Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri's equation
Rahmani, Faramarz; Golshani, Mehdi
2017-01-01
One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since, the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the ...
Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation
Rahmani, Faramarz; Golshani, Mehdi
2018-01-01
One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.
Geodesic deviation and Minikowski space
International Nuclear Information System (INIS)
Barraco, D.; Kozameh, C.; Newman, E.T.; Tod, P.
1990-01-01
The authors study the properties of the solution space of local surface-forming null sub-congruences in the neighborhood of a given null geodesic in a pseudo-Riemannian space-time. This solution space is a three-dimensional manifold, naturally endowed with a conformal Minkowski metric
Null geodesic deviation II. Conformally flat space--times
International Nuclear Information System (INIS)
Peters, P.C.
1975-01-01
The equation of geodesic deviation is solved in conformally flat space--time in a covariant manner. The solution is given as an integral equation for general geodesics. The solution is then used to evaluate second derivatives of the world function and derivatives of the parallel propagator, which need to be known in order to find the Green's function for wave equations in curved space--time. A method of null geodesic limits of two-point functions is discussed, and used to find the scalar Green's function as an iterative series
Higher-order geodesic deviations applied to the Kerr metric
Colistete, R J; Kerner, R
2002-01-01
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of a small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to orbits with low eccentricities, but with arbitrary possible values of (GM/Rc sup 2).
Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves
Heydari-Fard, M.; Hasani, S. N.
We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.
A comment on the null geodesic equations in Schwarzschild geometry
International Nuclear Information System (INIS)
Rosa, M.A.F.; Rodrigues Junior, W.A.
1986-01-01
An integration of the null geodesic equations in the Schwarzschild geometry, which is valid to first order in GM/Rc 2 is presented. The solution is compared with others published in the literature and their range of validity is analysed. Some misunderstandings are also clarified. (Author) [pt
Deviation equation in spaces with affine connection. Pts. 3 and 4
International Nuclear Information System (INIS)
Iliev, B.Z.
1987-01-01
The concept of a parallel transport is used to define a class of displacement vectors in spaces with affine connection. The nonlocal deviation equation in such spaces is introduced using a definition of the deviation vector based on the displacement vector. It turns out to be a special of the generalized deviation equation, but having an appropriate physical interpretation. The equation of geodesic deviation is presented as an example
Rational first integrals of geodesic equations and generalised hidden symmetries
International Nuclear Information System (INIS)
Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro
2016-01-01
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson–O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski–Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing–Yano tensors. (paper)
Twisting null geodesic congruences and the Einstein-Maxwell equations
International Nuclear Information System (INIS)
Newman, Ezra T; Silva-Ortigoza, Gilberto
2006-01-01
In a recent article, we returned to the study of asymptotically flat solutions of the vacuum Einstein equations with a rather unconventional point of view. The essential observation in that work was that from a given asymptotically flat vacuum spacetime with a given Bondi shear, one can find a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences where the class was uniquely given up to the arbitrary choice of a complex analytic 'worldline' in a four-dimensional complex space. By imitating certain terms in the Weyl tensor that are found in the algebraically special type II metrics, this complex worldline could be made unique and given-or assigned-the physical meaning as the complex centre of mass. Equations of motion for this case were found. The purpose of the present work is to extend those results to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically shear-free null geodesic congruences depending on a complex worldline in the same four-dimensional complex space. However in this case there will be, in general, two distinct but uniquely chosen worldlines, one of which can be assigned as the complex centre of charge while the other could be called the complex centre of mass. Rather than investigating the situation where there are two distinct complex worldlines, we study instead the special degenerate case where the two worldlines coincide, i.e., where there is a single unique worldline. This mimics the case of algebraically special Einstein-Maxwell fields where the degenerate principle null vector of the Weyl tensor coincides with a Maxwell principle null vector. Again we obtain equations of motion for this worldline-but explicitly found here only in an approximation. Though there are ambiguities in assigning physical meaning to different terms it appears as if reliance on the Kerr and charged Kerr metrics and classical electromagnetic radiation theory helps
An equation satisfied by the tangent to a shear-free, geodesic, null congruence
International Nuclear Information System (INIS)
Hogan, P.A.; Dublin Inst. for Advanced Studies
1987-01-01
A tensorial equation satisfied by the tangent to a shear-free geodesic, null congruence is presented. If the congruence is neither twist-free nor expansion-free then the equation defines a second, unique, null direction previously obtained, using the spinor formalism, by Somers. Some further properties of the equation are discussed. (orig.)
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Panou G.
2017-02-01
Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
Conformal gravity, the Einstein equations and spaces of complex null geodesics
Energy Technology Data Exchange (ETDEWEB)
Baston, R.J.; Mason, L.J.
1987-07-01
The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved.
Conformal gravity, the Einstein equations and spaces of complex null geodesics
International Nuclear Information System (INIS)
Baston, R.J.; Mason, L.J.
1987-01-01
The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved. (author)
Geodesic congruences in the Palatini f(R) theory
International Nuclear Information System (INIS)
Shojai, Fatimah; Shojai, Ali
2008-01-01
We shall investigate the properties of a congruence of geodesics in the framework of Palatini f(R) theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that f(R) Palatini theories do not necessarily lead to attractive forces. Also, we shall study energy condition for f(R) Palatini gravity via a perturbative analysis of the Raychaudhuri's equation.
Oscillations in deviating difference equations using an iterative technique
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George E Chatzarakis
2017-07-01
Full Text Available Abstract The paper deals with the oscillation of the first-order linear difference equation with deviating argument and nonnegative coefficients. New sufficient oscillation conditions, involving limsup, are given, which essentially improve all known results, based on an iterative technique. We illustrate the results and the improvement over other known oscillation criteria by examples, numerically solved in Matlab.
International Nuclear Information System (INIS)
Rowland, D R
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics
Pottmann, Helmut; Huang, Qixing; Deng, Bailin; Schiftner, Alexander; Kilian, Martin; Guibas, Leonidas J.; Wallner, Johannes
2010-01-01
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.
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.
On geodesics in low regularity
Sämann, Clemens; Steinbauer, Roland
2018-02-01
We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.
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
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.
Moderate Deviation Principles for Stochastic Differential Equations with Jumps
2014-01-15
N ŕ’"(dt; dy) and the controls ’" : X [0; T ] ! [0;1) are predictable processes satisfying LT (’") Ma2 (") for some constantM . Here LT denotes...space. Although in the moderate deviations problem one has the stronger bound LT (’") Ma2 (") on the cost of controls, the mere tightness of ’" does not...suitable quadratic form. For " > 0 and M ə, consider the spaces SM+;" : = f’ : X [0; T ]! R+j LT (’) Ma2 (")g (2.5) SM" : = f : X [0; T ]! Rj
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.
Large deviations for solutions to stochastic recurrence equations under Kesten's condition
DEFF Research Database (Denmark)
Buraczewski, Dariusz; Damek, Ewa; Mikosch, Thomas Valentin
2013-01-01
In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten’s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise...... sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest...... step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies...
Geodesic stability, Lyapunov exponents, and quasinormal modes
International Nuclear Information System (INIS)
Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.
