-01-01
In this paper, I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. Conformal superspace is a stratified manifold, with different strata corresponding to different isometry groups. Choosing space to be (homeomorphic to) $S^3$, conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point -- corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geome...
Drift effects on electromagnetic geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)
2015-02-15
A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)
Geodesic motion in a stationary dihole spacetime
Dubeibe, F L
2016-01-01
The knowledge of the properties of the different exact solutions modeling binary systems, is a necessary step towards the classification of physically suitable solutions and its corresponding limits of applicability. In the present paper, we perform an analysis of the geodesics around two counter--rotating Kerr--Newman black holes endowed with opposite electric charges, which achieve equilibrium by means of a strut between their constituents. We find that bounded and unbounded orbits are possible. However, test particles may cross between the black holes only if their angular momentum equals zero, otherwise, there exist a repulsive potential, which prohibits such orbits. Two important aspects are pointed out for these trajectories: ({\\it i}) the motion of photons is affected once crossing the strut; and ({\\it ii}) massive particles exhibit oscillatory motion, as a first analog of the Sitnikov problem in general relativity. The radius of the innermost stable circular orbit as a function of the physical paramet...
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian...... Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically....
A Visualization of Null Geodesics for the Bonnor Massive Dipole
Oliva-Mercado, Guillermo Andree; Cordero-García, Iván; Frutos-Alfaro, Francisco
2015-01-01
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
A visualization of null geodesics for the bonnor massive dipole
Directory of Open Access Journals (Sweden)
G. Andree Oliva Mercado
2015-08-01
Full Text Available In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
A dynamical system's approach to Schwarzschild null geodesics
Energy Technology Data Exchange (ETDEWEB)
Belbruno, Edward [Courant Institute of Mathematical Sciences, New York University, NY (United States); Pretorius, Frans, E-mail: belbruno@Princeton.edu, E-mail: fpretori@Princeton.edu [Department of Physics, Princeton University, Princeton, NJ (United States)
2011-10-07
The null geodesics of a Schwarzschild black hole are studied from a dynamical system's perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of the four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L| > |L{sub c}|, (1) the set that flow outward from the white hole, turn around, and then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L| < |L{sub c}|, (3) the set that flow outward from the white hole and continue to future null infinity and (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum L{sub c} corresponds to the unstable circular orbit at r = 3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r = 0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is that a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the L {yields} {infinity} limit, as described in Schwarzschild coordinates, these geodesics begin at r = 0, flow along t = constant lines, turn around at r = 2M, and then continue to r = 0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.
Solar performance of an electrochromic geodesic dome roof
Energy Technology Data Exchange (ETDEWEB)
Porta-Gandara, M.A. [Centro de Investigaciones Biologicas del Noroeste, BCS (Mexico); Gomez-Munoz, V. [Centro Interdisciplinario de Ciencas Marinas, BCS (Mexico)
2005-10-01
A Fuller type geodesic dome was modeled in terms of the variation of the solar energy that passes to the interior when the dome is covered with electrochromic glazing (ECG), compared with common glass, by means of two different solar control strategies: one discrete and the other continuous. With the discrete strategy, when a solar beam strikes any ECG pane at any angle, it is darkened to its maximum level. In the continuous strategy, each ECG pane is darkened by using a direct function of solar beam radiation. The results demonstrate the advantages of solar control achieved with the former strategy. For the discrete strategy, the daily reduction in solar energy intake, with respect to the ordinary glass, was around 86% for all considered latitudes along the year. The optimum values for the continuous strategy occurred during the equinoxes with a maximum reduction of 69% for all latitudes. During the summer solstice, the reduction percentages increase with the latitude from 52 to 57%. During the winter solstice, the energy reduction with the continuous strategy decreases with the latitude from 52% in the Equator to 46% at 40{sup o} north latitude. (author)
Geodesic family of spherical instantons and cosmic quantum creation
Lapiedra, Ramon
2015-01-01
The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\\^{\\i}}tre-Tolman-Bondi family and for a general $\\Lambda$-Friedmann-Lema{\\^{\\i}}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $\\Lambda$FLRW model is quantically creatable while the open and flat model...
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
and evaluate the method. The method uses deformable registration on computed tomography(CT) to find anatomical symmetry deviations of Head & Neck squamous cell carcinoma and combining it with positron emission tomography (PET) images. The method allows the use anatomical and symmetrical information of CT scans...... to improve automatic delineations. Materials: PET/CT scans from 30 patients were used for this study, 20 without cancer in hypopharyngeal volume and 10 with hypharyngeal carcinoma. An head and neck atlas was created from the 20 normal patients. The atlas was created using affine and non-rigid registration...... 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...
Large Deviations and Metastability
Olivieri, Enzo; Eulália Vares, Maria
2005-02-01
This self-contained account of the main results in large deviation theory includes recent developments and emphasizes the Freidlin-Wentzell results on small random perturbations. Metastability is described on physical grounds, followed by the development of more exacting approaches to its description. The first part of the book then develops such pertinent tools as the theory of large deviations which is used to provide a physically relevant dynamical description of metastability. Written for graduate students, this book affords an excellent route into contemporary research as well.
From geodesics of the multipole solutions to the perturbed Kepler problem
Hernandez-Pastora, J L; 10.1103/PhysRevD.82.104001
2010-01-01
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the Monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2$^4$-pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.
de Sitter geodesics: reappraising the notion of motion
Pereira, J G
2011-01-01
de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined by any one of these geodesics. By taking into account the appropriate transitivity properties, a new family of geodesics is obtained whose trajectories are able to connect any two points of the de Sitter spacetime. They are, furthermore, consistent with the de Sitter momentum conservation. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may be important at very-high energies, where conformal symmetry plays a significant role.
A Note on Geodesically Bounded ℝ-Trees
Directory of Open Access Journals (Sweden)
W. A. Kirk
2010-01-01
Full Text Available It is proved that a complete geodesically bounded R-tree is the closed convex hull of the set of its extreme points. It is also noted that if X is a closed convex geodesically bounded subset of a complete R-tree Y, and if a nonexpansive mapping T:X→Y satisfies inf{d(x,T(x:x∈X}=0, then T has a fixed point. The latter result fails if T is only continuous.
The Lorentzian oscillator group as a geodesic orbit space
Energy Technology Data Exchange (ETDEWEB)
Batat, W. [Ecole Normale Superieure d' Enseignement Technologique d' Oran, Departement de Mathematiques et Informatique, B.P. 1523, El M' Naouar, Oran (Algeria); Gadea, P. M. [Instituto de Fisica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid (Spain); Oubina, J. A. [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela (Spain)
2012-10-15
We prove that the four-dimensional oscillator group Os, endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so, in particular, null-geodesic) orbit space with some of its homogeneous descriptions corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in d-dimensional supergravity with at least 24 of the 32 possible supersymmetries.
Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
Manno, Gianni; Pavlov, Maxim V.
2017-03-01
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.
On the Possibility of Non-Geodesic Motion of the Massless Spinning Top
Armaza, Cristóbal; Koch, Benjamin; Zalaquett, Nicolás
2016-01-01
The motion of spinning massless particles in gravitationally curved backgrounds is revisited by considering new types of constraints. Those constraints guarantee zero mass ($P_\\mu P^\\mu=0$) and they allow for the possibility of trajectories which are not simply null geodesics. To exemplify this previously unknown possibility, the equations of motion are solved for radial motion in Schwarzschild background. It is found that the particle experiences a spin-induced energy shift, which is proportional to the Hawking temperature of the black hole background.
The geometry of a vorticity model equation
Escher, Joachim; Wunsch, Marcus
2010-01-01
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\\ge 2$.
Geodesic Motion in the Spacetime Of a SU(2)-Colored (A)dS Black Hole in Conformal Gravity
Hoseini, Bahareh; Soroushfar, Saheb
2016-01-01
In this paper we are interested to study the geodesic motion in the spacetime of a SU(2)-colored (A)dS black hole solving in conformal gravity. Using Weierstrass elliptic and Kleinian {\\sigma} hyperelliptic functions, we derive the analytical solutions for the equation of motion of test particles and light rays. Also, we classify the possible orbits according to the particle's energy and angular momentum.
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.
Coverings and integrability of the Gauss-Mainardi-Codazzi equations
Krasilchchik, I; Krasil'shchik, Joseph; Marvan, Michal
1998-01-01
Using covering theory approach (zero-curvature representations with the gauge group SL2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic coordinates. For each choice, four integrable systems are obtained.
Institute of Scientific and Technical Information of China (English)
Fan Aihua
2004-01-01
The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Sσ = ∑θ＜r≤σXr. We introduce and study the oscillations of the walk:Exact Hausdorff dimension of the set of such ξ 's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.
Equations of motion with respect to the (1 + 1 + 3) threading of a 5D universe
Energy Technology Data Exchange (ETDEWEB)
Bejancu, Aurel [Kuwait University, Department of Mathematics, Safat (Kuwait)
2016-01-15
We continue our research work started in Bejancu (Eur Phys J C 75:346, 2015), and obtain in a covariant form the equations of motion with respect to the (1+1+3) threading of a 5D universe (anti M, anti g). The natural splitting of the tangent bundle of anti M leads to the study of three categories of geodesics: spatial geodesics, temporal geodesics, and vertical geodesics. As an application of the general theory, we introduce and study what we call the 5D Robertson-Walker universe. (orig.)
A Finsler geodesic spray paradigm for wildfire spread modelling
DEFF Research Database (Denmark)
Markvorsen, Steen
2015-01-01
represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... sensitive - geodesic solutions to the wildfire spread problem. The methods presented here stem directly from first principles of 2-dimensional Finsler geometry, and they can be readily extracted from the seminal monographs [10] and [11], but we will take special care to introduce and exemplify the necessary...... framework for the implementation of the geometric machinery into this new application - not least in order to facilitate and support the dialog between geometers and the wildfire modelling community. The ‘integration’ part alluded to above is obtained via the geodesics of the ensuing Finsler metric which...
Geodesics on Surfaces with Helical Symmetry: Cavatappi Geometry
Jantzen, Robert T
2013-01-01
A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface of revolution like the torus which it contains as a special case. It serves as a simple example of helically symmetric surfaces which are the generalizations of surfaces of revolution in which an initial plane curve is screw-revolved around an axis in its plane. The physics description of geodesic motion on these surfaces requires a slightly more involved effective potential approach than the torus case due to the nonorthogonal coordinate grid necessary to describe this problem. Amazingly this discussion allows one to very nicely describe the geodesics of the surface of the more complicated ridged cavatappi pasta.
Wang, Xiaoting; Allegra, Michele; Jacobs, Kurt; Lloyd, Seth; Lupo, Cosmo; Mohseni, Masoud
2015-05-01
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
Circular geodesics of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
Stuchlik, Zdenek
2015-01-01
We study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and non-linear electrodynamics. They both are characterized by the mass parameter $m$ and the charge parameter $g$. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be sorrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter $g/m > 2$ can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phe...
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Directory of Open Access Journals (Sweden)
Timothy M. Adamo
2009-09-01
Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Directory of Open Access Journals (Sweden)
Timothy M. Adamo
2012-01-01
Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Null geodesics in a magnetically charged stringy black hole spacetime
Kuniyal, Ravi Shankar; Uniyal, Rashmi; Nandan, Hemwati; Purohit, K. D.
2016-04-01
We study the null geodesics of a four-dimensional magnetic charged black hole spacetime arising in string theory. The behaviour of effective potential in view of the different values of black hole parameters are analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results are compared to those obtained for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime in general relativity.
Coherent states and geodesics cut locus and conjugate locus
Berceanu, S
1997-01-01
The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point $0$ is equal to the set of coherent vectors orthogonal to $\\vert 0>$. A simple method to calculate the conjugate locus in Hermitian symmetric spaces with significance in the coherent state approach is presented. The results are illustrated on the complex Grassmann manifold.
Global structure and geodesics for Koenigs superintegrable systems
Valent, Galliano
2016-09-01
We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their superintegrability (SI) and most of them are shown to be globally defined on either ℝ2 or ℍ2. Their geodesic flows are easily determined thanks to their quadratic integrals. Using Carter (or minimal) quantization, we show that the formal SI is preserved at the quantum level and for two metrics, for which all of the geodesics are closed, it is even possible to compute the classical action variables and the point spectrum of the quantum Hamiltonian.
Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points
Institute of Scientific and Technical Information of China (English)
Fei LIU; Fang WANG
2016-01-01
In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
Large deviations from freeness
Kargin, Vladislav
2010-01-01
Let H=A+UBU* where A and B are two N-by-N Hermitian matrices and U is a Haar-distributed random unitary matrix, and let \\mu_H, \\mu_A, and \\mu_B be empirical measures of eigenvalues of matrices H, A, and B, respectively. Then, it is known (see, for example, Pastur-Vasilchuk, CMP, 2000, v.214, pp.249-286) that for large N, measure \\mu_H is close to the free convolution of measures \\mu_A and \\mu_B, where the free convolution is a non-linear operation on probability measures. The large deviations of the cumulative distribution function of \\mu_H from its expectation have been studied by Chatterjee in JFA, 2007, v. 245, pp.379-389. In this paper we improve Chatterjee's estimate and show that P {\\sup_x |F_H (x) -F_+ (x)| > \\delta} < exp [-f(\\delta) N^2], where F_H (x) and F_+ (x) denote the cumulative distribution functions of \\mu_H and the free convolution of \\mu_A and \\mu_B, respectively, and where f(\\delta) is a specific function.
On large deviations for ensembles of distributions
Energy Technology Data Exchange (ETDEWEB)
Khrychev, D A [Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow (Russian Federation)
2013-11-30
The paper is concerned with the large deviations problem in the Freidlin-Wentzell formulation without the assumption of the uniqueness of the solution to the equation involving white noise. In other words, it is assumed that for each ε>0 the nonempty set P{sub ε} of weak solutions is not necessarily a singleton. Analogues of a number of concepts in the theory of large deviations are introduced for the set (P{sub ε}, ε>0), hereafter referred to as an ensemble of distributions. The ensembles of weak solutions of an n-dimensional stochastic Navier-Stokes system and stochastic wave equation with power-law nonlinearity are shown to be uniformly exponentially tight. An idempotent Wiener process in a Hilbert space and idempotent partial differential equations are defined. The accumulation points in the sense of large deviations of the ensembles in question are shown to be weak solutions of the corresponding idempotent equations. Bibliography: 14 titles.
Saini, Sahil; Singh, Parampreet
2016-12-01
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.
Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
Energy Technology Data Exchange (ETDEWEB)
Alkalaev, Konstantin [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky ave. 53, Moscow, 119991 (Russian Federation); Department of General and Applied Physics, Moscow Institute of Physics and Technology, 7 Institutskiy per., Dolgoprudnyi, Moscow region, 141700 (Russian Federation)
2016-12-15
We study the semiclassical holographic correspondence between 2d CFT n-point conformal blocks and massive particle configurations in the asymptotically AdS{sub 3} space. On the boundary we use the heavy-light approximation in which case two of primary operators are the background for the other (n−2) operators considered as fluctuations. In the bulk the particle dynamics can be reduced to the hyperbolic time slice. Although lacking exact solutions we nevertheless show that for any n the classical n-point conformal block is equal to the length of the dual geodesic network connecting n−3 cubic vertices of worldline segments. To this end, both the bulk and boundary systems are reformulated as potential vector fields. Gradients of the conformal block and geodesic length are given respectively by accessory parameters of the monodromy problem and particle momenta of the on-shell worldline action represented as a function of insertion points. We show that the accessory parameters and particle momenta are constrained by two different algebraic equation systems which nevertheless have the same roots thereby guaranteeing the correspondence.
A Few Endpoint Geodesic Restriction Estimates for Eigenfunctions
Chen, Xuehua; Sogge, Christopher D.
2014-07-01
We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a TT* argument, simply by using the L 2-boundedness of the Hilbert transform on , we are able to improve the corresponding L 2-restriction bounds of Burq, Gérard and Tzvetkov (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009). Also, in the case of 2-dimensional compact manifolds with nonpositive curvature, we obtain improved L 4-estimates for restrictions to geodesics, which, by Hölder's inequality and interpolation, implies improved L p -bounds for all exponents p ≥ 2. We do this by using oscillatory integral theorems of Hörmander (Ark Mat 11:1-11, 1973), Greenleaf and Seeger (J Reine Angew Math 455:35-56, 1994) and Phong and Stein (Int Math Res Notices 4:49-60, 1991), along with a simple geometric lemma (Lemma 3.2) about properties of the mixed-Hessian of the Riemannian distance function restricted to pairs of geodesics in Riemannian surfaces. We are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that, in this case, there are many totally geodesic submanifolds.
Integrability of Invariant Geodesic Flows on n-Symmetric Spaces
Jovanovic, Bozidar
2010-01-01
In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata $n$-symmetric spaces $K^n/\\diag(K)$, where $K$ is a semisimple (respectively, simple) compact Lie group.
Monodromic vs geodesic computation of Virasoro classical conformal blocks
Directory of Open Access Journals (Sweden)
Konstantin Alkalaev
2016-03-01
Full Text Available We compute 5-point classical conformal blocks with two heavy, two light, and one superlight operator using the monodromy approach up to third order in the superlight expansion. By virtue of the AdS/CFT correspondence we show the equivalence of the resulting expressions to those obtained in the bulk computation for the corresponding geodesic configuration.
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan;
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....
Geodesic atlas-based labeling of anatomical trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2015-01-01
We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees...
Geodesic flow, connecting orbits and almost full foliation
Institute of Scientific and Technical Information of China (English)
CHENG; Jian; MENG; Long
2006-01-01
We study in this article a special dynamical behavior of geodesic flow on T2.Our example shows that there is an area-preserving monotone twist map for which all minimal periodic orbits can be connected,and at the same time for a certain rational rotation number the minimal set is almost an invariant curve.