2009-01-01
Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
Improved iterative oscillation tests for first-order deviating differential equations
Directory of Open Access Journals (Sweden)
George E. Chatzarakis
2018-01-01
Full Text Available In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \\(\\lim \\sup\\ and \\(\\lim \\inf\\ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations
International Nuclear Information System (INIS)
Roeckner, Michael; Zhang, Tusheng; Zhang Xicheng
2010-01-01
In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Roeckner and Zhang in Probab. Theory Relat. Fields 145(1-2), 211-267, 2009).
Influence of geometry variations on the gravitational focusing of timelike geodesic congruences
Seriu, Masafumi
2015-10-01
We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.
Geodesic in Godel type universes
International Nuclear Information System (INIS)
Galvao, M.O.
1985-01-01
We find out the timelike and null geodesics of a certain family of Goedel-like universes, carrying out, at first, a qualitative analysis through the method of the effective potential and, subsequently, proceeding to the exact integration of the equations of motion. (author) [pt
Geodesic distance in planar graphs
International Nuclear Information System (INIS)
Bouttier, J.; Di Francesco, P.; Guitter, E.
2003-01-01
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy
Directory of Open Access Journals (Sweden)
Xiaolin Gong
2015-01-01
Full Text Available To investigate the influences of causes of unreliability and bus schedule recovery phenomenon on microscopic segment-level travel time variance, this study adopts Structural Equation Modeling (SEM to specify, estimate, and measure the theoretical proposed models. The SEM model establishes and verifies hypotheses for interrelationships among travel time deviations, departure delays, segment lengths, dwell times, and number of traffic signals and access connections. The finally accepted model demonstrates excellent fitness. Most of the hypotheses are supported by the sample dataset from bus Automatic Vehicle Location system. The SEM model confirms the bus schedule recovery phenomenon. The departure delays at bus terminals and upstream travel time deviations indeed have negative impacts on travel time fluctuation of buses en route. Meanwhile, the segment length directly and negatively impacts travel time variability and inversely positively contributes to the schedule recovery process; this exogenous variable also indirectly and positively influences travel times through the existence of signalized intersections and access connections. This study offers a rational approach to analyzing travel time deviation feature. The SEM model structure and estimation results facilitate the understanding of bus service performance characteristics and provide several implications for bus service planning, management, and operation.
Singularities in geodesic surface congruence
International Nuclear Information System (INIS)
Cho, Yong Seung; Hong, Soon-Tae
2008-01-01
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.
First integrals of geodesics in the Einstein-Schwarzschild space
International Nuclear Information System (INIS)
Meshkov, A.G.; Dordzhiev, P.B.
1984-01-01
Linear and quadratic velocity integrals of geodesics in the Einstein-Schwarzschild space are calculated. The Schwarzschild geodesics equations have only four independent linear integrals. Quadratic integrals are polynomials from linear ones with constant coefficients. Total separation of variables in the Hamilton-Jacobi equation with Schwarzschild metric is possible only in two coordinate systems: ''spherical'' and ''conic'' systems
Complex Monge–Ampère equations and geodesics in the space of Kähler metrics
2012-01-01
The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruc...
Directory of Open Access Journals (Sweden)
Youliang Fu
2016-01-01
Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.
Geodesic congruences in warped spacetimes
International Nuclear Information System (INIS)
Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan
2011-01-01
In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.
Some remarks on geodesics in gauge groups and harmonic maps
International Nuclear Information System (INIS)
Valli, G.
1987-08-01
The following topics are discussed: Euler's equations for geodesics in the gauge groups and in gauge orbits of connections, conserved quantities and moment map, existence and uniqueness of solutions for the Cauchy problem, stationary solutions and harmonic bundles, harmonic gauges on Riemann surfaces and Lax pairs, low geodesics in gauge groups over Riemann surfaces produce, by Hodge decomposition, paths of holomorphic differentials. 19 refs
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.
Lagrangian averaging with geodesic mean.
Oliver, Marcel
2017-11-01
This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.
Directory of Open Access Journals (Sweden)
Changjin Xu
2014-01-01
Full Text Available This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results.
Directory of Open Access Journals (Sweden)
I. Orazov
2013-01-01
Full Text Available We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument. A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem.
Black hole decay as geodesic motion
International Nuclear Information System (INIS)
Gupta, Kumar S.; Sen, Siddhartha
2003-01-01
We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes
Wang, Zaihong
2013-01-01
We study the existence of periodic solutions of Liénard equation with a deviating argument $x\\mathrm{\\prime \\prime }+f\\left(x\\right)x\\mathrm{\\text{'}}+{n}^{\\mathrm{2}}x+g\\left(x\\left(t-\\tau \\right)\\right)=p\\left(t\\right),$ where $f,g,p:\\mathrm{R}\\to \\mathrm{R}$ are continuous and $p$ is $\\mathrm{2}\\pi $ -periodic, $\\mathrm{0}\\le \\tau
Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument
Czech Academy of Sciences Publication Activity Database
Drábek, P.; Kufner, Alois; Kuliev, K.
2017-01-01
Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059
Large deviation tail estimates and related limit laws for stochastic fixed point equations
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE) of the form $V \\stackrel{d}{=} A\\max\\{V, D\\}+B$, where $(A, B, D) \\in (0, \\infty)\\times {\\mathbb R}^2$, for both the stationary and explosive cases. In the stationary case (when ${\\bf E} [\\log \\: A......] explosive case (when ${\\bf E} [\\log \\: A] > 0)$, we establish a central limit theorem for the forward recursion generated by the SFPE, namely the process $V_n= A_n \\max\\{V_{n-1...
Perfect fluid cosmology with geodesic world lines
International Nuclear Information System (INIS)
Raychaudhuri, A.K.; Maity, S.R.
1978-01-01
It is shown that for a perfect fluid with an equation of state p = p (rho), if the world lines are geodesics, then they are hypersurface orthogonal and the scalars p, rho, sigma 2 , and theta 2 are all constants over these hypersurfaces, irrespective of any spatial-homogeneity assumption. However, an examination of some simple cases does not reveal any spatially nonhomogeneous solution with these properties
Efficiently computing exact geodesic loops within finite steps.
Xin, Shi-Qing; He, Ying; Fu, Chi-Wing
2012-06-01
Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.
On Geodesic Exponential Kernels
DEFF Research Database (Denmark)
Feragen, Aasa; Lauze, François; Hauberg, Søren
2015-01-01
This extended abstract summarizes work presented at CVPR 2015 [1]. Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, ......, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models....
Congruences of totally geodesic surfaces
International Nuclear Information System (INIS)
Plebanski, J.F.; Rozga, K.
1989-01-01
A general theory of congruences of totally geodesic surfaces is presented. In particular their classification, based on the properties of induced affine connections, is provided. In the four-dimensional case canonical forms of the metric tensor admitting congruences of two-dimensional totally geodesic surfaces of rank one are given. Finally, congruences of two-dimensional extremal surfaces are studied. (author)
Equatorial Geodesics Around the Magnetars
Alfradique, Viviane A. P.; Troconis, Orlenys N.; Negreiros, Rodrigo P.
Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than 1015 G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to 1017G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.
Focusing of geodesic congruences in an accelerated expanding Universe
International Nuclear Information System (INIS)
Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la
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 space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds
Focusing of geodesic congruences in an accelerated expanding Universe
Energy Technology Data Exchange (ETDEWEB)
Albareti, F.D.; Cembranos, J.A.R. [Departamento de Física Teórica I, Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid (Spain); Cruz-Dombriz, A. de la, E-mail: fdalbareti@estumail.ucm.es, E-mail: cembra@fis.ucm.es, E-mail: alvaro.delacruz-dombriz@uct.ac.za [Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, 7701 Rondebosch, Cape Town (South Africa)
2012-12-01
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 space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.
Arcmancer: Geodesics and polarized radiative transfer library
Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.
2018-05-01
Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.
Geodesics of black holes with dark energy
Ghaderi, K.
2017-12-01
Dark energy is the most popular hypothesis to explain recent observations suggesting that the world will increasingly expand. One of the models of dark energy is quintessence which is highly plausible. In this paper, we investigate the effect of dark energy on the null geodesics of Schwarzschild, Reissner-Nordström, Schwarzschild-de Sitter and Bardeen black holes. Using the definition of effective potential, the radius of the circular orbits, the period, the instability of the circular orbits, the force exerted on the photons and the deviation angle of light in quintessence field are calculated and the results are analyzed and discussed.
Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures
Directory of Open Access Journals (Sweden)
Ishikawa Goo
2015-06-01
Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.
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.
Space–time and spatial geodesic orbits in Schwarzschild geometry
Resca, Lorenzo
2018-05-01
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.
Non-integrability of geodesic flow on certain algebraic surfaces
International Nuclear Information System (INIS)
Waters, T.J.
2012-01-01
This Letter addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface xyz=1. We prove this is the case using the Morales–Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result. -- Highlights: ► The behaviour of geodesics on surfaces defined by algebraic expressions is studied. ► The non-integrability of the geodesic equations is rigorously proved using differential Galois theory. ► Morales–Ramis theory and Kovacic's algorithm is used and the normal variational equation is of Fuchsian type. ► Some extensions and limitations are discussed.
Polyaffine parametrization of image registration based on geodesic flows
DEFF Research Database (Denmark)
Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.
2012-01-01
Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which ...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....
Geodesics and symmetries of doubly spinning black rings
International Nuclear Information System (INIS)
Durkee, Mark
2009-01-01
This paper studies various properties of the Pomeransky-Sen'kov doubly spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the ergoregion. These geodesics are used to construct geometrically motivated coordinates that cover the black hole horizon. Finally, I relate this weak form of separability to the existence of a conformal Killing tensor in a particular four-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a related conformal Killing-Yano tensor only exists in the singly spinning case.
Geodesics in Goedel-type space-times
International Nuclear Information System (INIS)
Calvao, M.O.; Soares, I.D.; Tiomno, J.
1988-01-01
The geodesic curves of the homogeneous Goedel-type space-times, which constitute a two-parameter ({ l and Ω}) class of solutions presented to several theories of gravitation (general relativity, Einstein-Cartan and higher derivative) are investigated. The qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion are examined. It is shown that some of the qualitative features of the free motion in Godel's universe (l 2 =2Ω 2 ) are preserved in all space-times, namely the projections of the geodesics onto the 2-surface (r,ψ) are simple closed curves, and the geodesics for which the ratio of azymuthal angular momentum to total energy, υ is equal to zero always cross the origin r = o. However, two new cases appear: (i) radially unbounded geodesics with υ assuming any (real) value, which may occur only for the causal space-times (l 2 ≥ 4 Ω 2 ), and (ii) geodesics with υ bounded both below and above, which always occur for the circular family (l 2 [pt
Geodesic flows in a charged black hole spacetime with quintessence
Energy Technology Data Exchange (ETDEWEB)
Nandan, Hemwati [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Uniyal, Rashmi [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Government Degree College, Department of Physics, Tehri Garhwal, Uttarakhand (India)
2017-08-15
We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)
Geodesic flows in a charged black hole spacetime with quintessence
International Nuclear Information System (INIS)
Nandan, Hemwati; Uniyal, Rashmi
2017-01-01
We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)
An explicit local uniform large deviation bound for Brownian bridges
Wittich, O.
2005-01-01
By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.
A prescribing geodesic curvature problem
International Nuclear Information System (INIS)
Chang, K.C.; Liu, J.Q.
1993-09-01
Let D be the unit disk and k be a function on S 1 = δD. Find a flat metric which is pointwise conformal to the standard metric and has k as the geodesic curvature of S 1 . A sufficient condition for the existence of such a metric is that the harmonic extension of k in D has saddle points. (author). 11 refs
An exact Jacobi map in the geodesic light-cone gauge
Fanizza, G.; Marozzi, G.; Veneziano, G.
2013-11-07
The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodetic-deviation equation, and thus to derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J^A_B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J^A_B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on l...
Geodesic detection of Agulhas rings
Beron-Vera, F. J.; Wang, Y.; Olascoaga, M. J.; Goni, G. J.; Haller, G.
2012-12-01
Mesoscale oceanic eddies are routinely detected from instantaneous velocities. While simple to implement, this Eulerian approach gives frame-dependent results and often hides true material transport by eddies. Building on the recent geodesic theory of transport barriers, we develop an objective (i.e., frame-independent) method for accurately locating coherent Lagrangian eddies. These eddies act as compact water bodies, with boundaries showing no leakage or filamentation over long periods of time. Applying the algorithm to altimetry-derived velocities in the South Atlantic, we detect, for the first time, Agulhas rings that preserve their material coherence for several months, while eddy candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that current Eulerian estimates of the Agulhas leakage need significant revision.Temporal evolution of fluid patches identified as eddies by different methods. First column: eddies extracted using geodesic eddy identification [1,2]. Second column: eddies identified from sea surface height (SSH) using the methodology of Chelton et al. [2] with U/c > 1. Third column: eddies identified as elliptic regions by the Okubo-Weiss (OW) criterion [e.g., 3]. Fourth column: eddies identified as mesoelliptic (ME) regions by Mezic et al.'s [4] criterion. References: [1] Beron-Vera et al. (2012). Geodesic eddy detection suggests reassessment of Agulhas leakage. Proc. Nat. Acad. Sci. USA, submitted. [2] Haller & Beron-Vera (2012). Geodesic theory of transport barriers in two-dimensional flows. Physica D, in press. [2] Chelton et al. (2011). Prog. Oceanog. 91, 167. [3] Chelton et al. (2007). Geophys. Res. Lett. 34, L5606. [4] Mezic et al. (2010). Science 330, 486.
A Continuum Mechanical Approach to Geodesics in Shape Space
2010-01-01
mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto...P. W. Michor and D. Mumford. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc., 8:1–48, 2006. 37 [33] Peter W. Michor, David ... Cremers . Shape matching by variational computation of geodesics on a manifold. In Pattern Recognition, LNCS 4174, pages 142–151, 2006. [38] P
On certain geodesic conjugacies of flat cylinders
Indian Academy of Sciences (India)
Moreover, these base points must lie on different parallels. By continuity of F ◦α we conclude that the above parallel geodesics fill out a neighborhood of (r0, 0) in S. We conclude that f (r) = 0 for all r close to r0. This proves that R \\ A must be open. D. We call a closed geodesic slant if it is not a parallel geodesic. We have the ...