Non-Minimally Coupled Cosmology as Geodesic Motion
Elias, L A; Elias, Luciana A.; Saa, Alberto
2007-01-01
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
Geodesic chromaticity diagram based on variances of color matching by 14 normal observers.
Macadam, D L
1971-01-01
A nonlinear transformation of the CIE x,y chromaticity coordinates has been derived from the combined color-matching-variance data of 14 normal observers. In the resulting diagram, the series of equiluminous chromaticities entailing the least number of standard deviations of color matching (sigma-units) between any two-terminal, equiluminous chromaticities is the straight line drawn between the points that represent those terminal colors. The total number of sigma-unit differences between those terminal colors is the euclidean distance between those two points. According to Schrödinger's hypothesis, the loci of constant hue are the straight lines (geodesics) radiating from the point that represents hueless colors in this diagram. The horizontal coordinate in the geodesic chromaticity diagram is xi = 3751a(2) - 10a(4) - 520b(2) + 13295b(3) + 32327ab - 25491a(2)b - 41672ab(2) + 10a(3)b - 5227a((1/2)) + 2952(4)a((1/4)), where a = 10x/(2.4x + 34y + 1) and b = 10y/(2.4x + 34y + 1). The vertical coordinate in the geodesic chromaticity diagram is eta = 404b - 185b(2) + 52b(3) + 69a(1 - b(2)) - 3a(2)b + 30ab(2), where a = 10x/(4.2y - x + 1) and b = 10y/(4.2y - x + 1). These formulas were obtained by use of averages of data for two observers whose individual data were published in 1949 and the weighted averages for 12 young observers, which were published in 1957, together with the data for the single observer, PGN, whose data were published in 1942-45. On the basis of extensive studies of these data, the PGN data were assigned 30% weight in the derivation of the new xi,eta diagram. The 1949 data were assigned 44% weight, or 22% per observer, and the 1957 data were assigned 26%, or about 2.2% per observer. The best fit was found by assuming that the over-all mean of the standard deviation of color matching according to the 1949 data was 1.2 times as much as the standard deviation for PGN, and that the weighted-mean standard deviation for the 12 observers was 1.04 times the
Araki, Keisuke
2016-01-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Examinations of the stabilities of the hydrodynamic (HD, $\\alpha=0$) and magnetohydrodynamic (MHD, $\\alpha\\to0$) motions and the $O(\\alpha)$ Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where {\\alpha} represents the Hall-term strength parameter. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Els\\"asser variables (GEVs). It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the po...
Haustral loop extraction for CT colonography using geodesics.
Liu, Yongkai; Duan, Chaijie; Liang, Jerome; Hu, Jing; Lu, Hongbing; Luo, Mingyue
2017-03-01
The human colon has complex geometric structures because of its haustral folds, which are thin flat protrusions on the colon wall. The haustral loop is the curve (approximately triangular in shape) that encircles the highly convex region of the haustral fold, and is regarded as the natural landmark of the colon, intersecting the longitude of the colon in the middle. Haustral loop extraction can assist in reducing the structural complexity of the colon, and the loops can also serve as anatomic markers for computed tomographic colonography (CTC). Moreover, haustral loop sectioning of the colon can help with the performance of precise prone-supine registration. We propose an accurate approach of extracting haustral loops for CT virtual colonoscopy based on geodesics. First, the longitudinal geodesic (LG) connecting the start and end points is tracked by the geodesic method and the colon is cut along the LG. Second, key points are extracted from the LG, after which paired points that are used for seeking the potential haustral loops are calculated according to the key points. Next, for each paired point, the shortest distance (geodesic line) between the paired points twice is calculated, namely one on the original surface and the other on the cut surface. Then, the two geodesics are combined to form a potential haustral loop. Finally, erroneous and nonstandard potential loops are removed. To evaluate the haustral loop extraction algorithm, we first utilized the algorithm to extract the haustral loops. Then, we let the clinicians determine whether the haustral loops were correct and then identify the missing haustral loops. The extraction algorithm successfully detected 91.87% of all of the haustral loops with a very low false positive rate. We believe that haustral loop extraction may benefit many post-procedures in CTC, such as supine-prone registration, computer-aided diagnosis, and taenia coli extraction.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Institute of Scientific and Technical Information of China (English)
马小翠
2011-01-01
给出了{（X^s（t），Z^ε（t））；ε〉0，t∈[0，T]}的容度大偏差定理．其中X^ε（t）满足下面的随机微分方程：dX^ε（t）=（√εσ（t））dw（t）＋b（X^ε（t），Z^ε（t））dt，Z^ε（t）为有限个状态的随机过程．%In this paper, We discuss a large deviation principle of capacity for {（X^s（t）,Z^ε（t））;ε〉0,t∈[0,T]}determined by dX^ε（t）=（√εσ（t））dw（t）＋b（X^ε（t）,Z^ε（t））dt,Z^ε（t）is an n- state process.
Second--order hyperbolic Fuchsian systems. Asymptotic behavior of geodesics in Gowdy spacetimes
Beyer, Florian
2011-01-01
Recent work by the authors led to the development of a mathematical theory dealing with `second--order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this theory which provides one with a new tool to tackle the Einstein equations of general relativity (under certain symmetry assumptions). Specifically, we formulate the `Fuchsian singular initial value problem' and apply our general analysis to the broad class of vacuum Gowdy spacetimes with spatial toroidal topology. Our main focus is on providing a detailed description of the asymptotic geometry near the initial singularity of these inhomogeneous cosmological spacetimes and, especially, analyzing the asymptotic behavior of causal geodesics ---which represent the trajectories of freely falling observers. In particular, we numerically construct here Gowdy spacetimes which contain a black hole--like region together with a flat Minkowski--like region. By using the Fuchsian techn...
Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane
2016-12-01
The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
Excitation of kinetic geodesic acoustic modes by drift waves in nonuniform plasmas
Energy Technology Data Exchange (ETDEWEB)
Qiu, Z. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Chen, L. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Dept. Physics and Astronomy, Univ. of California, Irvine, California 92697-4575 (United States); Zonca, F. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Associazione Euratom-ENEA sulla Fusione, C.P. 65 - I-00044 - Frascati (Italy)
2014-02-15
Effects of system nonuniformities and kinetic dispersiveness on the spontaneous excitation of Geodesic Acoustic Mode (GAM) by Drift Wave (DW) turbulence are investigated based on nonlinear gyrokinetic theory. The coupled nonlinear equations describing parametric decay of DW into GAM and DW lower sideband are derived and then solved both analytically and numerically to investigate the effects on the parametric decay process due to system nonuniformities, such as nonuniform diamagnetic frequency, finite radial envelope of DW pump, and kinetic dispersiveness. It is found that the parametric decay process is a convective instability for typical tokamak parameters when finite group velocities of DW and GAM associated with kinetic dispersiveness and finite radial envelope are taken into account. When, however, nonuniformity of diamagnetic frequency is taken into account, the parametric decay process becomes, time asymptotically, a quasi-exponentially growing absolute instability.
Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
Ritter, P; Spallicci, A; Cordier, S
2015-01-01
The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
Null Geodesics in a Magnetically Charged Stringy Black Hole Spacetime
Kuniyal, Ravi Shankar; Nandan, Hemwati; Purohit, K D
2015-01-01
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of black hole parameters is analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in detail in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results obtained are then compared with those for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime. It is observed that there exists no stable circular orbit outside the event horizon for massless test particles.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, Kuantay; Abutalip, Marzhan; Kalymova, Zhanerke; Suleymanova, Sharara
2015-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
Detecting Einstein geodesics: Einstein metrics in projective and conformal geometry
Gover, A Rod
2013-01-01
Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the existence of such a metric, and in generic settings the vanishing of these is also sufficient. We also obtain results for the problem of metrisability (without the Einstein condition): We show that the odd Chern type invariants of an affine connection are projective invariants that obstruct the existence of a projectively related Levi-Civita connection. In addition we discuss a concrete link between projective and conformal geometry and the application of this to the projective-Einstein problem.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, K. A.; Quevedo, H.; Abutalip, M. S.; Kalymova, Zh. A.; Suleymanova, Sh. S.
2016-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
van Vleck determinants geodesic focussing and defocussing in Lorentzian spacetimes
Visser, M
1993-01-01
The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.
Quantization of black hole entropy from unstable circular null geodesics
Wei, Shao-Wen; Liu, Yu-Xiao; Fu, Chun-E.
2016-04-01
The quasinormal mode frequencies can be understood from the massless particles trapped at the unstable circular null geodesics and slowly leaking out to infinity. Based on this viewpoint, in this paper, we semiclassically construct the entropy spectrum of the static and stationary black holes from the null geodesics. The result shows that the spacing of the entropy spectrum only depends on the property of the black hole in the eikonal limit. Moreover, for a black hole far from the extremal case, the spacing is found to be smaller than 2πħ for any dimension, which is very different from the result of the previous work by using the usual quasinormal mode frequencies.
Geodesic motion of test particles in Korkina-Grigoryev metric
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under whi...
Lens rigidity with trapped geodesics in two dimensions
Croke, Christopher B
2011-01-01
We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat M\\"obius strip are determined by their lens data. We also see by example that the flat M\\"obius strip is not determined by it's scattering data. We then consider the case of negatively curved cylinders with convex boundary and show that they are lens rigid.
Firmly nonexpansive mappings in classes of geodesic spaces
Ariza-Ruiz, David; Lopez-Acedo, Genaro
2012-01-01
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, as (uniformly convex) $W$-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic egularity for the Picard iterations.
Geodesic completeness in a wormhole spacetime with horizons
Olmo, Gonzalo J; Sanchez-Puente, A
2015-01-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Adaptive geodesic transform for segmentation of vertebrae on CT images
Gaonkar, Bilwaj; Shu, Liao; Hermosillo, Gerardo; Zhan, Yiqiang
2014-03-01
Vertebral segmentation is a critical first step in any quantitative evaluation of vertebral pathology using CT images. This is especially challenging because bone marrow tissue has the same intensity profile as the muscle surrounding the bone. Thus simple methods such as thresholding or adaptive k-means fail to accurately segment vertebrae. While several other algorithms such as level sets may be used for segmentation any algorithm that is clinically deployable has to work in under a few seconds. To address these dual challenges we present here, a new algorithm based on the geodesic distance transform that is capable of segmenting the spinal vertebrae in under one second. To achieve this we extend the theory of the geodesic distance transforms proposed in1 to incorporate high level anatomical knowledge through adaptive weighting of image gradients. Such knowledge may be provided by the user directly or may be automatically generated by another algorithm. We incorporate information 'learnt' using a previously published machine learning algorithm2 to segment the L1 to L5 vertebrae. While we present a particular application here, the adaptive geodesic transform is a generic concept which can be applied to segmentation of other organs as well.
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
Guha, Sarbari; Bhattacharya, Pinaki
2010-01-01
In this paper, we have studied the timelike and null geodesics in the vicinity of a non-rotating, charged black hole in a five-dimensional Reissner-Nordstrom Anti-de Sitter spacetime. Here the solutions are uniquely characterized by their mass, charge and the cosmological constant. The line element and the horizon function has been defined and it is found that only one horizon is physically admissible. The spherical symmetry of the geometry helps us to reduce the problem to a study of three geodesic equations. In our analysis, we have used both the method of effective Newtonian orbit calculations and the dynamical systems method to analyze the particle trajectories. The equation of motion of a particle of unit mass is found. The effective potential under which any test particle moves with a given angular momentum at a given distance from the black hole, depends only on the mass and charge of the black hole and the cosmological constant. This equation is used to study radial motion and the corresponding stabil...
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.
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
Sheng-lan Chen
2014-01-01
Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
Sokołowski, Leszek M
2016-01-01
We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by $\\Lambda$, lying on a Euclidean two--plane. Then we outline an alternative proof for $AdS_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.
Deviations from LTE in a stellar atmosphere
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.
Simple computation of null-geodesics, with applications to vortex boundary detection
Serra, Mattia; Haller, George
2016-11-01
Recent results show that boundaries of coherent vortices (elliptic coherent structures) can be computed as closed null-geodesics of appropriate Lorentzian metrics defined on the physical domain of the underlying fluid. Here we derive a new method for computing null-geodesics of general Lorentzian metrics, founded on the geometry of geodesic flows. We also derive the correct set of initial conditions for the computation of closed null-geodesics, based on simple topological properties of planar closed curves. This makes the computation of coherent vortex boundaries fully automated, simpler and more accurate compared to the existing procedure. As an illustration, we compute objective coherent vortex boundaries in Oceanic and Atmospheric Flows.
Semantic Deviation in Oliver Twist
Institute of Scientific and Technical Information of China (English)
康艺凡
2016-01-01
Dickens, with his adeptness with language, applies semantic deviation skillfully in his realistic novel Oliver Twist. However, most studies and comments home and abroad on it mainly focus on such aspects as humanity, society, and characters. Therefore, this thesis will take a stylistic approach to Oliver Twist from the perspective of semantic deviation, which is achieved by the use of irony, hyperbole, and pun and analyze how the application of the technique makes the novel attractive.
Paroxysmal upgaze deviation: case report
Echeverría-Palacio CM; Benavidez-Fierro MA
2012-01-01
The paroxysmal upgaze deviation is a syndrome that described in infants for first time in 1988; there are just about 50 case reports worldwide ever since. Its etiology is unclear and though it prognosis is variable; most case reports indicate that during growth the episodes tend to decrease in frequency and duration until they disappear. It describes a 16-months old male child who since 11-months old presented many episodes of variable conjugate upward deviation of the eyes, compensatory neck...
Angle-deviation optical profilometer
Institute of Scientific and Technical Information of China (English)
Chen-Tai Tan; Yuan-Sheng Chan; Zhen-Chin Lin; Ming-Hung Chiu
2011-01-01
@@ We propose a new optical profilometer for three-dimensional (3D) surface profile measurement in real time.The deviation angle is based on geometrical optics and is proportional to the apex angle of a test plate.Measuring the reflectivity of a parallelogram prism allows detection of the deviation angle when the beam is incident at the nearby critical angle. The reflectivity is inversely proportional to the deviation angle and proportional to the apex angle and surface height. We use a charge-coupled device (CCD) camera at the image plane to capture the reflectivity profile and obtain the 3D surface profile directly.%We propose a new optical profilometer for three-dimensional (3D) surface profile measurement in real time.The deviation angle is based on geometrical optics and is proportional to the apex angle of a test plate.Measuring the refiectivity of a parallelogram prism allows detection of the deviation angle when the beam is incident at the nearby critical angle. The refiectivity is inversely proportional to the deviation angle and proportional to the apex angle and surface height. We use a charge-coupled device (CCD) camera at the image plane to capture the refiectivity profile and obtain the 3D surface profile directly.
Divided Spheres Geodesics and the Orderly Subdivision of the Sphere
Popko, Edward S
2012-01-01
This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.
Tifinagh Character Recognition Using Geodesic Distances, Decision Trees & Neural Networks
Directory of Open Access Journals (Sweden)
O.BENCHAREF
2011-09-01
Full Text Available The recognition of Tifinagh characters cannot be perfectly carried out using the conventional methods which are based on the invariance, this is due to the similarity that exists between some characters which differ from each other only by size or rotation, hence the need to come up with new methods to remedy this shortage. In this paper we propose a direct method based on the calculation of what is called Geodesic Descriptors which have shown significant reliability vis-à-vis the change of scale, noise presence and geometric distortions. For classification, we have opted for a method based on the hybridization of decision trees and neural networks.
A Mean Value Theorem for Closed Geodesics on Congruence Surfaces
Lukianov, Vladimir
2005-01-01
We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics of the eigenvalues of the Laplacian on the surface. In the case of the modular domain, E. Bogomolny, F. Leyvraz and C. Schmit gave a formula for the mean square, which was rigorously proved by M. Peter. In this paper we...
Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature
Mangoubi, Oren; Smith, Aaron
2016-01-01
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\\mathcal{M}$, which we call the $\\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 < \\mathfrak{m}_{2} \\leq C_{x}(u,v) \\leq \\mathfrak{M}_2 < \\infty$ is $\\mathcal{O}^*\\left(\\frac{\\mathfrak{M}_2}{\\mathfrak{m}_2}\\right)$. In particular, this bound on the mixing time does not depend expli...
Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2012-01-01
Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.
Dome, Sweet Dome--Geodesic Structures Teach Math, Science, and Technology Principles
Shackelford, Ray; Fitzgerald, Michael
2007-01-01
Today, geodesic domes are found on playgrounds, homes, over radar installations, storage facilities, at Disney's Epcot Center, and at World's Fairs. The inventor of the design, Buckminster Fuller, thought that geodesic domes could be used to cover large areas and even designed one to cover all of New York's Manhattan Island. This article details…
Optimal three-dimensional biped walking pattern generation based on geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2017-03-01
Full Text Available The innovative three-dimensional humanoid biped gait planning method using geodesics is introduced in this article. In order to control three-dimensional walking, the three-dimensional linear inverted pendulum model is studied in our energy-optimal gait planning based on geodesics. The kinetic energy of the three-dimensional linear inverted pendulum model is calculated at first. Based on this kinetic energy model, the Riemannian metric is defined and the Riemannian surface is further determined by this Riemannian metric. The geodesic is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the center of gravity because the kinetic energy along the geodesic is invariant according to the geometric property of geodesics and the walking is energy-saving. Finally, a simulation experiment using a 12-degree-of-freedom biped robot model is implemented. The gait sequences of the simulated RoboErectus humanoid robot are obtained in the ROS (Robot Operating System Gazebo environment. The proposed geodesics approach is compared with the traditional sinusoidal interpolation method by analyzing the torque feedback of each joint of both legs, and our geodesics optimization gait planning method for three-dimensional linear inverted pendulum model walking control is verified by the assessment results.
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Y.N.; Risager, Morten
2005-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on a random set of homology classes and certain arithmetic sets. We explain the analogues for free groups, conjugacy classes...