Do electromagnetic waves always propagate along null geodesics?
International Nuclear Information System (INIS)
Asenjo, Felipe A; Hojman, Sergio A
2017-01-01
We find exact solutions to Maxwell equations written in terms of four-vector potentials in non–rotating, as well as in Gödel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non–rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gödel and Kerr spacetimes do not exhibit that behavior. (paper)
Geodesics in thermodynamic state spaces of quantum gases
International Nuclear Information System (INIS)
Oshima, H.; Obata, T.; Hara, H.
2002-01-01
The geodesics for ideal quantum gases are numerically studied. We show that 30 ideal quantum state is connected to an ideal classical state by geodesics and that the bundle of geodesics for Bose gases have a tendency of convergence
Geodesic motion and confinement in Goedel's universe
International Nuclear Information System (INIS)
Novello, M.; Soares, I.D.; Tiomno, J.
1982-01-01
A complete study of geodesic motion in Goedel's universe, using the method of the Effective Potential is presented. It then emerges a clear physical picture of free motion and its stability in this universe. Geodesics of a large class have finite intervals in which the particle moves back in time (dt/ds [pt
Generating geodesic flows and supergravity solutions
Bergshoeff, E.; Chemissany, W.; Ploegh, A.; Trigiante, M.; Van Riet, T.
2009-01-01
We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacellike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike p-brane Solutions when they are lifted over a p-dimensional flat space. In particular, we consider
Symmetries and conserved quantities in geodesic motion
International Nuclear Information System (INIS)
Hojman, S.; Nunez, L.; Patino, A.; Rago, H.
1986-01-01
Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved
Newtonian potential and geodesic completeness in infinite derivative gravity
Edholm, James; Conroy, Aindriú
2017-08-01
Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.
Anatomy of geodesic Witten diagrams
Energy Technology Data Exchange (ETDEWEB)
Chen, Heng-Yu; Kuo, En-Jui [Department of Physics and Center for Theoretical Sciences, National Taiwan University,Taipei 10617, Taiwan (China); Kyono, Hideki [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2017-05-12
We revisit the so-called “Geodesic Witten Diagrams” (GWDs) https://www.doi.org/10.1007/JHEP01(2016)146, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related “split representation” for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Statistics of geodesics in large quadrangulations
International Nuclear Information System (INIS)
Bouttier, J; Guitter, E
2008-01-01
We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to the notion of 'spine trees', amenable to a direct enumeration. We obtain the generating functions for quadrangulations with a marked geodesic of fixed length, as well as with a set of 'confluent geodesics', i.e. a collection of non-intersecting minimal paths connecting two given points. In the limit of quadrangulations with a large area n, we find in particular an average number 3 x 2 i of geodesics between two fixed points at distance i >> 1 from each other. We show that, for generic endpoints, two confluent geodesics remain close to each other and have an extensive number of contacts. This property fails for a few 'exceptional' endpoints which can be linked by truly distinct geodesics. Results are presented both in the case of finite length i and in the scaling limit i ∼ n 1/4 . In particular, we give the scaling distribution of the exceptional points
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.
Revisiting scalar geodesic synchrotron radiation in Kerr spacetime
International Nuclear Information System (INIS)
Macedo, Caio F.B.; Crispino, Luis C.B.
2011-01-01
Full text: The Kerr solution [R. P. Kerr, Phys. Rev. D 11, 5 (1963)] is one of the most important black hole solutions of Einstein equations. It describes a chargeless rotating black hole, with Schwarzschild black hole as a particular case. It is estimated, inferred using distinct methods, that most black hole candidates have a considerable value of the rotation parameter [E. Berti, V. Cardoso, and A. Starinets, Classical Quantum Gravity 26, 163001 (2009)]. Although the Schwarzschild solution is suitable for a great variety of phenomena in star and black hole physics, the Kerr solution becomes very important in the explanation of the electrodynamical aspects of accretion disks for binary X-ray sources [The Kerr Spacetime: Rotating Black Holes in General Relativity, edited by D. L. Wiltshire, M. Visser, and S. M. Scott (Cambridge University Press, Cambridge, 2009)]. Thus, the investigation of how radiation emission processes are modified by the nontrivial curvature of rotating black holes is particularly important. As a first approximation to the problem, one can consider a moving particle, minimally coupled to the massless scalar field, in circular geodesic motion. The radiation emitted in this configuration is called scalar geodesic synchrotron radiation. In this work, we revisit the main aspects of scalar geodesic synchrotron radiation in Kerr spacetime, including some effects occurring in the high-frequency approximation. Our results can be readily compared with the results of the equivalent phenomena in Schwarzschild spacetime. (author)
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.)
Craniofacial Reconstruction Evaluation by Geodesic Network
Zhao, Junli; Liu, Cuiting; Wu, Zhongke; Duan, Fuqing; Wang, Kang; Jia, Taorui; Liu, Quansheng
2014-01-01
Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the or...
Geodesics on a hot plate: an example of a two-dimensional curved space
International Nuclear Information System (INIS)
Erkal, Cahit
2006-01-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion
Geodesics on a hot plate: an example of a two-dimensional curved space
Energy Technology Data Exchange (ETDEWEB)
Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)
2006-07-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.
From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos
Kuznetsov, Sergey P.
2016-12-01
Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.
Geodesic structure of Lifshitz black holes in 2+1 dimensions
International Nuclear Information System (INIS)
Cruz, Norman; Olivares, Marco; Villanueva, J.R.
2013-01-01
We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with z=3 and d=1 as found in Ayon-Beato et al. (Phys. Rev. D 80:104029, 2009). By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic p, σ, and ζ functions. (orig.)
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.
Deuschel, Jean-Dominique; Deuschel, Jean-Dominique
2001-01-01
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allow
Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
International Nuclear Information System (INIS)
Kubiznak, David; Frolov, Valeri P.; Connell, Patrick; Krtous, Pavel
2009-01-01
In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a nondegenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4, 5, 6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.
Kastor-Traschen black holes, null geodesics and conformal circles
International Nuclear Information System (INIS)
Casey, Stephen
2012-01-01
The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant Λ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the projection to the space of orbits of the timelike conformal retraction. It is found that these projected light rays arise as integral curves of a system of third-order ordinary differential equations. This system is not uniquely defined, however, and we use the inherent freedom to construct a new system whose integral curves coincide with the projection of distinguished null curves of Kastor-Traschen arising from a magnetic flow. We discuss our results in the one-centre case and demonstrate a link to conformal circles in the limit Λ → 0. We also show how to construct analytic expressions for the projected null geodesics of this metric by exploiting a well-known diffeomorphism between the K-T metric and extremal Reissner-Nordstrom-de Sitter. We make some remarks about the two-centre solution and demonstrate a link with the one-centre case. (paper)
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic...
Timelike geodesics around a charged spherically symmetric dilaton black hole
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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.