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Yiannis N.; Risager, Morten S.
2008-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any set with asymptotic density with respect to a specific norm. We explain the analogues for free groups, conjugacy classes...
Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
Stuchlík, Zdeněk; Schee, Jan
2015-12-01
In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.
Large deviations in Taylor dispersion
Kahlen, Marcel; Engel, Andreas; Van den Broeck, Christian
2017-01-01
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of the long-time regime for Taylor dispersion.
Standard Deviation for Small Samples
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…
Isometry group and geodesics of the Wagner lift of a riemannian metric on two-dimensional manifold
B., José Ricardo Arteaga
2010-01-01
In this paper we construct a functor from the category of two-dimensional Riemannian manifolds to the category of three-dimensional manifolds with generalized metric tensors. For each two-dimensional oriented Riemannian manifold $(M,g)$ we construct a metric tensor $\\hat g$ (in general, with singularities) on the total space $SO(M,g)$ of the principal bundle of the positively oriented orthonormal frames on $M$. We call the metric $\\hat g$ the Wagner lift of $g$. We study the relation between the isometry groups of $(M,g)$ and $(SO(M,g),\\hat g)$. We prove that the projections of the geodesics of $(SO(M,g),\\hat g)$ onto $M$ are the curves which satisfy the equation \\begin{equation*} \
Spectral segmentation via midlevel cues integrating geodesic and intensity.
Lu, Huchuan; Zhang, Ruixuan; Li, Shifeng; Li, Xuelong
2013-12-01
Image segmentation still remains as a challenge in image processing and pattern recognition when involving complex natural scenes. In this paper, we present a new affinity model for spectral segmentation based on midlevel cues. In contrast to most existing methods that operate directly on low-level cues, we first oversegment the image into superpixel images and then integrate the geodesic line edge and intensity cue to form the similarity matrix W so that it more accurately describes the similarity between data. The geodesic line edge could avoid strong boundary and represent the true boundary between two superpixels while the mean red green blue vector could describe the intensity of superpixels better. As far as we know, this is a totally new kind of affinity model to represent superpixels. Based on this model, we use the spectral clustering in the superpixel level and then achieve the image segmentation in the pixel level. The experimental results show that the proposed method performs steadily and well on various natural images. The evaluation comparisons also prove that our method achieves comparable accuracy and significantly performs better than most state-of-the-art algorithms.
Ricci magnetic geodesic motion of vortices and lumps
Alqahtani, L S
2014-01-01
Ricci magnetic geodesic (RMG) motion in a k\\"ahler manifold is the analogue of geodesic motion in the presence of a magnetic field proportional to the ricci form. It has been conjectured to model low-energy dynamics of vortex solitons in the presence of a Chern-Simons term, the k\\"ahler manifold in question being the $n$-vortex moduli space. This paper presents a detailed study of RMG motion in soliton moduli spaces, focusing on the cases of hyperbolic vortices and spherical $\\mathbb{C}P^1$ lumps. It is shown that RMG flow localizes on fixed point sets of groups of holomorphic isometries, but that the flow on such submanifolds does not, in general, coincide with their intrinsic RMG flow. For planar vortices, it is shown that RMG flow differs from an earlier reduced dynamics proposed by Kim and Lee, and that the latter flow is ill-defined on the vortex coincidence set. An explicit formula for the metric on the whole moduli space of hyperbolic two-vortices is computed (extending an old result of Strachan's), an...
Maxwell Fields and Shear-Free Null Geodesic Congruences
Newman, E
2004-01-01
We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the world-line. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, it can be given the following strange interpretation. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x^a take complex values, i.e., x^a => z^a=x^a+iy^a with co...
Cold Scalar-Tensor Black Holes Causal Structure, Geodesics, Stability
Bronnikov, K A; Constantinidis, C P; Fabris, J C
1998-01-01
We study the structure and stability of spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant $\\omega$. These solutions split into two classes, depending on finite (B1) or infinite (B2) proper time needed for an infalling particle to reach the horizon. Class B1 metrics can be extended through the horizon only for discrete values of mass and scalar charge, depending on two integers m and n. For even m-n, the space-time is globally regular; for odd m, the metric changes its signature on the horizon but remains Lorentzian. Geodesics are smoothly continued across the horizon, but for odd m timelike geodesics become spacelike and vice versa. Causality problems, arising in some cases, are discussed. Tidal forces are shown to grow infinitely near type B1 horizons. All vacuum static, spherically symmetric solutions of the Brans-Dicke theory with $\\omega<-3/2$ are found to be linearly stable again...
Dynamic realization of the Unruh effect for a geodesic observer
Lochan, Kinjalk; Padmanabhan, T
2016-01-01
We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\\to\\infty$) observers, around $x\\to\\infty$ and $x\\to-\\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity witness a thermal radiation, without experiencing any change of spacetime geometry all along their trajectories. They remain geodesic observers in a flat region of spacetime. Thus these observers measure a late time thermal radiation, with exactly the same temperature as measured by the observers at right null infinity, despite moving geodesically in flat spacetime throughout their trajectories. However such radia...
A thermodynamic study of zatrikean geodesics resulting from a discrete-geometry model
Geroyannis, V. S.; Dallas, T. G.
We attempt a connection between thermodynamics and zatrikean pregeometry, i.e., a chess-like pregeometry (Geroyannis 1993, hereafter G93). In zatrikean pregeometry space is represented by the abacus, a discrete chessboard-like structure consisting of a sufficiently large number of plaquettes called geobits. The particles move on the abacus from one geobit to the next following certain rules that resemble the game of chess. The sets of rules imposed on the motions of particles on the abacus are called premetrics. There is a variety of paths (called subabaces) leading from one geobit to another, and there is a class consisting of subabaces with the minimum number of geobits. These are called alyssoids (respectively, class of alyssoids) for the particular premetric, while those alyssoids with minimum length are called geodesics (respectively, class of geodesics) for the particular premetric. The so-called zatrikean geodesic was originally defined in G93 (Section 2) as the geodesic most closely following the line segment joining the two geobits. It is also called algorithmic geodesic since it is drawn with the assistance of four simple algorithms. This is a rectifiable curve; and a connection between rectifiable curves and thermodynamics is already available (DuPain, Kamae and Mendes-France 1986). Consequently, the so-called thermodynamic geodesic is defined as the particular member of the class of geodesics with maximum entropy. Since it does not necessarily correspond to the algorithmic geodesic, a new algorithm is devised that draws the geodesic with maximum entropy. Furthermore, the probability of each member of the class of geodesics can be determined as the difference of its entropy from the entropy of the thermodynamicgeodesic.
Paroxysmal upgaze deviation: case report
Directory of Open Access Journals (Sweden)
Echeverría-Palacio CM
2012-05-01
Full Text Available The paroxysmal upgaze deviation is a syndrome that described in infants for first time in 1988; there are just about 50 case reports worldwide ever since. Its etiology is unclear and though it prognosis is variable; most case reports indicate that during growth the episodes tend to decrease in frequency and duration until they disappear. It describes a 16-months old male child who since 11-months old presented many episodes of variable conjugate upward deviation of the eyes, compensatory neck flexion and down-beat saccades in attempted downgaze. These events are predominantly diurnal, and are exacerbated by stressful situations such as fasting or insomnia, however and improve with sleep. They have normal neurologic and ophthalmologic examination, and neuroimaging and EEG findings are not relevant.
Perception of aircraft Deviation Cues
Martin, Lynne; Azuma, Ronald; Fox, Jason; Verma, Savita; Lozito, Sandra
2005-01-01
To begin to address the need for new displays, required by a future airspace concept to support new roles that will be assigned to flight crews, a study of potentially informative display cues was undertaken. Two cues were tested on a simple plan display - aircraft trajectory and flight corridor. Of particular interest was the speed and accuracy with which participants could detect an aircraft deviating outside its flight corridor. Presence of the trajectory cue significantly reduced participant reaction time to a deviation while the flight corridor cue did not. Although non-significant, the flight corridor cue seemed to have a relationship with the accuracy of participants judgments rather than their speed. As this is the second of a series of studies, these issues will be addressed further in future studies.
48 CFR 2001.403 - Individual deviations.
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...
48 CFR 801.403 - Individual deviations.
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...
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F.; Armano, M.; Audley, H.; Auger, G.; Benedetti, M.; Binetruy, P.; Boatella, C.; Bogenstahl, J.; Bortoluzzi, D.; Bosetti, P.; Brandt, N.; Caleno, M.; Cavalleri, A.; Cesa, M.; Chmeissani, M.; Ciani, G.; Conchillo, A.; Congedo, G.; Cristofolini, I.; Cruise, M.; Danzmann, K.; De Marchi, F.; Diaz-Aguilo, M.; Diepholz, I.; Dixon, G.; Dolesi, R.; Dunbar, N.; Fauste, J.; Ferraioli, L.; Fertin, D.; Fichter, W.; Fitzsimons, E.; Freschi, M.; García Marin, A.; García Marirrodriga, C.; Gerndt, R.; Gesa, L.; Giardini, D.; Gibert, F.; Grimani, C.; Grynagier, A.; Guillaume, B.; Guzmán, F.; Harrison, I.; Heinzel, G.; Hewitson, M.; Hollington, D.; Hough, J.; Hoyland, D.; Hueller, M.; Huesler, J.; Jeannin, O.; Jennrich, O.; Jetzer, P.; Johlander, B.; Killow, C.; Llamas, X.; Lloro, I.; Lobo, A.; Maarschalkerweerd, R.; Madden, S.; Mance, D.; Mateos, I.; McNamara, P. W.; Mendes, J.; Mitchell, E.; Monsky, A.; Nicolini, D.; Nicolodi, D.; Nofrarias, M.; Pedersen, F.; Perreur-Lloyd, M.; Perreca, A.; Plagnol, E.; Prat, P.; Racca, G. D.; Rais, B.; Ramos-Castro, J.; Reiche, J.; Romera Perez, J. A.; Robertson, D.; Rozemeijer, H.; Sanjuan, J.; Schleicher, A.; Schulte, M.; Shaul, D.; Stagnaro, L.; Strandmoe, S.; Steier, F.; Sumner, T. J.; Taylor, A.; Texier, D.; Trenkel, C.; Tombolato, D.; Vitale, S.; Wanner, G.; Ward, H.; Waschke, S.; Wass, P.; Weber, W. J.; Zweifel, P.
2011-05-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Energy Technology Data Exchange (ETDEWEB)
Antonucci, F; Cavalleri, A; Congedo, G [Dipartimento di Fisica, Universita di Trento and INFN, Gruppo Collegato di Trento, 38050 Povo, Trento (Italy); Armano, M [European Space Astronomy Centre, European Space Agency, Villanueva de la Canada, 28692 Madrid (Spain); Audley, H; Bogenstahl, J [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik und Universitaet Hannover, 30167 Hannover (Germany); Auger, G; Binetruy, P [APC UMR7164, Universite Paris Diderot, Paris (France); Benedetti, M [Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Boatella, C [CNES, DCT/AQ/EC, 18 Avenue Edouard Belin, 31401 Toulouse, Cedex 9 (France); Bortoluzzi, D; Bosetti, P; Cristofolini, I [Dipartimento di Ingegneria Meccanica e Strutturale, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Brandt, N [Astrium GmbH Claude-Dornier-Strasse, 88090 Immenstaad (Germany); Caleno, M; Cesa, M [European Space Technology Centre, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk (Netherlands); Chmeissani, M [IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona (Spain); Ciani, G [Department of Physics, University of Florida, Gainesville, FL 32611-8440 (United States); Conchillo, A [ICE-CSIC/IEEC, Facultat de Ciencies, E-08193 Bellaterra, Barcelona (Spain); Cruise, M, E-mail: Stefano.Vitale@unitn.it [Department of Physics and Astronomy, University of Birmingham, Birmingham (United Kingdom)
2011-05-07
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
Geodesic motion of test particles in Korkina-Grigoryev metric
Bormotova, Irina
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under which the finite motion of particles occurs. From the behavior of the potential curves the radii of both stable and unstable circular orbits around a black hole are found, as well as the corresponding energies of the test particles. The effective-potential curves for the Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are compared. It is shown, that in the case of the Korkina-Grigoryev metric the stable orbits eventually vanish with increasing charge.
Geodesic acoustic mode in anisotropic plasma with heat flux
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2015-10-15
Geodesic acoustic mode (GAM) in an anisotropic tokamak plasma is investigated in fluid approximation. The collisionless anisotropic plasma is described within the 16-momentum magnetohydrodynamic (MHD) fluid closure model, which takes into account not only the pressure anisotropy but also the anisotropic heat flux. It is shown that the GAM frequency agrees better with the kinetic result than the standard Chew-Goldberger-Low (CGL) MHD model. When zeroing the anisotropy, the 16-momentum result is identical with the kinetic one to the order of 1/q{sup 2}, while the CGL result agrees with the kinetic result only on the leading order. The discrepancies between the results of the CGL fluid model and the kinetic theory are well removed by considering the heat flux effect in the fluid approximation.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking.
van Aart, Evert; Sepasian, Neda; Jalba, Andrei; Vilanova, Anna
2011-01-01
Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking
Directory of Open Access Journals (Sweden)
Evert van Aart
2011-01-01
Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Fanizza, Giuseppe
2016-01-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
2016-06-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F; Audley, H; Auger, G; Benedetti, M; Binetruy, P; Boatella, C; Bogenstahl, J; Bortoluzzi, D; Bosetti, P; Brandt, N; Caleno, M; Cavalleri, A; Cesa, M; Chmeissani, M; Ciani, G; Conchillo, A; Congedo, G; Cristofolini, I; Cruise, M; Danzmann, K; De Marchi, F; Diaz-Aguilo, M; Diepholz, I; Dixon, G; Dolesi, R; Dunbar, N; Fauste, J; Ferraioli, L; Fertin, D; Fichter, W; Fitzsimons, E; Freschi, M; Marin, A García; Marirrodriga, C García; Gerndt, R; Gesa, L; Giardini, D; Gibert, F; Grimani, C; Grynagier, A; Guillaume, B; Guzmán, F; Harrison, I; Heinzel, G; Hewitson, M; Hollington, D; Hough, J; Hoyland, D; Hueller, M; Huesler, J; Jeannin, O; Jennrich, O; Jetzer, P; Johlander, B; Killow, C; Llamas, X; Lloro, I; Lobo, A; Maarschalkerweerd, R; Madden, S; Mance, D; Mateos, I; McNamara, P W; Mendestì, J; Mitchell, E; Monsky, A; Nicolini, D; Nicolodi, D; Nofrarias, M; Pedersen, F; Perreur-Lloyd, M; Perreca, A; Plagnol, E; Prat, P; Racca, G D; Rais, B; Ramos-Castro, J; Reiche, J; Perez, J A Romera; Robertson, D; Rozemeijer, H; Sanjuan, J; Schleicher, A; Schulte, M; Shaul, D; Stagnaro, L; Strandmoe, S; Steier, F; Sumner, T J; Taylor, A; Texier, D; Trenkel, C; Tombolato, D; Vitale, S; Wanner, G; Ward, H; Waschke, S; Wass, P; Weber, W J; Zweifel, P
2010-01-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware and flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor two of the LISA requirement at 1 mHz and within a factor 10 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement, that will guarantee the LISA performance.
Spotting deviations from R^2 inflation
de la Cruz-Dombriz, Alvaro; Odintsov, Sergei D; Saez-Gomez, Diego
2016-01-01
We discuss the soundness of inflationary scenarios in theories beyond the Starobinsky model, namely a class of theories described by arbitrary functions of the Ricci scalar and the K-essence field. We discuss the pathologies associated with higher-order equations of motion which will be shown to constrain the stability of this class of theories. We provide a general framework to calculate the slow-roll parameters and the corresponding mappings to the theory parameters. For paradigmatic gravitational models within the class of theories under consideration we illustrate the power of the Planck/Bicep2 latest results to constrain such gravitational Lagrangians. Finally, bounds for potential deviations from Starobinsky-like inflation are derived.
Powers of the space forms curvature operator and geodesics of the tangent bundle
Saharova, Yelena; Yampolsky, Alexander
2005-01-01
It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all its geodesic curvatures constant. In this paper we consider the case of tangent (sphere) bundle over the real, complex and quaternionic space form and give a unified proof of the following property: all geodesic curvatures of projected curve are zero starting from k_3,k_6 and k_{10} for the real, complex and quaternio...
On the number and location of short geodesics in moduli space
Leininger, Christopher J
2011-01-01
A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
Large deviations and portfolio optimization
Sornette, Didier
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation. A major item is that risk, usually thought of as one-dimensional in the conventional mean-variance approach, has to be addressed by the full distribution of losses. Furthermore, the time-horizon of the investment is shown to play a major role. We show the importance of accounting for large fluctuations and use the theory of Cramér for large deviations in this context. We first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes, and the different optimal strategies for the investors depending on their size. We then analyze the case of assets whose price variations are distributed according to exponential laws, a situation that is found to describe daily price variations reasonably well. Several portfolio optimization strategies are presented that aim at controlling large risks. We end by extending the standard mean-variance portfolio optimization theory, first within the quasi-Gaussian approximation and then using a general formulation for non-Gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena.
Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
Adamo, T M; Newman, E T
2009-01-01
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtai...
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
Energy Technology Data Exchange (ETDEWEB)
Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Geodesic motion in equal angular momenta Myers-Perry-AdS spacetimes
Delsate, Térence; Santarelli, Raphael
2015-01-01
We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-AdS black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable spherical orbits (ISSOs) for these asymptotically anti-de Sitter (AdS) spacetimes, as well as the location of null spherical orbits. We find that the ISSO dives below the ergosurface for black holes rotating close to extremality and merges with the event horizon exactly at extremality, in analogy with the four-dimensional Kerr case. For sufficiently massive black holes in AdS there exists a spin parameter range in which the background spacetime...
Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma
Ren, Haijun
2017-01-01
Energetic particle (EP) driven geodesic acoustic modes (EGAMs) in toroidally rotating tokamak plasmas are analytically investigated using the hybrid kinetic-fluid model and gyrokinetic equations. By ignoring high-order terms and ion Landau damping, the kinetic dispersion relation is reduced to the hybrid one in the large safety factor limit. There is one high-frequency branch with a frequency larger than {ωt0} , the transit frequency of EPs with initial energy, which is always stable. Two low-frequency solutions with a frequency smaller than {ωt0} are complex conjugates in the hybrid limit. In the presence of ion Landau damping, the growth rate of the unstable branch is decreased and the damping rate of the damped branch is increased. The toroidal Mach number is shown to increase {{ Ω }\\text{r}} , the normalized real frequency of both branches. Although not affecting the instability critical condition, the Mach number decreases the growth rate when {{ Ω }\\text{r}} is larger than a critical value Ω \\text{r}\\text{cri} and enlarges the growth rate when {{ Ω }\\text{r}}Landau damping effect is negligible for large M. But the discrepancy between the kinetic dispersion relation and the hybrid one becomes ignorable only for q≳ 7 .
48 CFR 1301.403 - Individual deviations.
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 401.403 - Individual deviations.
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...
48 CFR 2801.403 - Individual deviations.
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...
48 CFR 301.403 - Individual deviations.
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 1501.403 - Individual deviations.
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...
48 CFR 501.403 - Individual deviations.
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...
48 CFR 2401.403 - Individual deviations.
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...
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas.
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-30
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Are eikonal quasinormal modes linked to the unstable circular null geodesics?
Konoplya, R. A.; Stuchlík, Z.
2017-08-01
In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.
Proper Accelerations of Time-Like Curves near a Null Geodesic
Institute of Scientific and Technical Information of China (English)
田贵花; 赵峥
2003-01-01
It is well known that when given a null geodesic γ0(λ) with a point r in (p, q) conjugate to p along γ0(λ), there will be a variation of γ0(λ) which can give a time-like curve from p to q. Here we prove that the time-like curves coming from the above-mentioned variation (with the second derivative β2 ≠ 0) have a proper acceleration A = √AaAa which approaches infinity as the time-like curve approaches the null geodesic. Because the curve obtained from variation of the null geodesic must be everywhere time-like, we also discuss the constraint of the vector field Za on the null geodesic γ0(λ) cannot be zero.
Menon, Govind
2008-01-01
The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.
Physical meaning of the conserved quantities on anti-de Sitter geodesics
Cotǎescu, Ion I.
2017-05-01
The geodesic motion on anti-de Sitter spacetimes is studied, pointing out how the trajectories are determined by the ten independent conserved quantities associated with the specific S O (2 ,3 ) isometries of these manifolds. The new result is that there are two conserved S O (3 ) vectors which play the same role as the Runge-Lenz vector of the Kepler problem, determining the major and minor semiaxes of the ellipsoidal anti-de Sitter geodesics.
On the Mass Neutrino Phase calculations along the geodesic line and the null line
Zhang, C. M.; Beesham, A.
2000-01-01
On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting error--factor of 2 when comparing the geodesic phase with the null phase. For the mass neutrino propagation in the flat spacetime, we study the neutrino interference phase calculation in the Minkowski diagram and find that the double counting effect originates from despising the velocity difference between two mass neutrinos. Moreover, we compare the phase cal...
Geometry of Cyclic Quotients; 1, Knotted Totally Geodesic Submanifolds in Positively Curved Spheres
Reznikov, A G
1994-01-01
We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic projective plane with Euler number four. Surpisingly, the technique borrows a lot from the Mostow-Siu-Gromov-Thurston constuction of exotic negatively curved manifolds.
Finsler geodesics in the presence of a convex function and their applications
Energy Technology Data Exchange (ETDEWEB)
Caponio, Erasmo; Masiello, Antonio [Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari (Italy); Javaloyes, Miguel Angel [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada (Spain)], E-mail: caponio@poliba.it, E-mail: ma.javaloyes@gmail.com, E-mail: majava@ugr.es, E-mail: masiello@poliba.it
2010-04-24
In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.
Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem
Krishnaswami, Govind S.; Senapati, Himalaya
2016-10-01
The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation isometries in addition to scaling isometries for the inverse-square potential with zero energy E. The geodesic flow on the full configuration space ℂ3 (with collision points excluded) leads to corresponding flows on its Riemannian quotients: the center of mass configuration space ℂ2 and shape space ℝ3 (as well as 𝕊3 and the shape sphere 𝕊2 for the inverse-square potential when E = 0). The corresponding Riemannian submersions are described explicitly in "Hopf" coordinates which are particularly adapted to the isometries. For equal masses subject to inverse-square potentials, Montgomery shows that the zero-energy "pair of pants" JM metric on the shape sphere is geodesically complete and has negative gaussian curvature except at Lagrange points. We extend this to a proof of boundedness and strict negativity of scalar curvatures everywhere on ℂ2, ℝ3, and 𝕊3 with collision points removed. Sectional curvatures are also found to be largely negative, indicating widespread geodesic instabilities. We obtain asymptotic metrics near collisions, show that scalar curvatures have finite limits, and observe that the geodesic reformulation "regularizes" pairwise and triple collisions on ℂ2 and its quotients for arbitrary masses and allowed energies. For the Newtonian potential with equal masses and zero energy, we find that the scalar curvature on ℂ2 is strictly negative though it could have either sign on ℝ3. However, unlike for the inverse-square potential, geodesics can encounter curvature singularities at collisions in finite geodesic time.
Geodesic active fields--a geometric framework for image registration.
Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe
2011-05-01
In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to
On static solutions of the Einstein - Scalar Field equations
Reiris, Martin
2015-01-01
In this note we study the Einstein-ScalarField static equations in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential $V(\\phi)$, and provide full global geometric estimates when the solutions exist. As a special case it is shown that when $V(\\phi)$ is the Klein-Gordon potential, i.e. $V(\\phi)=m^{2}|\\phi|^{2}$, geodesically complete solutions are necessarily Ricci-flat, have constant lapse and are vacuum, (that is $\\phi=\\phi_{0}$ with $\\phi_{0}=0$ if $m\
On geodesic dynamics in deformed black-hole fields
Semerák, Oldřich
2015-01-01
"Almost all" seems to be known about isolated stationary black holes in asymptotically flat space-times and about the behaviour of {\\em test} matter and fields in their backgrounds. The black holes likely present in galactic nuclei and in some X-ray binaries are commonly being represented by the Kerr metric, but actually they are not isolated (they are detected only thanks to a strong interaction with the surroundings), they are not stationary (black-hole sources are rather strongly variable) and they also probably do not live in an asymptotically flat universe. Such "perturbations" may query the classical black-hole theorems (how robust are the latter against them?) and certainly affect particles and fields around, which can have observational consequences. In the present contribution we examine how the geodesic structure of the static and axially symmetric black-hole space-time responds to the presence of an additional matter in the form of a thin disc or ring. We use several different methods to show that ...
Perfect imaging analysis of the spherical geodesic waveguide
González, Juan C.; Benítez, Pablo; Miñano, Juan C.; Grabovičkić, Dejan
2012-12-01
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to λ/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.
Extreme super-resolution using the spherical geodesic waveguide
Miñano, Juan Carlos; González, Juan Carlos; Benítez, Pablo; Grabovičkić, Dejan
2012-06-01
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.
Circuital model for the spherical geodesic waveguide perfect drain
González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.
2012-08-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.
Self-gravitating stellar collapse: explicit geodesics and path integration
Directory of Open Access Journals (Sweden)
Jayashree Balakrishna
2016-11-01
Full Text Available We extend the work of Oppenheimer-Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Comment on "Quantum Raychaudhuri equation"
Lashin, E. I.; Dou, Djamel
2017-03-01
We address the validity of the formalism and results presented in S. Das, Phys. Rev. D 89, 084068 (2014), 10.1103/PhysRevD.89.084068 with regard to the quantum Raychaudhuri equation. The author obtained the so-called quantum Raychaudhuri equation by replacing classical geodesics with quantal trajectories arising from Bhommian mechanics. The resulting modified equation was used to draw some conclusions about the inevitability of focusing and the formation of conjugate points and therefore singularity. We show that the whole procedure is full of problematic points, on both physical relevancy and mathematical correctness. In particular, we illustrate the problems associated with the technical derivation of the so-called quantum Raychaudhuri equation, as well as its invalid physical implications.
Small shape deviations causes complex dynamics in large electric generators
Lundström, Niklas L. P.; Grafström, Anton; Aidanpää, Jan-Olov
2014-05-01
We prove that combinations of small eccentricity, ovality and/or triangularity in the rotor and stator can produce complex whirling motions of an unbalanced rotor in large synchronous generators. It is concluded which structures of shape deviations that are more harmful, in the sense of producing complex whirling motions, than others. For each such structure, we derive simplified equations of motions from which we conclude analytically the relation between shape deviations and mass unbalance that yield non-smooth whirling motions. Finally we discuss validity of our results in the sense of modeling of the unbalanced magnetic pull force.
Entanglement Equilibrium and the Einstein Equation.
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.
Computation of the shortest path between two curves on a parametric surface by geodesic-like method
Chen, Wen-Haw
2010-01-01
In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in $\\mathbb{R}^3$. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.
The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths
Institute of Scientific and Technical Information of China (English)
Chun Gen LIU
2005-01-01
In this paper, we consider the relation of the Morse index of a closed geodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closed geodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), we construct a symplectic path γ(t) starting from identity I and ending at P, such that the Morse index of the closed geodesic c equals the Maslov-type index of γ. As an application of this result, we study the parity of the Morse index of any closed geodesic.
48 CFR 2501.403 - Individual deviations.
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....
48 CFR 1901.403 - Individual deviations.
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...
48 CFR 201.403 - Individual deviations.
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)...
48 CFR 1.403 - Individual deviations.
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....
48 CFR 601.403 - Individual deviations.
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....
48 CFR 3401.403 - Individual deviations.
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...
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.
Timelike and null equatorial geodesics in the Bonnor-Sackfield relativistic disk
Directory of Open Access Journals (Sweden)
Guillermo A. González
2011-06-01
Full Text Available A study of timelike and null equatorial geodesics in the BonnorSackfield relativistic thin disk is presented. The motion of test particles in the equatorial plane is analyzed, both for the newtonian thin disk model as for the corresponding relativistic disk. The nature of the possible orbits is studied by means of a qualitative analysis of the effective potential and by numerically solving the motion equation for radial and non-radial equatorial trajectories. The existence of stable, unstable and marginally stable circular orbits is analyzed, both for the newtonian and relativistic case. Examples of the numerical results, obtained with some simple values of the parameters, are presented. Resumen. En este trabajo se presenta un estudio de las geodésicas temporales y nulas en el disco delgado relativista y newtoniano de Bonnor-Sackfield. Se analiza el movimiento de las partículas de prueba en el plano ecuatorial, tanto para el modelo newtoniano del disco delgado como para el disco relativista correspondiente. La naturaleza de las órbitas posibles se estudia por medio de un análisis cualitativo del potencial efectivo, y numéricamente mediante la solución de la ecuación de movimiento de las trayectorias ecuatorial radial y no radial: Se analiza la existencia de órbitas estables, circulares inestables y estables marginalmente, tanto para el caso newtoniano, como el relativista. Se presentan ejemplos de los resultados numéricos obtenidos con algunos valores de los parámetros simples.
Geodesic distance on a Grassmannian for monitoring the progression of Alzheimer's disease.
Gui, Liangyan; Tang, Xiaoying; Moura, José M F
2017-02-01
We propose a geodesic distance on a Grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi, amygdalas, and lateral ventricles in healthy control (HC), mild cognitive impairment (MCI), and Alzheimer's disease (AD). Longitudinal magnetic resonance imaging (MRI) scans of 754 subjects (3092 scans in total) were used in this study. Longitudinally, the geodesic distance was found to be proportional to the elapsed time separating the two scans in question. Cross-sectionally, utilizing a linear mixed-effects statistical model, we found that each structure's annualized rate of change in the geodesic distance followed the order of AD>MCI>HC, with statistical significance being reached in every case. In addition, for each of the six structures of interest, within the same time interval (e.g., from baseline to the 6th month), we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the ADAS-cog increase and the MMSE decrease. Furthermore, as the disease progresses over time, this linkage between the inter-shape geodesic distance and the cognitive decline becomes considerably stronger and more significant.
3D Facial Similarity Measure Based on Geodesic Network and Curvatures
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.
Large Deviation Functional of the Weakly Asymmetric Exclusion Process
Enaud, C.; Derrida, B.
2004-02-01
We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1/L. We recover as limiting cases the expressions derived recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP limit, the non linear differential equation one needs to solve can be analysed by a method which resembles the WKB method.
Derivation of Klein-Gordon-Fock equation from General relativity in a time-space symmetrical model
Van Thuan, Vo
2016-01-01
Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic" cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, as the squared Dirac equations of leptons and as a sub-solution with pseudo-axion. This result would serve an explicit approach to consistency between quantum mechanics and general relativity.
Cosolvency and deviations from log-linear solubilization.
Rubino, J T; Yalkowsky, S H
1987-06-01
The solubilities of three nonpolar drugs, phenytoin, diazepam, and benzocaine, have been measured in 14 cosolvent-water binary mixtures. The observed solubilities were examined for deviations from solubilities calculated by the equation log Sm = f log Sc + (1 - f) log Sw, where Sm is the solubility of the drug in the cosolvent-water mixture, Sc is the solubility of the drug in neat cosolvent, f is the volume fraction of cosolvent, and Sw is the solubility of the drug in water. When presented graphically, the patterns of the deviations were similar for all three drugs in mixtures of amphiprotic cosolvents (glycols, polyols, and alcohols) and water as well as nonpolar, aprotic cosolvents (dioxane, triglyme, dimethyl isosorbide) and water. The deviations were positive for phenytoin and benzocaine but negative for diazepam in mixtures of dipolar, aprotic cosolvents (dimethylsulfoxide, dimethylformamide, and dimethylacetamide) and water. The source of the deviations could not consistently be attributed to physical properties of the cosolvent-water mixtures or to alterations in the solute crystal. Similarities between the results of this study and those of previous investigations suggest that changes in the structure of the solvent play a role in the deviations from the expected solubilities.
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole
2011-01-01
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant......-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine...... that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE...
The Degasperis-Procesi equation as a non-metric Euler equation
Escher, Joachim
2009-01-01
In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\\'echet space of all smooth functions on the circle.
Educational Facilities Labs., Inc., New York, NY.
A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…
A numerical study of the correspondence between paths in a causal set and geodesics in the continuum
Ilie, R; Thompson, G B; Ilie, Raluca; Reid, David D.; Thompson, Gregory B.
2006-01-01
This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.
Directory of Open Access Journals (Sweden)
Kun-Lin Wu
2016-01-01
Full Text Available In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.
LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
Institute of Scientific and Technical Information of China (English)
Liu Li; Wan Chenggao; Feng Yanqin
2011-01-01
In this article, we obtain the large deviations and moderate deviations for negatively dependent (ND) and non-identically distributed random variables defined on (-∞, +∞). The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, Marcelo B.
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical...
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, M B
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
A Fortran code for null geodesic solutions in the Lemaître-Tolman-Bondi spacetime
Ribeiro, Marcelo B.
2002-10-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaître-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
Impact of Energetic-Particle-Driven Geodesic Acoustic Modes on Turbulence
Zarzoso, D.; Sarazin, Y.; Garbet, X.; Dumont, R.; Strugarek, A.; Abiteboul, J.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-03-01
The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.
On geodesics with negative energies in the ergoregions of dirty black holes
Zaslavskii, O B
2014-01-01
We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov, and V. D. Vertogradov, Mod. Phys. Lett. 29, 1450110 (2014) [arXiv:1304.7360].
Paiva, F M
2011-01-01
In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular motion with constant velocity, particularly closed timelike curves, and time travel of a voyager. ------------------- ^Ce la ^Generala Relativeco, en homogena metriko de Som-Raychaudhuri, ni studas geodeziojn de la tri tipoj: tempa, nula, kaj spaca, speciale la malmulte konatajn samtempajn geodeziojn. Ni anka^u studas ne-geodezian cirklan movadon kun konstanta rapido, speciale fermitajn kurbojn de tempa tipo, kaj movadon de voja^ganto al estinto.
48 CFR 1201.403 - Individual deviations.
2010-10-01
...) 48 CFR 1.405(e) applies). However, see TAM 1201.403. ... 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...
48 CFR 1401.403 - Individual deviations.
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...
48 CFR 3001.403 - Individual deviations.
2010-10-01
.... 3001.403 Section 3001.403 Federal Acquisition Regulations System DEPARTMENT OF HOMELAND SECURITY... from the FAR and HSAR 3001.403 Individual deviations. Unless precluded by law, executive order, or..., including complete documentation of the justification for the deviation (See HSAM 3001.403)....
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...
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... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Deviations. 435.4 Section 435.4 Employees' Benefits SOCIAL SECURITY ADMINISTRATION UNIFORM ADMINISTRATIVE REQUIREMENTS FOR GRANTS AND AGREEMENTS WITH... General § 435.4 Deviations. The Office of Management and Budget (OMB) may grant exceptions for classes...
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James;
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots ...
Santoprete, Manuele
2002-01-01
Resorting to classical techniques of Riemannian geometry we develop a geometrical method suitable to investigate the nonintegrability of geodesic flows and of natural Hamiltonian systems. Then we apply such method to the Anisotropic Kepler Problem (AKP) and we prove that it is not analytically integrable.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces Y
Visinescu, Mihai
2017-01-01
We use action-angle variables to describe the geodesic motions in the 5-dimensional Sasaki-Einstein spaces Y. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequencies is zero, indicating chaotic behavior when the system is perturbed.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz. PMID:28134324
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots...