Diffeomorphometry and geodesic positioning systems for human anatomy.
Miller, Michael I; Younes, Laurent; Trouvé, Alain
2014-03-01
The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry . Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning . As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates . These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system . We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.
International Nuclear Information System (INIS)
Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi; Sasaki, Misao
2014-01-01
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing
Nonlinear excitation of geodesic acoustic modes by drift waves
International Nuclear Information System (INIS)
Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.
2007-01-01
In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs
Deng, Gao-Ming; Huang, Yong-Chang
2018-03-01
The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.
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...
Maxwell fields and shear-free null geodesic congruences
International Nuclear Information System (INIS)
Newman, Ezra T
2004-01-01
We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the worldline. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, the following strange interpretation can be given. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x a take complex values, i.e., x a → z a = x a + iy a with complex metric g η ab dz a dz b , the real vacuum Maxwell equations can be extended into the complex space and rewritten as curl W=i W radical, div W=0 with W=E+iB. This subcase of Maxwell fields can then be extended into the complex space so as to have as source, a complex analytic worldline, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space (z a = x a ), they possess a real principal null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex worldline is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities
Vacuum non-expanding horizons and shear-free null geodesic congruences
International Nuclear Information System (INIS)
Adamo, T M; Newman, E T
2009-01-01
We investigate the geometry of a particular class of null surfaces in spacetime called vacuum non-expanding horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex worldline in a complex four-dimensional space, each such choice induces a CR structure on the horizon, and a particular worldline (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.
Do extended objects move along the geodesics in the Riemann space-time
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.
1981-01-01
Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru
Drift effects on electromagnetic geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)
2015-02-15
A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)
A regularized approach for geodesic-based semisupervised multimanifold learning.
Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun
2014-05-01
Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.
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.
Instantons from geodesics in AdS moduli spaces
Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas
2018-03-01
We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.
Surfaces foliated by planar geodesics: a model forcurved wood design
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens
2017-01-01
Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle......Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle...
From geodesics of the multipole solutions to the perturbed Kepler problem
International Nuclear Information System (INIS)
Hernandez-Pastora, J. L.; Ospino, J.
2010-01-01
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2 4 -pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.
GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION
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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.
The Distance Standard Deviation
Edelmann, Dominic; Richards, Donald; Vogel, Daniel
2017-01-01
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. New representations for the distance standard deviation are obtained in terms of Gini's mean difference and in terms of the moments of spacings of order statistics. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini's mean difference. Further, it is ...
Do extended bodies move alon.o the geodesics of the Riemannian space-time
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.
1980-01-01
Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8
Geodesics in hypercomplex number systems. Application to commutative quaternions
International Nuclear Information System (INIS)
Catoni, Francesco; Zampetti, Paolo; Cannata, Roberto; Bordoni, Luciana
1997-10-01
The functions of hypercomplex variable can be related to the physical fields. Following the Einstein's ideas, by which the Theory of General Relativity was developed, they want to verify if a generalisation is possible, in order to described the motion of a body in a gravitational field, by the geodesics in spaces ''deformed'' by functional transformations of hypercomplex variables. These number systems introduce new space symmetries. This paper is just a first step in the more extended study. As a first application they consider the ''commutative quaternions'' system that may be considered as a composition of complex and hyperbolic numbers. By using in this system the same functional transformations valid for the two dimensional case, elliptical geodesics are obtained, with the eccentricity related to the angle between the orbit plane and a reference plane. These geodesics do not describe the Kepler orbits, but they show a space anisotropy that might be related to planet orbits of the solar system
Superintegrability of geodesic motion on the sausage model
Arutyunov, Gleb; Heinze, Martin; Medina-Rincon, Daniel
2017-06-01
Reduction of the η-deformed sigma model on AdS_5× S5 to the two-dimensional squashed sphere (S^2)η can be viewed as a special case of the Fateev sausage model where the coupling constant ν is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model. This paper is a tribute to the memory of Prof Petr Kulish.
Spherical null geodesics of rotating Kerr black holes
International Nuclear Information System (INIS)
Hod, Shahar
2013-01-01
The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r ph (a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii r ph (a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√(3)−√(59))/4≲cosi ph (a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=√(4/7), above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.
Null solution of the Yang-Mills equations
International Nuclear Information System (INIS)
Tafel, J.
1986-05-01
We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays. (orig.)
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 Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation.
Adamo, Timothy M; Newman, Ezra T; Kozameh, Carlos
2012-01-01
A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, [Formula: see text]-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
of the CT-scans into a single atlas. Afterwards the standard deviation of anatomical symmetry for the 20 normal patients was evaluated using non-rigid registration and registered onto the atlas to create an atlas for normal anatomical symmetry deviation. The same non-rigid registration was used on the 10...... hypopharyngeal cancer patients to find anatomical symmetry and evaluate it against the standard deviation of the normal patients to locate pathologic volumes. Combining the information with an absolute PET threshold of 3 Standard uptake value (SUV) a volume was automatically delineated. The overlap of automated....... The standard deviation of the anatomical symmetry, seen in figure for one patient along CT and PET, was extracted for normal patients and compared with the deviation from cancer patients giving a new way of determining cancer pathology location. Using the novel method an overlap concordance index...
Ergodic Properties of the Quantum Geodesic Flow on Tori
Energy Technology Data Exchange (ETDEWEB)
Klimek, SLawomir [Indiana University Purdue University Indianapolis, Department of Mathematics (United States); Kondracki, Witold [Polish Academy of Sciences, Institute of Mathematics (Poland)
2005-05-15
We study ergodic averages for a class of pseudo-differential operators on the flat N-dimensional torus with respect to the Schroedinger evolution. The later can be consider a quantization of the geodesic flow on T{sup N}. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.
On the Robinson theorem and shearfree geodesic null congruences
International Nuclear Information System (INIS)
Tafel, J.
1985-01-01
Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)
DEFF Research Database (Denmark)
Rocha, Vera; Van Praag, Mirjam; Carneiro, Anabela
This paper studies three related questions: To what extent otherwise similar startups employ different quantities and qualities of human capital at the moment of entry? How persistent are initial human capital choices over time? And how does deviating from human capital benchmarks influence firm......, founders human capital, and the ownership structure of startups (solo entrepreneurs versus entrepreneurial teams). We then study the survival implications of exogenous deviations from these benchmarks, based on spline models for survival data. Our results indicate that (especially negative) deviations from...... the benchmark can be substantial, are persistent over time, and hinder the survival of firms. The implications may, however, vary according to the sector and the ownership structure at entry. Given the stickiness of initial choices, wrong human capital decisions at entry turn out to be a close to irreversible...
Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity
International Nuclear Information System (INIS)
Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston
2010-01-01
The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.
Can geodesics in extra dimensions solve the cosmological horizon problem?