Null geodesics in the Reissner-Nordstr\\"om Anti-de Sitter black holes
Cruz, Norman; Saavedra, Joel; Villanueva, J R
2011-01-01
In this work we address the study of null geodesics in the background of Reissner-Nordstr\\"om Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.
Coupled equations for K\\"ahler metrics and Yang-Mills connections
Alvarez-Consul, Luis; Garcia-Prada, Oscar
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, Mabuchi functional and geodesic stability. We finish by giving some examples of solutions.
Moderate Deviation Principle for dynamical systems with small random perturbation
ma, Yutao; Wu, Liming
2011-01-01
Consider the stochastic differential equation in $\\rr^d$ dX^{\\e}_t&=b(X^{\\e}_t)dt+\\sqrt{\\e}\\sigma(X^\\e_t)dB_t X^{\\e}_0&=x_0,\\quad x_0\\in\\rr^d where $b:\\rr^d\\rightarrow\\rr^d$ is $C^1$ such that $ \\leq C(1+|x|^2)$, $\\sigma:\\rr^d\\rightarrow \\MM(d\\times n)$ is locally Lipschitzian with linear growth, and $B_t$ is a standard Brownian motion taking values in $\\rr^n$. Freidlin-Wentzell's theorem gives the large deviation principle for $X^\\e$ for small $\\e$. In this paper we establish its moderate deviation principle.
Araki, Keisuke
2017-06-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Elsässer variables (GEVs). Examinations of the stabilities of the hydrodynamic (HD, α=0 ) and magnetohydrodynamic (MHD, α\\to0 ) motions and the O(α) Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where α represents the Hall-term strength parameter. It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the positive (stable) and negative (unstable) values, while that of the HD system between two complex helical waves was observed to be negative definite. Moreover, for the MHD case, negative sectional curvatures were found to occur only when mode interaction was ‘local’, i.e. the wavenumber moduli of the main flow (say p) and perturbation (say k) were relatively close to each other. However, in the nonlocal limit (k\\ll p or k\\gg p ), the sectional curvatures were always positive. This result leads to the conjecture that the MHD interactions mainly excite wavy or non-growing motions; however, some local interactions cause dynamical instability that leads to chaotic or turbulent plasma motions. Additionally, it was found that the tendencies of the O(α) effects are opposite between the ion cyclotron and whistler modes. Comparison with the energy-Casimir method is also discussed using a remarkable constant of motion which relates the Riemannian curvature to the second variation of the
Large Deviations in Quantum Spin Chain
Ogata, Yoshiko
2008-01-01
We show the full large deviation principle for KMS-states and $C^*$-finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle's transfer operator method.
Large deviations for a random speed particle
Lefevere, Raphael; Zambotti, Lorenzo
2011-01-01
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is absorbed and re-emitted from the left boundary with a new random speed, taken from an i.i.d. sequence. It turns out that this simple model, often used to simulate a heat bath, displays unusually complex large deviations features, that we explain in detail. In particular, if the tail of the update distribution of the speed is sufficiently oscillating, then the empirical measure does not satisfy a large deviations principle, and we exhibit optimal lower and upper large deviations functionals.
Large deviations for fractional Poisson processes
Beghin, Luisa
2012-01-01
We present large deviation results for two versions of fractional Poisson processes: the main version which is a renewal process, and the alternative version where all the random variables are weighted Poisson distributed. We also present a sample path large deviation result for suitably normalized counting processes; finally we show how this result can be applied to the two versions of fractional Poisson processes considered in this paper.
The large deviations theorem and ergodicity
Energy Technology Data Exchange (ETDEWEB)
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2007-12-15
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.
Elimination of Nonlinear Deviations in Thermal Lattice BGK Models
Chen, Y; Hongo, T; Chen, Yu; Ohashi, Hirotada; Akiyam, Mamoru
1993-01-01
Abstracet: We present a new thermal lattice BGK model in D-dimensional space for the numerical calculation of fluid dynamics. This model uses a higher order expansion of equilibrium distribution in Maxwellian type. In the mean time the lattice symmetry is upgraded to ensure the isotropy of 6th order tensor. These manipulations lead to macroscopic equations free from nonlinear deviations. We demonstrate the improvements by conducting classical Chapman-Enskog analysis and by numerical simulation of shear wave flow. The transport coefficients are measured numerically, too.
On a periodic two-component Hunter-Saxton equation
Kohlmann, Martin
2011-01-01
We determine the solution of the geodesic equation associated with a periodic two-component Hunter-Saxton system on a semidirect product obtained from the diffeomorphism group of the circle, modulo rigid rotations, and a space of scalar functions. In particular, we compute the time of breakdown of the geodesic flow. As a further goal, we establish a local well-posedness result for the two-component Hunter-Saxton system in the smooth category. The paper gets in line with some recent results for the generalized Hunter-Saxton equation provided by Escher, Wu and Wunsch in [J. Escher, Preprint 2010] and [H. Wu, M. Wunsch, arXiv:1009.1688v1 [math.AP
Large deviations for stochastic flows and their applications
Institute of Scientific and Technical Information of China (English)
GAO; Fuqing(
2001-01-01
［1］Yoshida, N., A large deviation principle for (r,p)-capacities on the Wiener space, Proba. Th. Rel. Fields, 1993, 94:473-488.［2］Gao, F. Q., Large deviations of (r,p)-capacities for diffusion processes, Advances in Math. (in Chinese), 1996, 25:500-509.［3］Millet, A., Nualart, D., Sanz, M., Large deviations for a class of anticipating stochastic differential equations, Ann.Prob.. 1993, 20: 1902-1931.［4］Millet, A., Nualart, D., Sans, M., Composition of large deviation principles and applications, in Stochastic Analysis (ed.Mayer, E. ), San Diego: Academic Press, 1991, 383-395.［5］Ocone, D., Pardoux, E., A generalized Ito-Ventzell formula, Applications to a class of anticipating stochastic differentialequations, Ann. Inst. Poincaré, Sect. B, 1989, 25: 39-71.［6］Malliavin, P., Nualart, D., Quasi sure analysis of stochastic flows and Banach space valued smooth functionals on the Wiener space, J. Funct. Anal., 1993, 112: 287-317.［7］Huang, Z., Ren, J. , Quasi sure stochastic flows, Stoch. Stoch. Rep. , 1990, 33: 149-157.［8］Gao, E. Q., Large deviations for diffusion processes in Hslder norm, Advances in Math. (in Chinese), 1997, 26: 147-158.［9］Arous, B. G. , Ledoux, M., Grandes déviations sur la déviations de Freidlin-Wentzell en norme holderienne, 1994, Lecr.Notes in Math. , 1994, 987: 1583.［10］Baldi, P. , Sanz, M. , Une remarque sur la théorie des grandes deviations, Lect. Notes Math., 1991, 1485: 345-348.［11］Airault, H., Malliavin, P., Intégration géometrique sur l'espace de Wiener, Bull. Sci. Math., 1988, 112: 3-52.［12］Ikeda, N. , Watanabe, S., Stochastic Differential Equations and Diffusion Processes, 2nd ed., Amsterdam-Kodansha-Tokyo:North-Holland, 1988.［13］Malliavin, P., Stochastic Analysis, Grundlehren der Mathematischen Wissenschaften 313, Berlin: Springer-Verlag, 1997.［14］Brzezniak, Z., Elworthy, K. D., Stochastic flows of diffeomorphism. In Stochastic Analysis and Applications (eds. Davies,I. M.. Truman
Functional differential equations of third order
Directory of Open Access Journals (Sweden)
Tuncay Candan
2005-04-01
Full Text Available In this paper, we consider the third-order neutral functional differential equation with distributed deviating arguments. We give sufficient conditions for the oscillatory behavior of this functional differential equation.
Large deviations of the maximal eigenvalue of random matrices
Borot, Gaëtan; Majumdar, Satya; Nadal, Céline
2011-01-01
We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.
Anterior septal deviation and contralateral alar collapse.
Schalek, P; Hahn, A
2011-01-01
Septal deviation is often found in conjunction with other pathological conditions that adversely affect nasal patency. Anterior septal deviation, together with contralateral alar collapse, is a relatively rare type of anatomical and functional incompetence. In our experience, it can often be resolved with septoplasty, without the necessity of surgery involving the external valve. The aim of this paper was to verify this hypothesis prospectively. Twelve patients with anterior septal deviation and simultaneous alar collapse on the opposite side were prospectively enrolled in the study. Subjective assessment of nasal patency was made on post-operative day 1, and again 6 months after surgery, using a subjective evaluation of nasal breathing. The width of the nostril (alar-columellar distance) on the side with the alar collapse was measured during inspiration pre-operatively, 1 day after surgery and again 6 months after surgery. Immediately after surgery, all patients reported improved or excellent nasal breathing on the side of the original septal deviation. On the collapsed side, one patient reported no change in condition. With the exception of one patient, all measurements showed some degree of improvement in the extension of the alar-columellar distance. The average benefit 6 months after surgery was an improvement of 4.54 mm. In our group of patients (anterior septal deviation and simultaneous contralateral alar collapse and no obvious structural changes of the alar cartilage) we found septoplasty to be entirely suitable and we recommend it as the treatment of choice in such cases.
Waterline extraction in optical images and InSAR coherence maps based on the geodesic time concept
Soares, Fernando; Nico, Giovanni
2010-10-01
An algorithm for waterline extraction from SAR images is presented based on the estimation of the geodesic path, or minimal path (MP) between two pixels on the waterline. For two given pixels, geodesic time is determined in terms of the time shortest path, between them. The MP is determined by estimating the mean value for all pairs of neighbor pixels that can be part of a possible path connecting the initial given pixels. A MP is computed as the sum of those two geodesic image functions. In general, a MP is obtained with the knowledge of two end pixels. Based on the 2-dimensional spreading of the estimated geodesic time function, the concepts of propagation energy and strong pixels are introduced and tested for the waterline extraction by marking only one pixel in the image.
One dimensional Newton's equation with variable mass
Mazharimousavi, S Habib
2013-01-01
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a 1+1-dimensional spacetime. As a reflection of the equivalence principle geodesics equation gives the Newton's law of motion leaving the right hand side to be supplemented by the external forces. The resulting equation involves the speed of light so that our equation of motion addresses a wider scope than the customary classical mechanics. In the limit of infinite light speed which amounts to instantaneous interaction we recover the classical results.
Investigating deviations from norms in court interpreting
DEFF Research Database (Denmark)
Dubslaff, Friedel; Martinsen, Bodil
, in some cases, all - professional users involved (judges, lawyers, prosecutors). As far as the non-Danish speaking users are concerned, it has, with one notable exception, unfortunately not been possible to obtain data from this group via questionnaires. As this type of data, however, is important...... behaviour, explore why the deviations in question occur, find out what happens if deviations are perceived as such by the other participants involved in the interpreted event. We will reconstruct the norms in question by examining interpreters' and (mainly) professional users' behaviour in the course...... deviations and sanctions in every case. By way of example: Several judges, who had given their consent to recordings of authentic data in connection with the research project, reported that they had experienced problems with insufficient language proficiency on the part of untrained interpreters speaking...
Quantifying prosthetic gait deviation using simple outcome measures
Kark, Lauren; Odell, Ross; McIntosh, Andrew S; Simmons, Anne
2016-01-01
AIM: To develop a subset of simple outcome measures to quantify prosthetic gait deviation without needing three-dimensional gait analysis (3DGA). METHODS: Eight unilateral, transfemoral amputees and 12 unilateral, transtibial amputees were recruited. Twenty-eight able-bodied controls were recruited. All participants underwent 3DGA, the timed-up-and-go test and the six-minute walk test (6MWT). The lower-limb amputees also completed the Prosthesis Evaluation Questionnaire. Results from 3DGA were summarised using the gait deviation index (GDI), which was subsequently regressed, using stepwise regression, against the other measures. RESULTS: Step-length (SL), self-selected walking speed (SSWS) and the distance walked during the 6MWT (6MWD) were significantly correlated with GDI. The 6MWD was the strongest, single predictor of the GDI, followed by SL and SSWS. The predictive ability of the regression equations were improved following inclusion of self-report data related to mobility and prosthetic utility. CONCLUSION: This study offers a practicable alternative to quantifying kinematic deviation without the need to conduct complete 3DGA. PMID:27335814
Geodesic-length functions and the Weil-Petersson curvature tensor
Wolpert, Scott A
2010-01-01
An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower bound for sectional curvature in terms of the systole is presented. The curvature tensor expansion is applied to establish continuity properties at the frontier strata of the augmented Teichm\\"{u}ller space. The curvature tensor has the asymptotic product structure already observed for the metric and covariant derivative. The product structure is combined with the earlier negative sectional curvature results to establish a classification of asymptotic flats. Furthermore, tangent subspaces of more than half the dimension of Teichm\\"{u}ller space contain sections with a definite amount of negative curvature. Proofs combine estimates for uniformization group exponential-distance sums and potential theory bounds.
Singh, Nikhil; Hinkle, Jacob; Joshi, Sarang; Fletcher, P Thomas
2013-04-01
This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a closed-form update for template estimation in both the geodesic regression and atlas estimation problems. While we show that the theoretical optimal solution is equivalent to the scalar momenta case, the simplification of the optimization problem leads to more stable and efficient estimation in practice. We demonstrate the effectiveness of our method for atlas estimation and geodesic regression using synthetically generated shapes and 3D MRI brain scans.
Geodesic mode instability driven by electron and ion fluxes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Elfimov, A. G., E-mail: elfimov@if.usp.br; Camilo de Souza, F.; Galvão, R. M. O. [Institute of Physics, University of São Paulo, São Paulo 05508-090 (Brazil)
2015-11-15
The effect of the parallel electron current and plasma flux on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current and plasma flow, modeled by shifted Maxwell distributions of electrons and ions, may overcome the ion Landau damping generating the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity of sidebands, Rqω. The instability is driven by the electron current and the parallel ion flux cross term. Possible applications to tokamak experiments are discussed. The existence of the geodesic ion sound mode due to plasma flow is shown.
Geodesic least squares regression for scaling studies in magnetic confinement fusion
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2015-01-13
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
Equatorial geodesics of dyonic Kerr-Newman black hole pierced by a cosmic string
Sharif, M.; Iftikhar, Sehrish
2016-12-01
This paper is devoted to study the circular geodesics of the dyonic Kerr-Newman black hole with a cosmic string passing through it. We investigate circular geodesics of null and timelike particle. In this context, we find the circular photon orbit as well as the innermost stable circular orbit. The angular velocity and time period for the timelike particle are calculated. The effect of electric and magnetic charge as well as of the cosmic string parameter on the effective potential is analyzed numerically. Finally, we discuss the role of these parameters on the energy extraction by the Penrose process. We conclude that the string parameter does not affect the gain energy of the particle but it decreases with respect to charge.
AdS/CFT prescription for angle-deficit space and winding geodesics
Aref'eva, Irina Ya
2016-01-01
We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS$_3$ space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical Green functions for a scalar field in the bulk with conical defect and use them to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of $\\mathbb{Z}_r$-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.
Single Past Null Geodesic in the Lemaitre-Tolman-Bondi Cosmology
Nogueira, Felipe A M G
2013-01-01
This work provides a general discussion of the spatially inhomogeneous Lema\\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift. As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, comparing it to the spatially homogeneous Einstein-de Sitter cosmology. The results obtained indicate that the standard model, in this case represented by the Einstein-de Sitter cosmology, can be equivalently described by a fractal distribution of matter, as we found that different single fractal dimensions describe different scale ranges of the parabolic LTB matter distribution. It is shown that at large ranges the parabolic LTB model with fractal dimension equal to 0.5 approximates the matter distribution of the Einstein-de Sitter univers...
The Differential of the Exponential Map, Jacobi Fields and Exact Principal Geodesic Analysis
Sommer, Stefan; Nielsen, Mads
2010-01-01
The importance of manifolds and Riemannian geometry in mathematics is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry. The transfer of interest has created demand for methods for computing classical constructs of geometry on manifolds occurring in practical applications. This paper develops initial value problems for the computation of the differential of the exponential map and Jacobi fields on parametrically and implicitly represented manifolds. It is shown how the solution to these problems allow for determining sectional curvatures and provides upper bounds for injectivity radii. In addition, when combined with the second derivative of the exponential map, the initial value problems allow for solving the problem of computing Principal Geodesic Analysis, a non-linear version of the Principal Component Analysis procedure for estimating variability in datasets. The paper develops algorithms for computing Principal Geodesic Analysis with...
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.
Directory of Open Access Journals (Sweden)
Edgar F. Vargas
2007-01-01
Full Text Available The deviations observed in the solubility of ibuprofen (IBP and naproxen (NAP in propylene glycol (PG + water (W cosolvent mixtures with respect to the logarithmic-linear model proposed by Yalkowsky have been analyzed at 25.00 ± 0.05 ºC. Negative deviations were obtained in all cosolvent compositions for both drugs; they were greater for IBP. Another treatment, based on Gibbs free energy relationships, was also employed showing an apparent hydrophobicity chameleonic effect, because at low PG proportions NAP is more hydrophobic, whereas at high PG proportions IBP is more hydrophobic. The results are discussed in terms of solute-solvent and solvent-solvent interactions.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$
Visinescu, Mihai
2016-01-01
We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequency is zero indicating a chaotic behavior when the system is perturbed.
Multi-focal spherical media and geodesic lenses in geometrical optics
Sarbort, Martin
2013-01-01
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains.
Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation
Herrera, L; Ospino, J
2015-01-01
Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution, unless the dissipative flux vanishes. In this latter case the vorticity also must vanish, and the resulting spacetime is Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational radiation.