International Nuclear Information System (INIS)
Chung, Daniel J. H.; Freese, Katherine
2000-01-01
We demonstrate a non-inflationary solution to the cosmological horizon problem in scenarios in which our observable universe is confined to three spatial dimensions (a three-brane) embedded in a higher dimensional space. A signal traveling along an extra-dimensional null geodesic may leave our three-brane, travel into the extra dimensions, and subsequently return to a different place on our three-brane in a shorter time than the time a signal confined to our three-brane would take. Hence, these geodesics may connect distant points which would otherwise be ''outside'' the four dimensional horizon (points not in causal contact with one another). (c) 2000 The American Physical Society
MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS
International Nuclear Information System (INIS)
Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.
2013-01-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.
The Jacobi metric for timelike geodesics in static spacetimes
Gibbons, G. W.
2016-01-01
It is shown that the free motion of massive particles moving in static spacetimes is given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the massless limit Jacobi's metric coincides with the energy independent Fermat or optical metric. For stationary metrics, it is known that the motion of massless particles is given by the geodesics of an energy independent Finslerian metric of Randers type. The motion of massive particles is governed by neither a Riemannian nor a Finslerian metric. The properies of the Jacobi metric for massive particles moving outside the horizon of a Schwarschild black hole are described. By constrast with the massless case, the Gaussian curvature of the equatorial sections is not always negative.
A Finsler geodesic spray paradigm for wildfire spread modelling
DEFF Research Database (Denmark)
Markvorsen, Steen
2015-01-01
represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... and thence eventually constitute the local and global structure of the wildfire spread....
Geodesic atlas-based labeling of anatomical trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2015-01-01
We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...... equally complete airway trees, and comparable in performance to that of experts in pulmonary medicine, emphasizing the suitability of the labeling algorithm for clinical use....
Average geodesic distance of skeleton networks of Sierpinski tetrahedron
Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao
2018-04-01
The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.
International Nuclear Information System (INIS)
Paudel, Eak Raj
2007-01-01
Gravitational field of Schwarzschild and Schwarzschild de-sitter Black hole with a straight string passing through it. In such space analytical and numerical solutions of null and time like geodesics are investigated. The string parameter a + is found to affect both the angle of deflection in null geodesics and the precession of perihelion on time like geodesics .It is seen that the deflection of null and time like geodesics near the gravitating mass of de-sitter space time increases with t he gravitational field of a straight string in flat space time has the property that the Newtonian potential vanishes yet there are non trivial gravitational effects. A test particle is neither attracted nor repelled by a string, yet the conical nature of space outside of string produces observable effects such as light deflection . Schwarzschild Black hole is a mathematical solution to the Einstein's field equations and corresponds to the gravitational field of massive compact spherically symmetric ob normal. References 1. Aryal, M.M, A. Vilenkin and L.H Ford, 1986, Phys.Rev. D32 ,2262 2. Moriyasu ,K ., 1980 , An introduction to gauge Invariance 3. Vilenkin A., 1985 , Physical reports , cosmic strings and Domain walls 4. Berry, M. , 1976 , Principle of cosmology and Gravitation 5. Mishner , C.W ., K.S .Throne , J.A wheeler , 1973. (Author)
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.
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.
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.
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.
On integrability of the Killing equation
Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori
2018-04-01
Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.
Detecting deviating behaviors without models
Lu, X.; Fahland, D.; van den Biggelaar, F.J.H.M.; van der Aalst, W.M.P.; Reichert, M.; Reijers, H.A.
2016-01-01
Deviation detection is a set of techniques that identify deviations from normative processes in real process executions. These diagnostics are used to derive recommendations for improving business processes. Existing detection techniques identify deviations either only on the process instance level
International Nuclear Information System (INIS)
Winter, J.
1985-01-01
A covariant generalization of the Wigner transformation of quantum equations is proposed for gravitating many-particle systems, which modifies the Einstein-Liouville equations for the coupled gravity-matter problem by inclusion of quantum effects of the matter moving in its self-consistent classical gravitational field, in order to extend their realm of validity to higher particle densities. The corrections of the Vlasov equation (Liouville equation in one-particle phase space) are exhibited as combined effects of quantum mechanics and the curvature of space-time arranged in a semiclassical expansion in powers of h 2 , the first-order term of which is explicitly calculated. It is linear in the Riemann tensor and in its gradient; the Riemann tensor occurs in a similar position as the tensor of the Yang-Mills field strength in a corresponding Vlasov equation for systems with local gauge invariance in the purely classical limit. The performance of the Wigner transformation is based on expressing the equation of motion for the two-point function of the Klein-Gordon field, in particular the Beltrami operator, in terms of a midpoint and a distance vector covariantly defined for the two points. This implies the calculation of deviations of the geodesic between these points, the standard concept of which has to be refined to include infinitesimal variations of the second order. A differential equation for the second-order deviation is established
Semi-local inversion of the geodesic ray transform in the hyperbolic plane
International Nuclear Information System (INIS)
Courdurier, Matias; Saez, Mariel
2013-01-01
The inversion of the ray transform on the hyperbolic plane has applications in geophysical exploration and in medical imaging techniques (such as electrical impedance tomography). The geodesic ray transform has been studied in more general geometries and including attenuation, but all of the available inversion formulas require knowledge of the ray transform for all the geodesics. In this paper we present a different inversion formula for the ray transform on the hyperbolic plane, which has the advantage of only requiring knowledge of the ray transform in a reduced family of geodesics. The required family of geodesics is directly related to the set where the original function is to be recovered. (paper)
Equations of motion derived from a generalization of Einstein's equation for the gravitational field
International Nuclear Information System (INIS)
Mociutchi, C.
1980-01-01
The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)
The topology of geodesically complete space-times
International Nuclear Information System (INIS)
Lee, C.W.
1983-01-01
Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....... In tree-space, the airway tree topology and geometry change continuously, giving a natural way to automatically handle anatomical differences and noise. The algorithm is made efficient using a hierarchical approach, in which labels are assigned from the top down. We only use features of the airway...
Fundamental geodesic deformations in spaces of treelike shapes
DEFF Research Database (Denmark)
Feragen, Aasa; Lauze, Francois Bernard; Nielsen, Mads
2010-01-01
This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which...... is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees....
Geodesic acoustic modes in noncircular cross section tokamaks
Energy Technology Data Exchange (ETDEWEB)
Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com; Lakhin, V. P. [National Research Center “Kurchatov Institute,” (Russian Federation); Konovaltseva, L. V. [People’s Friendship University of Russia (Russian Federation); Ilgisonis, V. I. [National Research Center “Kurchatov Institute,” (Russian Federation)
2017-03-15
The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.
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.
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.
MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS
Energy Technology Data Exchange (ETDEWEB)
Florinski, V. [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States); Guo, X. [Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Balsara, D. S.; Meyer, C. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States)
2013-04-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.
Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion
Barack, Leor
The question of motion in a gravitationally bound two-body system is a longstanding open problem of General Relativity. When the mass ratio eta; is small, the problem lends itself to a perturbative treatment, wherein corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in η, using the language of an effective gravitational self-force. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will give a brief survey of this activity and its achievements so far, and will identify the challenges that lie ahead. As concrete examples, I will discuss recent calculations of certain conservative post-geodesic effects of the self-force, including the O(η ) correction to the precession rate of the periastron. I will highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.
Properties of an Arithmetic Code for Geodesic Flows
International Nuclear Information System (INIS)
Chaves, Daniel P B; Palazzo, Reginaldo Jr; Rios Leite, Jose R
2011-01-01
Topological analysis of chaotic dynamical systems emerged in the nineties as a powerful tool in the study of strange attractors in low-dimensional dynamical systems. It is based on identifying the stretching and squeezing mechanisms responsible for creating a strange attractor and organize all the unstable periodic orbits in this attractor. This method is concerned with the manifold generated by the chaotic system. Furthermore, as a mathematical object, the manifolds have a well studied geometric and algebraic structure, particularly for the case of compact surfaces. Intending to use this structure in the analysis and application of chaotic systems through their topological characteristics, we determine properties of geodesic codes for compact surfaces necessary for the construction of encoders from the symbolic sequences of experimental data generated by the unstable periodic orbits of the strange attractor (related to the behavior changes of the system with the variation of control parameters) to the geodesic code sequences, which permits to use the surface structure to study the system orbits.
Investigation of energetic particle induced geodesic acoustic mode
Schneller, Mirjam; Fu, Guoyong; Chavdarovski, Ilija; Wang, Weixing; Lauber, Philipp; Lu, Zhixin
2017-10-01
Energetic particles are ubiquitous in present and future tokamaks due to heating systems and fusion reactions. Anisotropy in the distribution function of the energetic particle population is able to excite oscillations from the continuous spectrum of geodesic acoustic modes (GAMs), which cannot be driven by plasma pressure gradients due to their toroidally and nearly poloidally symmetric structures. These oscillations are known as energetic particle-induced geodesic acoustic modes (EGAMs) [G.Y. Fu'08] and have been observed in recent experiments [R. Nazikian'08]. EGAMs are particularly attractive in the framework of turbulence regulation, since they lead to an oscillatory radial electric shear which can potentially saturate the turbulence. For the presented work, the nonlinear gyrokinetic, electrostatic, particle-in-cell code GTS [W.X. Wang'06] has been extended to include an energetic particle population following either bump-on-tail Maxwellian or slowing-down [Stix'76] distribution function. With this new tool, we study growth rate, frequency and mode structure of the EGAM in an ASDEX Upgrade-like scenario. A detailed understanding of EGAM excitation reveals essential for future studies of EGAM interaction with micro-turbulence. Funded by the Max Planck Princeton Research Center. Computational resources of MPCDF and NERSC are greatefully acknowledged.
New non-linear modified massless Klein-Gordon equation
Energy Technology Data Exchange (ETDEWEB)
Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2017-11-15
The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)
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.
International Nuclear Information System (INIS)
Grunau, Saskia; Kagramanova, Valeria
2011-01-01
We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstroem space-time in terms of the Weierstrass weierp, σ, and ζ elliptic functions. Based on the study of the polynomials in the θ and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstroem space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstroem space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.
Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.
2018-05-01
We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.
Visualizing the Sample Standard Deviation
Sarkar, Jyotirmoy; Rashid, Mamunur
2017-01-01
The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…
Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak
Czech Academy of Sciences Publication Activity Database
Seidl, Jakub; Krbec, Jaroslav; Hron, Martin; Adámek, Jiří; Hidalgo, C.; Markovič, Tomáš; Melnikov, A.V.; Stöckel, Jan; Weinzettl, Vladimír; Aftanas, Milan; Bílková, Petra; Bogár, Ondrej; Böhm, Petr; Eliseev, L.G.; Háček, Pavel; Havlíček, Josef; Horáček, Jan; Imríšek, Martin; Kovařík, Karel; Mitošinková, Klára; Pánek, Radomír; Tomeš, Matěj; Vondráček, Petr
2017-01-01
Roč. 57, č. 12 (2017), č. článku 126048. ISSN 0029-5515 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA AV ČR(CZ) GA16-24724S; GA ČR(CZ) GA15-10723S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : geodesic acoustic mode * tokamak * turbulence * COMPASS Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016
Geodesic acoustic modes excited by finite beta drift waves
DEFF Research Database (Denmark)
Chakrabarti, Nikhil Kumar; Guzdar, P.N.; Kleva, R.G.
2008-01-01
Presented in this paper is a mode-coupling analysis for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by finite beta drift waves. The finite beta effects give rise to a strong stabilizing influence on the parametric excitation process. The dominant finite beta...... effect is the combination of the Maxwell stress, which has a tendency to cancel the primary drive from the Reynolds stress, and the finite beta modification of the drift waves. The zonal magnetic field is also excited at the GAM frequency. However, it does not contribute to the overall stability...... of the three-wave process for parameters of relevance to the edge region of tokamaks....
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking
Directory of Open Access Journals (Sweden)
Evert van Aart
2011-01-01
Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Quasilocal contribution to the scalar self-force: Geodesic motion
International Nuclear Information System (INIS)
Ottewill, Adrian C.; Wardell, Barry
2008-01-01
We consider a scalar charge travelling in a curved background space-time. We calculate the quasilocal contribution to the scalar self-force experienced by such a particle following a geodesic in a general space-time. We also show that if we assume a massless field and a vacuum background space-time, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analogs are of immediate physical interest for the calculation of radiation-reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results
Geodesic Monitoring of Settling in Vertical Fuel Tanks
Directory of Open Access Journals (Sweden)
Luis Enrique Acosta-González
2017-07-01
Full Text Available The behavior of the settling in a vertical tank used for fuel storage was studied. Monitoring was conducted using the geodesic model for the geometric leveling of high accuracy category II. The original project varied during construction by replacing deep foundations with a surface one applying compaction techniques to improve soil resistance. The deformation values obtained provided valuable information on the implementation of the proposed foundation alternative depending on time and loads. The maximum settling was reported to be 132,6 mm. The displacements in the control points located in the perimeter of the tank had a distinct nature with a maximum of 44,2 mm, which caused the foundation structure to crack.
Stringy Jacobi fields in Morse theory
International Nuclear Information System (INIS)
Cho, Yong Seung; Hong, Soon-Tae
2007-01-01
We consider the variation of the surface spanned by closed strings in a spacetime manifold. Using the Nambu-Goto string action, we induce the geodesic surface equation and the geodesic surface deviation equation which yields a Jacobi field, and we define the index form of a geodesic surface as in the case of point particles to discuss conjugate strings on the geodesic surface
Optimized curve design for image analysis using localized geodesic distance transformations
Braithwaite, Billy; Niska, Harri; Pöllänen, Irene; Ikonen, Tiia; Haataja, Keijo; Toivanen, Pekka; Tolonen, Teemu
2015-03-01
We consider geodesic distance transformations for digital images. Given a M × N digital image, a distance image is produced by evaluating local pixel distances. Distance Transformation on Curved Space (DTOCS) evaluates shortest geodesics of a given pixel neighborhood by evaluating the height displacements between pixels. In this paper, we propose an optimization framework for geodesic distance transformations in a pattern recognition scheme, yielding more accurate machine learning based image analysis, exemplifying initial experiments using complex breast cancer images. Furthermore, we will outline future research work, which will complete the research work done for this paper.
Fidelity deviation in quantum teleportation
Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir
2018-01-01
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel---we here consider the so-called Werner channel. To characterize our resu...