Geodesic motions of test particles in a relativistic core-shell spacetime
Liu, Lei; Wu, Xin; Huang, Guoqing
2017-02-01
In this paper, we discuss the geodesic motions of test particles in the intermediate vacuum between a monopolar core and an exterior shell of dipoles, quadrupoles and octopoles. The radii of the innermost stable circular orbits at the equatorial plane depend only on the quadrupoles. A given oblate quadrupolar leads to the existence of two innermost stable circular orbits, and their radii are larger than in the Schwarzschild spacetime. However, a given prolate quadrupolar corresponds to only one innermost stable circular orbit, and its radius is smaller than in the Schwarzschild spacetime. As to the general geodesic orbits, one of the recently developed extended phase space fourth order explicit symplectic-like methods is efficiently applicable to them although the Hamiltonian of the relativistic core-shell system is not separable. With the aid of both this fast integrator without secular growth in the energy errors and gauge invariant chaotic indicators, the effect of these shell multipoles on the geodesic dynamics of order and chaos is estimated numerically.
Derivation of Geodesic Flow Fields and Spectrum in Digital Topographic Basins
Directory of Open Access Journals (Sweden)
Sin Liang Lim
2008-01-01
Full Text Available We present a framework to characterize terrestrial functions—surficial and bottom topographic regions that are represented, respectively, as raster digital elevation models (DEMs and digital bathymetric models (DBMs—through analysis of flow fields that are simulated via geodesic morphology. Characterization of such functions is done via a new descriptor. Computation of this new descriptor involves the following steps: (i basin in digital form representing topographic fluctuations as an input, (ii threshold decomposition of basin—that consists of channelized and nonchannelized regions—into sets, (iii proper indexing of these sets to decide the marker set(s and its (their corresponding mask set(s, (iv performing geodesic propagation that provides basic flow field structures, and (v finally providing a new basin descriptor—geodesic spectrum. We demonstrated this five-step framework on five different synthetic and/or realistic DEMs and/or DBMs. This study provides potentially invaluable insights to further study the travel-time flood propagation within basins of both fluvial and tidal systems.
Small scale structure of spacetime: van Vleck determinant and equi-geodesic surfaces
Stargen, D Jaffino
2015-01-01
It has recently been argued that if spacetime $\\mathcal M$ possesses non-trivial structure at small scales, an appropriate semi-classical description of it should be based on non-local bi-tensors instead of local tensors such as the metric $g_{ab}$. Two most relevant bi-tensors in this context are Synge's World function $\\Omega(p,p_0)$ and the van Vleck determinant (VVD) $\\Delta(p,p_0)$, as they encode the metric properties of spacetime and (de)focussing behaviour of geodesics. They also characterize the leading short distance behavior of two point functions of the d'Alembartian $_{p_0} \\square_p$. We begin by discussing the intrinsic and extrinsic geometry of equi-geodesic surfaces $\\Sigma_{G,p_0}$ defined by $\\Omega(p,p_0)=constant$ in a geodesically convex neighbourhood of an event $p_0$, and highlight some elementary identities relating the VVD with geometry of these surfaces. As an aside, we also comment on the contribution of $\\Sigma_{G,p_0}$ to the surface term in the Einstein-Hilbert (EH) action and s...
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
Benvenuti, S; Benvenuti, Sergio; Kruczenski, Martin
2006-01-01
The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analisys simplifies for the special case of the Lpqq models, which are shown to correspond to the known "generalized conifolds". These geometries can break conformal invariance through toric deformations of the c...
Bodily Deviations and Body Image in Adolescence
Vilhjalmsson, Runar; Kristjansdottir, Gudrun; Ward, Dianne S.
2012-01-01
Adolescents with unusually sized or shaped bodies may experience ridicule, rejection, or exclusion based on their negatively valued bodily characteristics. Such experiences can have negative consequences for a person's image and evaluation of self. This study focuses on the relationship between bodily deviations and body image and is based on a…
Bodily Deviations and Body Image in Adolescence
Vilhjalmsson, Runar; Kristjansdottir, Gudrun; Ward, Dianne S.
2012-01-01
Adolescents with unusually sized or shaped bodies may experience ridicule, rejection, or exclusion based on their negatively valued bodily characteristics. Such experiences can have negative consequences for a person's image and evaluation of self. This study focuses on the relationship between bodily deviations and body image and is based on a…
2010-10-01
... 45 Public Welfare 4 2010-10-01 2010-10-01 false Deviations. 2543.4 Section 2543.4 Public Welfare Regulations Relating to Public Welfare (Continued) CORPORATION FOR NATIONAL AND COMMUNITY SERVICE GRANTS AND AGREEMENTS WITH INSTITUTIONS OF HIGHER EDUCATION, HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS General...
Voice Deviations and Coexisting Communication Disorders.
St. Louis, Kenneth O.; And Others
1992-01-01
This study examined the coexistence of other communicative disorders with voice disorders in about 3,400 children in grades 1-12 at 100 sites throughout the United States. The majority of voice-disordered children had coexisting articulation deviations and also differed from controls on two language measures and mean pure-tone hearing thresholds.…
41 CFR 109-1.5304 - Deviations.
2010-07-01
... Secretary for Procurement and Assistance Management. A HFO's decision not to provide life-cycle control... through the cognizant HFO to the Deputy Assistant Secretary for Procurement and Assistance Management. ... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviations....
2010-10-01
... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Deviations. 12.904 Section 12.904 Public Lands: Interior Office of the Secretary of the Interior ADMINISTRATIVE AND AUDIT REQUIREMENTS AND COST PRINCIPLES FOR ASSISTANCE PROGRAMS Uniform Administrative Requirements for Grants and Agreements...
Association between septal deviation and sinonasal papilloma.
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.
Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations
Sergeev, A.
2017-03-01
In this paper we deal with the (2 + 1)-dimensional Higgs model governed by the Ginzburg-Landau Lagrangian. The static solutions of this model, called otherwise vortices, are described by the theorem of Taubes. This theorem gives, in particular, an explicit description of the moduli space of vortices (with respect to gauge transforms). However, much less is known about the moduli space of dynamical solutions. A description of slowly moving solutions may be given in terms of the adiabatic limit. In this limit the dynamical Ginzburg-Landau equations reduce to the adiabatic equation coinciding with the Euler equation for geodesics on the moduli space of vortices with respect to the Riemannian metric (called T-metric) determined by the kinetic energy of the model. A similar adiabatic limit procedure can be used to describe approximately solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this case the geodesics of T-metric are replaced by the pseudoholomorphic curves while the solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂-equation which can be considered as a complex analogue of the adiabatic equation. Respectively, the arising pseudoholomorphic curves may be considered as complex analogues of adiabatic geodesics in (2 + 1)-dimensional case. In this sense the Seiberg-Witten model may be treated as a (2 + 1)-dimensional analogue of the (2 + 1)-dimensional Abelian Higgs model2.
Large Deviation Strategy for Inverse Problem
Ojima, Izumi
2011-01-01
Taken traditionally as a no-go theorem against the theorization of inductive processes, Duheme-Quine thesis may interfere with the essence of statistical inference. This difficulty can be resolved by \\textquotedblleft Micro-Macro duality\\textquotedblright\\ \\cite{Oj03, Oj05} which clarifies the importance of specifying the pertinent aspects and accuracy relevant to concrete contexts of scientific discussions and which ensures the matching between what to be described and what to describe in the form of the validity of duality relations. This consolidates the foundations of the inverse problem, induction method, and statistical inference crucial for the sound relations between theory and experiments. To achieve the purpose, we propose here Large Deviation Strategy (LDS for short) on the basis of Micro-Macro duality, quadrality scheme, and large deviation principle. According to the quadrality scheme emphasizing the basic roles played by the dynamics, algebra of observables together with its representations and ...
Large deviations for tandem queueing systems
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Roland L. Dobrushin
1994-01-01
Full Text Available The crude asymptotics of the large delay probability in a tandem queueing system is considered. The main result states that one of the two channels in the tandem system defines the crude asymptotics. The constant that determines the crude asymptotics is given. The results obtained are based on the large deviation principle for random processes with independent increments on an infinite interval recently established by the authors.
Stochastic gene expression conditioned on large deviations
Horowitz, Jordan M.; Kulkarni, Rahul V.
2017-06-01
The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare events motivates the analysis of large deviations in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics have led to a framework for analyzing Markovian processes conditioned on rare events and for representing such processes by conditioning-free driven Markovian processes. We use this framework, in combination with approaches based on queueing theory, to analyze a general class of stochastic models of gene expression. Modeling gene expression as a Batch Markovian Arrival Process (BMAP), we derive exact analytical results quantifying large deviations of time-integrated random variables such as promoter activity fluctuations. We find that the conditioning-free driven process can also be represented by a BMAP that has the same form as the original process, but with renormalized parameters. The results obtained can be used to quantify the likelihood of large deviations, to characterize system fluctuations conditional on rare events and to identify combinations of model parameters that can give rise to dynamical phase transitions in system dynamics.
离差在微分几何中的应用%Role of Deviation in Differential Geometry
Institute of Scientific and Technical Information of China (English)
洪涛清
2014-01-01
将微分几何课程中的主要概念通过＂离差＂这一桥梁统一起来，指出相对曲率、挠率、法曲率、测地曲率等都是曲线或曲面上点与某平面间的离差的不同表现形式。其次，利用离差推导出与这些概念相关的许多经典结论。在将数学概念系统化的同时，沟通解析几何与微分几何两门课程的教学。%Deviation can be used to unify main concepts in the course of differential geometry . Relative curvature ,torsion ,normal curvature ,and geodesic curvature are all deviations between a point and a plane .Many classical results associated with these concepts are deducted through deviation . Analytic Geometry and Differential Geometry can be linked well when the mathematical concepts are systemized as above .
Directory of Open Access Journals (Sweden)
Ion BULAC
2016-05-01
Full Text Available The technological (geometrical deviations which inevitable appear during the manufacturing and montage process at the component elements of the mechanism lead to supplementary efforts in the kinematic pairs.Being statically undetermined, for calculating the reactions it is using the elastic linear calculation For this is necessary the knowledge the forms of the technical (geometrical deviations in the general system of reference for writing the the equations of elastic balanced.This paper presents the calculation modality of these deviations .
Directory of Open Access Journals (Sweden)
Guohua Cao
2017-01-01
Full Text Available The dynamic responses of parallel hoisting system with time-varying length and rigid guidance under drive deviation are investigated considering tension and torsion characteristics of the ropes. The variable-domain three-node elements of rope are employed and the corresponding differential algebraic equations (DAEs are derived using Lagrange’s equations of the first kind. The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs. The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. However, the torsion of the corresponding rope is active. And unreasonable discordance between ropes should be controlled for the design and manufacture of drum on super deep parallel hoisting system.
Litvin, Faydor L.; Kuan, Chihping; Zhang, YI
1991-01-01
A numerical method is developed for the minimization of deviations of real tooth surfaces from the theoretical ones. The deviations are caused by errors of manufacturing, errors of installment of machine-tool settings and distortion of surfaces by heat-treatment. The deviations are determined by coordinate measurements of gear tooth surfaces. The minimization of deviations is based on the proper correction of initially applied machine-tool settings. The contents of accomplished research project cover the following topics: (1) Descriptions of the principle of coordinate measurements of gear tooth surfaces; (2) Deviation of theoretical tooth surfaces (with examples of surfaces of hypoid gears and references for spiral bevel gears); (3) Determination of the reference point and the grid; (4) Determination of the deviations of real tooth surfaces at the points of the grid; and (5) Determination of required corrections of machine-tool settings for minimization of deviations. The procedure for minimization of deviations is based on numerical solution of an overdetermined system of n linear equations in m unknowns (m much less than n ), where n is the number of points of measurements and m is the number of parameters of applied machine-tool settings to be corrected. The developed approach is illustrated with numerical examples.
LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES
Institute of Scientific and Technical Information of China (English)
Hu Yijun; Ming Ruixing; Yang Wenquan
2007-01-01
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved.Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
Meiosis and its deviations in polyploid plants.
Grandont, L; Jenczewski, E; Lloyd, A
2013-01-01
Meiosis is a fundamental process in all sexual organisms that ensures fertility and genome stability and creates genetic diversity. For each of these outcomes, the exclusive formation of crossovers between homologous chromosomes is needed. This is more difficult to achieve in polyploid species which have more than 2 sets of chromosomes able to recombine. In this review, we describe how meiosis and meiotic recombination 'deviate' in polyploid plants compared to diploids, and give an overview of current knowledge on how they are regulated. See also the sister article focusing on animals by Stenberg and Saura in this themed issue.
Guessing Revisited: A Large Deviations Approach
Hanawal, Manjesh Kumar
2010-01-01
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. Other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed. This approach highlights the importance of the information spectrum in determining the limiting guessing exponent. All known prior results are then re-derived as example applications of our unifying approach.
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Verdoolaege, G.; Shabbir, A.; Hornung, G.
2016-11-01
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field
Zimdahl, Winfried
2014-01-01
We investigate a Boltzmann gas in equilibrium with its center of mass moving on a circular geodesics in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the solar system as well as to strong-field configurations of neutron stars and black holes.
Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field
Zimdahl, Winfried; Kremer, Gilberto M.
2015-01-01
We investigate a Boltzmann gas at equilibrium with its center of mass moving on a circular geodesic in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the Solar System as well as to strong-field configurations of neutron stars and black holes.
Geodesic Motions in AdS Soliton Background Space-time
Shi, Han-qing
2016-01-01
We study both massive and massless particle's geodesic motion in the background of general dimensional AdS-Sol space-time. We find that the massive particles oscillate along the radial direction, while massless particles experience one-time bouncing as they approach the "horizon" line of the soliton. Our results provide a direct way to understand the negative energy/masses leading to the AdS-Sol geometry. As a potential application, we extend the point particle to a 3-brane and fix the background as a 5+1 dimension AdS-Sol, thus obtain a very natural bouncing/cyclic cosmological model.
Becerril, Ricardo; Valdez-Alvarado, Susana; Nucamendi, Ulises
2016-12-01
The mass parameters of compact objects such as boson stars, Schwarzschild, Reissner-Nordström, and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred , zblue ) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We find bounds for the values of (zred , zblue ) that may be observed. For the case of the Kerr black hole, recent observational estimates of Sgr A* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
Effective potential and geodesic motion in Kerr-de Sitter space-time
Poudel, P C
2013-01-01
In the present work, geodesic trajectories in Kerr-de Sitter geometry is analyzed. From the mathematical solution of Lagrangian formalism appropriate to motions in the equatorial plane (for which 'theta' = 0 and 'theta' = (constant)= pi/2) can give potential energy of massive and massless particles for rotating axisymetric black hole. From this, for a particular value of cosmological constant, Kerr parameter, mass, angular momentum and impact parameter; variation of potential with distance can be found. Similarly, for a particular value of cosmological constant, mass and Kerr parameter; variation of velocity with distance can be found.
Finite-orbit-width effects on the geodesic acoustic mode in the toroidally rotating tokamak plasma
Ren, Haijun
2016-01-01
The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating tokamak plasma is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical result is shown to agree well with the numerical solution. The dependence of the damping rate on the toroidal Mach number $M$ relies on $k_r \\rho_i$. For sufficiently small $k_r \\rho_i$, the damping rate monotonically decreases with $M$. For relatively large $k_r \\rho_i$, the damping rate increases with $M$ until approaching the maximum and then decreases with $M$.
On the realizable topology of a manifold with attractors of geodesics
Fenille, Marcio Colombo
2017-01-01
We discuss the so-called realizable topology of a Riemannian manifold with attractors of geodesics, which we understand as its topological properties, mainly that related to its fundamental group, investigated from a viewpoint that may be considered realizable in a sense. In the special approach in which the manifold is understood as a model physical universe, we conclude that its realizable fundamental group is isomorphic to the classical fundamental group of its observable portion. For a universe of dimension at least three whose unobservable components are all contractible, this conclusion ensures the possibility to get real inferences about its classical fundamental group through observational methods.
The properties and geodesics related to the NUT-Taub-like spacetime
Institute of Scientific and Technical Information of China (English)
Wu Ya-Bo; Zhao Guo-Ming; Deng Xue-Mei; Yang Xiu-Yi; Lü Jian-Bo; Li Song
2006-01-01
Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m* = 0 and m* < M,respectively.
Non-classical large deviations for a noisy system with non-isolated attractors
Bouchet, Freddy; Touchette, Hugo
2012-05-01
We study the large deviations of a simple noise-perturbed dynamical system having continuous sets of steady states, which mimic those found in some partial differential equations related, for example, to turbulence problems. The system is a two-dimensional nonlinear Langevin equation involving a dissipative, non-potential force, which has the essential effect of creating a line of stable fixed points (attracting line) touching a line of unstable fixed points (repelling line). Using different analytical and numerical techniques, we show that the stationary distribution of this system satisfies, in the low-noise limit, a large deviation principle containing two competing terms: (i) a 'classical' but sub-dominant large deviation term, which can be derived from the Freidlin-Wentzell theory of large deviations by studying the fluctuation paths or instantons of the system near the attracting line, and (ii) a dominant large deviation term, which does not follow from the Freidlin-Wentzell theory, as it is related to fluctuation paths of zero action, referred to as sub-instantons, emanating from the repelling line. We discuss the nature of these sub-instantons, and show how they arise from the connection between the attracting and repelling lines. We also discuss in a more general way how we expect these to arise in more general stochastic systems having connected sets of stable and unstable fixed points, and how they should determine the large deviation properties of these systems.
Allan deviation analysis of financial return series
Hernández-Pérez, R.
2012-05-01
We perform a scaling analysis for the return series of different financial assets applying the Allan deviation (ADEV), which is used in the time and frequency metrology to characterize quantitatively the stability of frequency standards since it has demonstrated to be a robust quantity to analyze fluctuations of non-stationary time series for different observation intervals. The data used are opening price daily series for assets from different markets during a time span of around ten years. We found that the ADEV results for the return series at short scales resemble those expected for an uncorrelated series, consistent with the efficient market hypothesis. On the other hand, the ADEV results for absolute return series for short scales (first one or two decades) decrease following approximately a scaling relation up to a point that is different for almost each asset, after which the ADEV deviates from scaling, which suggests that the presence of clustering, long-range dependence and non-stationarity signatures in the series drive the results for large observation intervals.
Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics
Cardin, Franco; Favretti, Marco; Lovison, Alberto
2017-09-01
In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.
Theory of Deviation and Its Application in College English Teaching
Institute of Scientific and Technical Information of China (English)
Xu Yanqiu
2008-01-01
Deviation is an important concept in stylistics.Besides Shklovskij and Mukarovsky,who made a theoreti cal generalization of deviational phenomena,Leech is the one who studies deviation systematically and catego rizes it into groups.To apply the theory of deviation to College English teaching is an effective way to culti rate students' interest in and aesthetic ability of English texts.
Hypotropic Dissociated Vertical Deviation; a Case Report
Directory of Open Access Journals (Sweden)
Zhale Rajavi
2013-01-01
Full Text Available Purpose: To report the clinical features of a rare case of hypotropic dissociated vertical deviation (DVD. Case report: A 25-year-old female was referred with unilateral esotropia, hypotropia and slow variable downward drift in her left eye. She had history of esotropia since she had been 3-4 months of age. Best corrected visual acuity was 20/20 in her right eye and 20/40 in the left one when hyperopia was corrected. She underwent bimedial rectus muscle recession of 5.25mm for 45 prism diopters (PDs of esotropia. She was orthophoric 3 months after surgery and no further operation was planned for correction of the hypotropic DVD. Conclusion: This rare case of hypotropic DVD showed only mild amblyopia in her non-fixating eye. The etiology was most probably acquired considering hyperopia as a sign of early onset accommodative esotropia.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Euclidean geodesic loops on high-genus surfaces applied to the morphometry of vestibular systems.
Xin, Shi-Qing; He, Ying; Fu, Chi-Wing; Wang, Defeng; Lin, Shi; Chu, Winnie C W; Cheng, Jack C Y; Gu, Xianfeng; Lui, Lok Ming
2011-01-01
This paper proposes a novel algorithm to extract feature landmarks on the vestibular system (VS), for the analysis of Adolescent Idiopathic Scoliosis (AIS) disease. AIS is a 3-D spinal deformity commonly occurred in adolescent girls with unclear etiology. One popular hypothesis was suggested to be the structural changes in the VS that induce the disturbed balance perception, and further cause the spinal deformity. The morphometry of VS to study the geometric differences between the healthy and AIS groups is of utmost importance. However, the VS is a genus-3 structure situated in the inner ear. The high-genus topology of the surface poses great challenge for shape analysis. In this work, we present a new method to compute exact geodesic loops on the VS. The resultant geodesic loops are in Euclidean metric, thus characterizing the intrinsic geometric properties of the VS based on the real background geometry. This leads to more accurate results than existing methods, such as the hyperbolic Ricci flow method. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than. We applied our algorithm to the VS of normal and AIS subjects. The promising experimental results demonstrate the efficacy of our method and reveal more statistically significant shape difference in the VS between right-thoracic AIS and normal subjects.
Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
Alkalaev, K B
2016-01-01
We study the semiclassical holographic correspondence between 2d CFT n-point conformal blocks and massive particle configurations in the asymptotically AdS3 space. On the boundary we use the heavy-light approximation in which case two of primary operators are the background for the other (n-2) operators considered as fluctuations. In the bulk the particle dynamics can be reduced to the hyperbolic time slice. Although lacking exact solutions we nevertheless show that for any n the classical n-point conformal block is equal to the length of the dual geodesic network connecting n-3 cubic vertices of worldline segments. To this end, both the bulk and boundary systems are reformulated as potential vector fields. Gradients of the conformal block and geodesic length are given respectively by accessory parameters of the monodromy problem and particle momenta of the on-shell worldline action represented as a function of insertion points. We show that the accessory parameters and particle momenta are constrained by two...
Implementation of a PMN-PT piezocrystal-based focused array with geodesic faceted structure.
Qiu, Zhen; Qiu, Yongqiang; Demore, Christine E M; Cochran, Sandy
2016-07-01
The higher performance of relaxor-based piezocrystals compared with piezoceramics is now well established, notably including improved gain-bandwidth product, and these materials have been adopted widely for biomedical ultrasound imaging. However, their use in other applications, for example as a source of focused ultrasound for targeted drug delivery, is hindered in several ways. One of the issues, which we consider here, is in shaping the material into the spherical geometries used widely in focused ultrasound. Unlike isotropic unpoled piezoceramics that can be shaped into a monolithic bowl then poled through the thickness, the anisotropic structure of piezocrystals make it impossible to machine the bulk crystalline material into a bowl without sacrificing performance. Instead, we report a novel faceted array, inspired by the geodesic dome structure in architecture, which utilizes flat piezocrystal material and maximizes fill factor. Aided by 3D printing, a prototype with f#≈ 1.2, containing 96 individually addressable elements was manufactured using 1-3 connectivity PMN-PT piezocrystal-epoxy composite. The fabrication process is presented and the array was connected to a 32-channel controller to shape and steer the beam for preliminary performance demonstration. At an operating frequency of 1MHz, a focusing gain around 30 was achieved and the side lobe intensities were all at levels below -12dB compared to main beam. We conclude that, by taking advantage of contemporary fabrication techniques and driving instrumentation, the geodesic array configuration is suitable for focused ultrasound devices made with piezocrystal.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-05-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-01-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Zhang, Zhijun; Liu, Feng; Deng, Fuqin; Tsui, Hungtat
2014-11-01
Due to the variance between subjects, there is usually ambiguity in intensity-based intersubject registration. The topological constraint in the brain cortical surface might be violated because of the highly convolved nature of the human cortical cortex. We propose an intersubject brain registration method by combining the intensity and the geodesic closest point-based similarity measurements. Each of the brain hemispheres can be topologically equal to a sphere and a one-to-one mapping of the points on the spherical surfaces of the two subjects can be achieved. The correspondences in the cortical surface are obtained by searching the geodesic closest points in the spherical surface. The corresponding features on the cortical surfaces between subjects are then used as anatomical landmarks for intersubject registration. By adding these anatomical constraints of the cortical surfaces, the intersubject registration results are more anatomically plausible and accurate. We validate our method by using real human datasets. Experimental results in visual inspection and alignment error show that the proposed method performs better than the typical joint intensity- and landmark-distance-based methods.
An discussion on Graphological Deviation in Oliver Twist
Institute of Scientific and Technical Information of China (English)
肖潇
2016-01-01
In stylistic analysis,when we identifying the stylistic features in literary works,deviation serves as an important sign.According to Leech,there are eight types of deviation in poetry:lexical deviation,grammatical deviation,phonological deviation,graphological deviation,semantic deviation,dialectal deviation,deviation of register,deviation of historical period. Realism marks as an significant development in the history of fiction,for its success in achieving an exposure of the truth of people’s real life and fierce social problems.And foregrounded feature is inevitable part that constitute his language style.We will focus on Oliver Twist,for it is presented with unique writing style,which worthy our investigation.
Sanfilippo, Paul G; Hammond, Christopher J; Staffieri, Sandra E; Kearns, Lisa S; Melissa Liew, S H; Barbour, Julie M; Hewitt, Alex W; Ge, Dongliang; Snieder, Harold; Mackinnon, Jane R; Brown, Shayne A; Lorenz, Birgit; Spector, Tim D; Martin, Nicholas G; Wilmer, Jeremy B; Mackey, David A
2012-10-01
Strabismus represents a complex oculomotor disorder characterized by the deviation of one or both eyes and poor vision. A more sophisticated understanding of the genetic liability of strabismus is required to guide searches for associated molecular variants. In this classical twin study of 1,462 twin pairs, we examined the relative influence of genes and environment in comitant strabismus, and the degree to which these influences can be explained by factors in common with refractive error. Participants were examined for the presence of latent ('phoria') and manifest ('tropia') strabismus using cover-uncover and alternate cover tests. Two phenotypes were distinguished: eso-deviation (esophoria and esotropia) and exo-deviation (exophoria and exotropia). Structural equation modeling was subsequently employed to partition the observed phenotypic variation in the twin data into specific variance components. The prevalence of eso-deviation and exo-deviation was 8.6% and 20.7%, respectively. For eso-deviation, the polychoric correlation was significantly greater in monozygotic (MZ) (r = 0.65) compared to dizygotic (DZ) twin pairs (r = 0.33), suggesting a genetic role (p = .003). There was no significant difference in polychoric correlation between MZ (r = 0.55) and DZ twin pairs (r = 0.53) for exo-deviation (p = .86), implying that genetic factors do not play a significant role in the etiology of exo-deviation. The heritability of an eso-deviation was 0.64 (95% CI 0.50-0.75). The additive genetic correlation for eso-deviation and refractive error was 0.13 and the bivariate heritability (i.e., shared variance) was less than 1%, suggesting negligible shared genetic effect. This study documents a substantial heritability of 64% for eso-deviation, yet no corresponding heritability for exo-deviation, suggesting that the genetic contribution to strabismus may be specific to eso-deviation. Future studies are now needed to identify the genes associated with eso-deviation and
Large Deviations for Random Matricial Moment Problems
Nagel, Jan; Gamboa, Fabrice; Rouault, Alain
2010-01-01
We consider the moment space $\\mathcal{M}_n^{K}$ corresponding to $p \\times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \\rightarrow \\infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\\times p$ matrices. Then we lift a random element of $\\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carth\\'eodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.
Meiosis and its deviations in polyploid animals.
Stenberg, P; Saura, A
2013-01-01
We review the different modes of meiosis and its deviations encountered in polyploid animals. Bisexual reproduction involving normal meiosis occurs in some allopolyploid frogs with variable degrees of polyploidy. Aberrant modes of bisexual reproduction include gynogenesis, where a sperm stimulates the egg to develop. The sperm may enter the egg but there is no fertilization and syngamy. In hybridogenesis, a genome is eliminated to produce haploid or diploid eggs or sperm. Ploidy can be elevated by fertilization with a haploid sperm in meiotic hybridogenesis, which elevates the ploidy of hybrid offspring such that they produce diploid gametes. Polyploids are then produced in the next generation. In kleptogenesis, females acquire full or partial genomes from their partners. In pre-equalizing hybrid meiosis, one genome is transmitted in the Mendelian fashion, while the other is transmitted clonally. Parthenogenetic animals have a very wide range of mechanisms for restoring or maintaining the mother's ploidy level, including gamete duplication, terminal fusion, central fusion, fusion of the first polar nucleus with the product of the first division, and premeiotic duplication followed by a normal meiosis. In apomictic parthenogenesis, meiosis is replaced by what is effectively mitotic cell division. The above modes have different evolutionary consequences, which are discussed. See also the sister article by Grandont et al. in this themed issue.
Large deviations in the random sieve
Grimmett, Geoffrey
1997-05-01
The proportion [rho]k of gaps with length k between square-free numbers is shown to satisfy log[rho]k=[minus sign](1+o(1))(6/[pi]2) klogk as k[rightward arrow][infty infinity]. Such asymptotics are consistent with Erdos's challenge to prove that the gap following the square-free number t is smaller than clogt/log logt, for all t and some constant c satisfying c>[pi]2/12. The results of this paper are achieved by studying the probabilities of large deviations in a certain ‘random sieve’, for which the proportions [rho]k have representations as probabilities. The asymptotic form of [rho]k may be obtained in situations of greater generality, when the squared primes are replaced by an arbitrary sequence (sr) of relatively prime integers satisfying [sum L: summation operator]r1/sr<[infty infinity], subject to two further conditions of regularity on this sequence.
Directory of Open Access Journals (Sweden)
Wafaa Batat
2010-02-01
Full Text Available In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
Giambo', R; Piccione, P
2010-01-01
In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous Seifert conjecture (formulated in 1948) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level.
Institute of Scientific and Technical Information of China (English)
JI Xue-Feng; ZHOU Zi-Xiang
2005-01-01
@@ The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)-dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.
Evaluation of dynamic electromagnetic tracking deviation
Hummel, Johann; Figl, Michael; Bax, Michael; Shahidi, Ramin; Bergmann, Helmar; Birkfellner, Wolfgang
2009-02-01
Electromagnetic tracking systems (EMTS's) are widely used in clinical applications. Many reports have evaluated their static behavior and errors caused by metallic objects were examined. Although there exist some publications concerning the dynamic behavior of EMTS's the measurement protocols are either difficult to reproduce with respect of the movement path or only accomplished at high technical effort. Because dynamic behavior is of major interest with respect to clinical applications we established a simple but effective modal measurement easy to repeat at other laboratories. We built a simple pendulum where the sensor of our EMTS (Aurora, NDI, CA) could be mounted. The pendulum was mounted on a special bearing to guarantee that the pendulum path is planar. This assumption was tested before starting the measurements. All relevant parameters defining the pendulum motion such as rotation center and length are determined by static measurement at satisfactory accuracy. Then position and orientation data were gathered over a time period of 8 seconds and timestamps were recorded. Data analysis provided a positioning error and an overall error combining both position and orientation. All errors were calculated by means of the well know equations concerning pendulum movement. Additionally, latency - the elapsed time from input motion until the immediate consequences of that input are available - was calculated using well-known equations for mechanical pendulums for different velocities. We repeated the measurements with different metal objects (rods made of stainless steel type 303 and 416) between field generator and pendulum. We found a root mean square error (eRMS) of 1.02mm with respect to the distance of the sensor position to the fit plane (maximum error emax = 2.31mm, minimum error emin = -2.36mm). The eRMS for positional error amounted to 1.32mm while the overall error was 3.24 mm. The latency at a pendulum angle of 0° (vertical) was 7.8ms.
Properties of an affine transport equation and its holonomy
Vines, Justin; Nichols, David A.
2016-10-01
An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity. In this paper, we investigate local properties of this transport equation in greater detail. Associated with this transport equation is a map between the tangent spaces at two points on a curve. This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space. For closed curves, the affine transport equation defines a "generalized holonomy" that takes the form of an affine map on the tangent space. We explore the local properties of this generalized holonomy by using covariant bitensor methods to compute the generalized holonomy around geodesic polygon loops. We focus on triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order linear holonomy (˜ Riemann × area), and we derive the leading-order inhomogeneous part of the generalized holonomy (˜ Riemann × area^{3/2}). Our bitensor methods let us naturally compute higher-order corrections to these leading results. These corrections reveal the form of the finite-size effects that enter into the holonomy for larger loops; they could also provide quantitative errors on the leading-order results for finite loops.
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics
Finch, Tehani K.
2015-01-01
We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.
Study of Geodesics and the Frame-dragging effect in a Rotating Traversable Wormhole
Pradhan, Parthapratim
2016-01-01
The complete equatorial causal geodesic structure of a rotating traversable wormhole is analyzed and it has been shown that the ISCO (Innermost Stable Circular Orbit) coincides at the throat of the wormhole for the retrograde rotation. By studying the effective potential we also find the radius of the circular photon orbit. The Periastron precession frequency and the nodal precession frequency have been derived for both of the direct and retrograde rotation. Moreover, we derive the exact Lense-Thirring precession frequency of a test gyro for the said wormhole and we show that this frequency is inversely proportional to the angular momentum $(a)$ of the wormhole along the pole in a certain range of $r \\,\\, (r < 16a^2)$ whereas it is directly proportional to the angular momentum of the spacetime for the other compact objects like black holes and pulsars.
Toroidal symmetry of the geodesic acoustic mode zonal flow in a tokamak plasma.
Zhao, K J; Lan, T; Dong, J Q; Yan, L W; Hong, W Y; Yu, C X; Liu, A D; Qian, J; Cheng, J; Yu, D L; Yang, Q W; Ding, X T; Liu, Y; Pan, C H
2006-06-30
The toroidal symmetry of the geodesic acoustic mode (GAM) zonal flows is identified with toroidally distributed three step Langmuir probes at the edge of the HuanLiuqi-2A (commonly referred to as HL-2A) tokamak plasmas for the first time. High coherence of both the GAM and the ambient turbulence for the toroidally displaced measurements along a magnetic field line is observed, in contrast with the high coherence of the GAM but low coherence of the ambient turbulence when the toroidally displaced measurements are not along the same field line. The radial and poloidal features of the flows are also simultaneously determined. The nonlinear three wave coupling between the high frequency turbulent fluctuations and the flows is demonstrated to be a plausible formation mechanism of the flows.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Breton, N
2016-01-01
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for singular, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparison is shown with the QNMs of the linear electromagnetic counterpart, their Reissner-Nordstr\\"{o}m black hole.
Rigidity of geodesic completeness in the Brinkmann class of gravitational wave spacetimes
Silva, Ivan P Costa e; Herrera, Jonatan
2016-01-01
We consider restrictions placed by geodesic completeness on spacetimes possessing a null parallel vector field, the so-called Brinkmann spacetimes. This class of spacetimes includes important idealized gravitational wave models in General Relativity, namely the plane-fronted waves with parallel rays, or pp-waves, which in turn have been intensely and fruitfully studied in the mathematical and physical literatures for over half a century. More concretely, we prove a restricted version of a conjectural analogue for Brinkmann spacetimes of a rigidity result obtained by M.T. Anderson for stationary spacetimes. We also highlight its relation with a long-standing 1962 conjecture by Ehlers and Kundt. Indeed, it turns out that the subclass of Brinkmann spacetimes we consider in our main theorem is enough to settle an important special case of the Ehlers-Kundt conjecture in terms of the well known class of Cahen-Wallach spaces.
Energy Technology Data Exchange (ETDEWEB)
Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Singh, Rameswar; Morel, P. [Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, UPMC, UPSud, 91128 Palaiseau (France); Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Ghendrih, P. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Görler, T. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany)
2015-06-15
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
Storelli, A.; Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Görler, T.; Singh, Rameswar; Morel, P.; Grandgirard, V.; Ghendrih, P.
2015-06-01
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
Evolution of geodesic congruences in a gravitationally collapsing scalar field background
Shaikh, Rajibul; DasGupta, Anirvan
2014-01-01
The evolution of timelike and null geodesic congruences in a non-static, inhomogeneous spacetime representing the gravitational collapse of a massless scalar field, is investigated in detail. We show explicitly how the initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature along the congruence, influence the evolution and focusing of trajectories in different ways. The role of initial conditions on the focusing time is explored and highlighted. In certain specific cases, the expansion scalar is found to exhibit a finite jump (from negative to positive value) before focusing. The issue of singularity formation and the effect of the central inhomogeneity in the spacetime, on the evolution of the kinematic variables, is discussed. In summary, our analysis does seem to throw some light on how a family of trajectories evolve in a specific model of gravitational collapse.
Schottky-type groups and minimal sets of horocycle and geodesic flows
Kulikov, M. S.
2004-02-01
In the first part of the paper the following conjecture stated by Dal'bo and Starkov is proved: the geodesic flow on a surface M=\\mathbb H^2/\\Gamma of constant negative curvature has a non-compact non-trivial minimal set if and only if the Fuchsian group \\Gamma is infinitely generated or contains a parabolic element. In the second part interesting examples of horocycle flows are constructed: 1) a flow whose restriction to the non-wandering set has no minimal subsets, and 2) a flow without minimal sets.In addition, an example of an infinitely generated discrete subgroup of \\operatorname{SL}(2,\\mathbb R) with all orbits discrete and dense in \\mathbb R^2 is constructed.
Synchronization of Geodesic Acoustic Modes and Magnetic Fluctuations in Toroidal Plasmas
Zhao, K. J.; Nagashima, Y.; Diamond, P. H.; Dong, J. Q.; Itoh, K.; Itoh, S.-I.; Yan, L. W.; Cheng, J.; Fujisawa, A.; Inagaki, S.; Kosuga, Y.; Sasaki, M.; Wang, Z. X.; Wei, L.; Huang, Z. H.; Yu, D. L.; Hong, W. Y.; Li, Q.; Ji, X. Q.; Song, X. M.; Huang, Y.; Liu, Yi.; Yang, Q. W.; Ding, X. T.; Duan, X. R.
2016-09-01
The synchronization of geodesic acoustic modes (GAMs) and magnetic fluctuations is identified in the edge plasmas of the HL-2A tokamak. Mesoscale electric fluctuations (MSEFs) having components of a dominant GAM, and m /n =6 /2 potential fluctuations are found at the same frequency as that of the magnetic fluctuations of m /n =6 /2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m /n =6 /2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. Such nonlinear synchronization may also contribute to low-frequency zonal flow formation, reduction of turbulence level, and thus confinement regime transitions.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Bretón, Nora; López, L. A.
2016-11-01
The expressions for the quasinormal modes (QNM) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNM of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNM of four nonlinear electromagnetic black holes, two singular and two regular, namely, from Euler-Heisenberg and Born-Infeld theories, for singular ones, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparing with the QNM of the linear electromagnetic counterpart, their Reissner-Nordström black hole is done.
A Unified Spatiotemporal Prior based on Geodesic Distance for Video Object Segmentation.
Wang, Wenguan; Shen, Jianbing; Yang, Ruigang; Porikli, Fatih
2017-01-31
Video saliency, aiming for estimation of a single dominant object in a sequence, offers strong object-level cues for unsupervised video object segmentation. In this paper, we present a geodesic distance based technique that provides reliable and temporally consistent saliency measurement of superpixels as a prior for pixel-wise labeling. Using undirected intra-frame and inter-frame graphs constructed from spatiotemporal edges or appearance and motion, and a skeleton abstraction step to further enhance saliency estimates, our method formulates the pixel-wise segmentation task as an energy minimization problem on a function that consists of unary terms of global foreground and background models, dynamic location models, and pairwise terms of label smoothness potentials. We perform extensive quantitative and qualitative experiments on benchmark datasets. Our method achieves superior performance in comparison to the current state-of-the-art in terms of accuracy and speed.
Equations of motion in Double Field Theory: from classical particles to quantum cosmology
Kan, Nahomi; Shiraishi, Kiyoshi
2012-01-01
The equation of motion for a point particle in the background field of double field theory is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by analysis on the particle motion, we propose a modified model of quantum string cosmology, which includes two scale factors. The report is based on Phys. Rev. D84 (2011) 124049 [arXiv:1108.5795].
Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT.
Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi
2015-07-01
This work aims to develop a robust and efficient method to track the fuzzy borders between liver and the abutted organs where automatic liver segmentation usually suffers, and to investigate its applications in automatic liver segmentation on noncontrast-enhanced planning computed tomography (CT) images. In order to track the fuzzy liver-chestwall and liver-heart borders where oversegmentation is often found, a starting point and an ending point were first identified on the coronal view images; the fuzzy border was then determined as a geodesic curve constructed by minimizing the gradient-weighted path length between these two points near the fuzzy border. The minimization of path length was numerically solved by fast-marching method. The resultant fuzzy borders were incorporated into the authors' automatic segmentation scheme, in which the liver was initially estimated by a patient-specific adaptive thresholding and then refined by a geodesic active contour model. By using planning CT images of 15 liver patients treated with stereotactic body radiation therapy, the liver contours extracted by the proposed computerized scheme were compared with those manually delineated by a radiation oncologist. The proposed automatic liver segmentation method yielded an average Dice similarity coefficient of 0.930 ± 0.015, whereas it was 0.912 ± 0.020 if the fuzzy border tracking was not used. The application of fuzzy border tracking was found to significantly improve the segmentation performance. The mean liver volume obtained by the proposed method was 1727 cm(3), whereas it was 1719 cm(3) for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. The proposed method was shown to provide accurate segmentation for liver in the planning CT images where contrast agent is not applied. The authors' results also clearly demonstrated that the application of tracking the fuzzy
Juxta-vascular nodule segmentation based on flow entropy and geodesic distance.
Sun, Shenshen; Guo, Yang; Guan, Yubao; Ren, Huizhi; Fan, Linan; Kang, Yan
2014-07-01
Computed aided diagnosis of lung CT data is a new quantitative analysis technique to distinguish malignant nodules from benign ones. Nodule growth rate is a key indicator to discriminate between benign and malignant nodules. Accurate nodule segmentation is the essential for calculating the nodule growth rate. However, it is difficult to segment juxta-vascular nodules, due to the similar gray levels in nodule and attached blood vessels. To distinguish the nodule region from the adjacent vessel region, a flowing direction feature, referred to as the direction of the normal vector for a pixel, is introduced. Since blood is flowing in one single direction through a vessel, the normal vectors of pixels in the vessel region typically point in similar orientations while the directions of those in the nodule region can be viewed as disorganized. The entropy value of the flowing direction features in a neighboring region for a vessel pixel is smaller than that for a nodule pixel. Moreover, vessel pixels typically have a larger geodesic distance to the nodule center than nodule pixels. Based on k -means clustering method, the flow entropy, combined with the geodesic distance, is used to segment vessel attached nodules. The validation of the proposed segmentation algorithm was carried out on juxta-vascular nodules, identified in the Chinalung-CT screening trial and on Lung Image Database Consortium (LIDC) dataset. In fully automated mode, accuracies of 92.9% (26/28), 87.5%(7/8), and 94.9% (149/157) are reached for the outlining of juxta-vascular nodules in the Chinalung-CT, and the first and second datasets of LIDC, respectively. Furthermore, it is demonstrated that the proposed method has low time complexity and high accuracies.
9 CFR 318.308 - Deviations in processing.
2010-01-01
... AGENCY ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY...) Deviations in processing (or process deviations) must be handled according to: (1)(i) A HACCP plan for canned...) of this section. (c) (d) Procedures for handling process deviations where the HACCP plan...
21 CFR 330.11 - NDA deviations from applicable monograph.
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...
Large deviations for Glauber dynamics of continuous gas
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems.We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology,while it does not satisfy the large deviation principles in the T-topology.
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Escher, Joachim; Lenells, Jonatan
2010-01-01
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of the diffeomorphism group of the circle $\\Diff(S^1)$ with some space of sufficiently smooth functions on the circle. Our goals are to understand the geometric properties of these two-component systems and to prove local well-posedness in various function spaces. Furthermore, we perform some explicit curvature calculations for the two-component Camassa-Holm equation, giving explicit examples of large subspaces of positive curvature.
Directory of Open Access Journals (Sweden)
I. I. Kravchenko
2016-01-01
Full Text Available There is a variety of objectives for measuring deviations of flatness, size and mutual arrangement of flat surfaces, namely: processing accuracy control, machinery condition monitoring, treatment process control in terms of shape deviation, comparative analysis of machine rigidity. If for a processing accuracy control it is sufficient to obtain the flatness deviation, as the maximum adjoining surface deviation, the choice of the adjoining surface as a zero reference datum deviation leads to considerable difficulties in creating devices and in particular devices for measuring size and shape variations. The flat surface is characterized by mutual arrangement of its points and can be represented by equation in the selected coordinate system. The objective of this work is to provide analytical construction of the vector field F, which describes the real surface with an appropriate approximation upon modelling the face milling of the flat surfaces of body parts in conditions of anisotropic rigidity of technological system. To determine the numerical value of shape and size deviation characteristics the average surfaces can serve a basis for the zero reference values of vectors. A mean value theorem allows to obtain measurement information about deviations in shape, size and arrangement of processed flat surfaces in terms of metrology, as well as about the process parameters such as depth of cut, feed, cutting speed, anisotropic rigidity of technological system that characterize the specific processing conditions. The machining center MS 12-250 was used to carry out a number of experiments with processing the surfaces of the prism-shaped body parts (300x300x250 and the subsequent measurements of flatness on the IS-49 optical line to prove the correlation between expected and observed values of the vectors of flatness deviations.
Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence
Derrida, Bernard; Shi, Zhan
2016-06-01
The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of generalizations of the BBM and of the BRW have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles. Here we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations: the L-BBM, the N-BBM, and the coalescing branching random walk (CBRW) which is closely related to the noisy FKPP equation. Our approach allows us to obtain only upper bounds on these large deviation functions. One noticeable feature of our results is their non analytic dependence on the parameters (such as the coalescence rate in the CBRW).
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E
2015-01-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Mourragui, Mustapha
2011-01-01
We consider a boundary driven exclusion process associated to particles evolving under Kawasaki (conservative) dynamics and long range interaction in a regime in which at equilibrium phase separation might occur. We show that the empirical density under the diffusive scaling solves a non linear integro differential evolution equation with Dirichlet boundary conditions and we prove the associated dynamical large deviations principle. Further, tuning suitable the intensity of the interaction, in the uniqueness phase regime, we show that under the stationary measure the empirical density solves a non local, stationary, transport equation.
Directory of Open Access Journals (Sweden)
Ion BULAC
2016-05-01
Full Text Available The technological (geometrical deviations determine in the intermediate couples of the mechanism supplementary efforts due to restrained movement. The 4R asymmetrical spherical quadrilateral mechanism is multiple statically indeterminate, and for calculating the reactions from the kinematic pairs it is applied the elastic linear calculation using the relative displacements method. The equations of elastic balanced are written in the general system of reference.For this is necessary the knowledge the forms of the technical (geometrical deviations in the general system of reference.This paper presents the calculation modality these deviations .
Directory of Open Access Journals (Sweden)
Geert Verdoolaege
2015-07-01
Full Text Available In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS is the most popular. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS. The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.
Kabirzadeh, Rasoul
The GEODESIC sounding rocket encountered hundreds of localized, VLF-wave-filled density depletions in an auroral return current region at altitudes between 900--1000 km. While these are similar to well-studied lower-hybrid "spikelets", which are electrostatic, many of the GEODESIC events exhibited strong VLF magnetic field enhancements as well. In the present study we show that these magnetic field fluctuations can be interpreted as the result of geomagnetic field-aligned electron currents driven by fluctuating electric fields parallel to the geomagnetic field lines. This observation suggests that the electromagnetic wave-filled cavities are signatures of unstable filaments of return current fluctuating at VLF frequencies. We argue that the cavities' spatial dimensions, their location inside the return current region and their total radiated power are consistent with the properties of VLF saucer source regions inferred from earlier satellite observations taken at higher altitudes.
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
between the forward and backward recursions and develop techniques for estimating the exceedance probability. In the process, we establish an interesting connection between the regularity properties of $\\{V_n\\}$ and the recurrence properties of an associated $\\xi$-shifted Markov chain. We illustrate...
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Projectively related metrics, Weyl nullity, and metric projectively invariant equations
Gover, A Rod
2015-01-01
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described. We obtain strong local and global results on the nature of solutions and also on the nature of the geometries admitting such solutions, obtaining ...
Mechanism Modeling and Simulation Based on Dimensional Deviation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
To analyze the effects on motion characteristics of mechanisms of dimensional variations, a study on random dimensional deviation generation techniques for 3D models on the basis of the present mechanical modeling software was carried out, which utilized the redeveloped interfaces provided by the modeling software to develop a random dimensional deviation generation system with certain probability distribution characteristics. This system has been used to perform modeling and simulation of the specific mechanical time delayed mechanism under multiple deviation varieties, simulation results indicate the dynamic characteristics of the mechanism are influenced significantly by the dimensional deviation in the tolerance distribution range, which should be emphasized in the design.
Deviation and rotation of the larynx in computer tomography
Energy Technology Data Exchange (ETDEWEB)
Shibusawa, Mitsunobu (Tokyo Medical and Dental Univ., Tokyo (Japan). Medical Research Institute); Yano, Kazuhiko
1990-01-01
Many authors described the clinical importance of asymmetry of the laryngeal framework. However, its pathogenesis is generally unknown. In this study, CT images of 315 Japanese subjects were investigated to define the laryngeal position relative to the midline of the cervical vertebra. The CT slice of each subject within 5 mm cephalad of the cricoarytenoid joint was traced. Then, the deviation and rotation angles were measured using our method. Seventy one percent of the subjects' larynges deviated and/or rotated to the right side, while 17% to the left side. Six percent showed neither deviation nor rotation. As to the rest of 6%, deviation and rotation were in opposite directions. Besides, the length of the thyroid alae were measured in 282 subjects. Left ala was longer in 55%, and right was in 23%, and almost equal in 22%. The conclusions are as follows. The majority of the subjects' CT images showed deviation and/or rotation of the laryngeal framework to the right side. So called idiopathic laryngeal deviation is a case which observed in those cases with remarkable deviation and/or rotation of the laryngeal framework. Aging seemed to be an important factor in accerelation of the laryngeal deviation and rotation. The type of diseases and the side of mass lesions had no statistical significance in deviation and rotation of the larynx. (author).
Large-deviation statistics of vorticity stretching in isotropic turbulence.
Johnson, Perry L; Meneveau, Charles
2016-03-01
A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity stretching Cramér function. This function is computed from a direct numerical simulation data set at a Taylor-scale Reynolds number of Re(λ)=433 and compared to those of the finite-time Lyapunov exponents (FTLE) for material deformation. As expected, the mean cumulative vorticity stretching is slightly less than that of the most-stretched material line (largest FTLE), due to the vorticity's preferential alignment with the second-largest eigenvalue of strain rate and the material line's preferential alignment with the largest eigenvalue. However, the vorticity stretching tends to be significantly larger than the second-largest FTLE, and the Cramér functions reveal that the statistics of vorticity stretching fluctuations are more similar to those of the largest FTLE. In an attempt to relate the vorticity stretching statistics to the vorticity magnitude probability density function in statistically stationary conditions, a model Kramers-Moyal equation is constructed using the statistics encoded in the Cramér function. The model predicts a stretched-exponential tail for the vorticity magnitude probability density function, with good agreement for the exponent but significant difference (35%) in the prefactor.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
On Gaussian Beams Described by Jacobi's Equation
Smith, Steven Thomas
2013-01-01
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) It is shown that the \\v{C}erven\\'y equations for the amplitude and phase are equivalent to the classical Jacobi Equation of differential geometry. The \\v{C}erven\\'y equations describe Gaussian beams using Hamilton-Jacobi theory, whereas the Jacobi Equation expresses how Gaussian and Riemannian curvature determine geodesic flow on a Riemannian manifold. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gauss...
Generalized Mattig's relation in Brans-Dicke-Rastall gravity
Salako, Ines G; Jawad, Abdul
2016-01-01
The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $\\eta(z)$ and observer area distance $r_0(z)$ and compare the results with $\\Lambda$CDM model.
Flux Tensor Constrained Geodesic Active Contours with Sensor Fusion for Persistent Object Tracking
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Filiz Bunyak
2007-08-01
Full Text Available This paper makes new contributions in motion detection, object segmentation and trajectory estimation to create a successful object tracking system. A new efficient motion detection algorithm referred to as the flux tensor is used to detect moving objects in infrared video without requiring background modeling or contour extraction. The flux tensor-based motion detector when applied to infrared video is more accurate than thresholding ”hot-spots”, and is insensitive to shadows as well as illumination changes in the visible channel. In real world monitoring tasks fusing scene information from multiple sensors and sources is a useful core mechanism to deal with complex scenes, lighting conditions and environmental variables. The object segmentation algorithm uses level set-based geodesic active contour evolution that incorporates the fusion of visible color and infrared edge informations in a novel manner. Touching or overlapping objects are further refined during the segmentation process using an appropriate shapebased model. Multiple object tracking using correspondence graphs is extended to handle groups of objects and occlusion events by Kalman filter-based cluster trajectory analysis and watershed segmentation. The proposed object tracking algorithm was successfully tested on several difficult outdoor multispectral videos from stationary sensors and is not confounded by shadows or illumination variations.