Geodesic acoustic mode driven by energetic particles with bump-on-tail distribution
Ren, Haijun; Wang, Hao
2018-04-01
Energetic-particle-driven geodesic acoustic mode (EGAM) is analytically investigated by adopting the bump-on-tail distribution for energetic particles (EPs), which is created by the fact that the charge exchange time (τcx ) is sufficiently shorter than the slowing down time (τsl ). The dispersion relation is derived in the use of gyro-kinetic equations. Due to the finite ratio of the critical energy and the initial energy of EPs, defined as τc , the dispersion relation is numerically evaluated and the effect of finite τc is examined. Following relative simulation and experimental work, we specifically considered two cases: τsl/τcx = 3.4 and τsl/τcx = 20.4 . The pitch angle is shown to significantly enhance the growth rate and meanwhile, the real frequency is dramatically decreased with increasing pitch angle. The excitation of high-frequency EGAM is found, and this is consistent with both the experiment and the simulation. The number density effect of energetic particles, represented by \
Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency
Energy Technology Data Exchange (ETDEWEB)
Lakhin, V.P. [NRC “Kurchatov Institute”, Moscow (Russian Federation); Sorokina, E.A., E-mail: sorokina.ekaterina@gmail.com [NRC “Kurchatov Institute”, Moscow (Russian Federation); Peoples' Friendship University of Russia, Moscow (Russian Federation)
2014-01-24
The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.
Are eikonal quasinormal modes linked to the unstable circular null geodesics?
Directory of Open Access Journals (Sweden)
R.A. Konoplya
2017-08-01
Full Text Available In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein–Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein–Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.
Are eikonal quasinormal modes linked to the unstable circular null geodesics?
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.
International Nuclear Information System (INIS)
Stuchlik, Zdenek; Hledik, Stanislav; Soltes, Jiri; Ostgaard, Erlend
2001-01-01
Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild--de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an 'effective potential.' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild--de Sitter spacetimes
Twisting null geodesic congruences, scri, H-space and spin-angular momentum
International Nuclear Information System (INIS)
Kozameh, Carlos; Newman, E T; Silva-Ortigoza, Gilberto
2005-01-01
The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat spacetime with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world line in a four-parameter complex space. Surprisingly, this parameter space turns out to be the H-space that is associated with the real physical spacetime under consideration. The main development in this work is the demonstration of how this complex world line can be made both unique and also given a physical meaning. More specifically, by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world line is uniquely determined and becomes (by several arguments) identified as the 'complex centre of mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum. One should think of this work as developing a generalization of the properties of the algebraically special spacetimes in the sense that the term that is forced here to vanish is automatically vanishing (among many other terms) for all the algebraically special metrics. This is demonstrated in the several given examples. It was, in fact, an understanding of the algebraically special metrics and their associated shear-free null congruence that led us to this construction of the asymptotically shear-free congruences and the unique complex world line. The Robinson-Trautman metrics and the Kerr and charged Kerr metrics with their properties are explicit examples of the construction given here
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.
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
International Nuclear Information System (INIS)
González, Juan C; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C
2012-01-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000. (paper)
Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration
International Nuclear Information System (INIS)
Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.
2016-01-01
We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration
Energy Technology Data Exchange (ETDEWEB)
Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)
2016-11-25
We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Deviations from LTE in a stellar atmosphere
International Nuclear Information System (INIS)
Kalkofen, W.; Klein, R.I.; Stein, R.F.
1979-01-01
Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section αsub(ν) grows with frequency ν faster than ν 2 ; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of αsub(ν). Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature. (author)
Deviations from LTE in a stellar atmosphere
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.
Computer generation of random deviates
International Nuclear Information System (INIS)
Cormack, John
1991-01-01
The need for random deviates arises in many scientific applications. In medical physics, Monte Carlo simulations have been used in radiology, radiation therapy and nuclear medicine. Specific instances include the modelling of x-ray scattering processes and the addition of random noise to images or curves in order to assess the effects of various processing procedures. Reliable sources of random deviates with statistical properties indistinguishable from true random deviates are a fundamental necessity for such tasks. This paper provides a review of computer algorithms which can be used to generate uniform random deviates and other distributions of interest to medical physicists, along with a few caveats relating to various problems and pitfalls which can occur. Source code listings for the generators discussed (in FORTRAN, Turbo-PASCAL and Data General ASSEMBLER) are available on request from the authors. 27 refs., 3 tabs., 5 figs
Solutions of the spin coefficient equations with nongeodesic eigenrays
International Nuclear Information System (INIS)
Kota, J.; Lukacs, B.; Perjes, Z.
1982-01-01
Among the many significant results obtained by spin coefficient techniques in general relativity, the exact integrals of gravitational equations have enjoyed particular attention. These integration procedures were first carried out with respect to a congruence of null geodesic curves. The authors show that spin coefficient equations can sometimes be exactly solved when the selected null congruence is nongeodesic. They derive metrics with this property and, among them, a new solution of the coupled Einstein-Maxwell equations. (Auth.)
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.
Fidelity deviation in quantum teleportation
Bang, Jeongho; Ryu, Junghee; Kaszlikowski, Dagomir
2018-04-01
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.
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.
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…
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole
2011-01-01
that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE......An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant......-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine...
Stability of geodesic imcompleteness for Robertson-Walker space-times
International Nuclear Information System (INIS)
Beem, J.K.
1981-01-01
Let (M,g) be a Lorentzian warped product space-time M = (a, b) X H,g = -dt 2 x fh, where -infinity -infinity and (H,h) is homogeneous, then the past incompleteness of every timelike geodesic of (M,g) is stable under small C 0 perturbations in the space Lor(M) of Lorentzian metrics for M. Also it is shown that if (H,h) is isotropic and (M,g) contains a past-inextendible, past-incomplete null geodesic, then the past incompleteness of all null geodesics is stable under small C 1 perturbations in Lor(M). Given either the isotropy or homogeneity of the Riemannian factor, the background space-time (M,g) is globally hyperbolic. The results of this paper, in particular, answer a question raised by D. Lerner for big bang Robertson-Walker cosmological models affirmatively. (author)
Geodesic paths and topological charges in quantum systems
Grangeiro Souza Barbosa Lima, Tiago Aecio
This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum
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.
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…
Null geodesics in black hole metrics with non-zero cosmological constant
International Nuclear Information System (INIS)
Stuchlik, Z.; Calvani, M.
1990-02-01
We study the radial motion along null geodesics in the Reissner-Nordstroem-de Sitter and Kerr-de Sitter space-times. We analyze the properties of the effective potential and we discuss circular orbits. We find that the radii of circular geodesics in the Reissner-Nordstroem-de Sitter space-time do not depend on the cosmological constant, and we explain this property using the optical reference geometry. In addition, we describe the unusual consequences of the interplay between rotation of the source and cosmological repulsion. (author). 16 refs, 8 figs
On geodesics with negative energies in the ergoregions of dirty black holes
Zaslavskii, O. B.
2015-03-01
We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov and V. D. Vertogradov, Mod. Phys. Lett.29, 1450110 (2014), arXiv:1304.7360.
Unique Two-Way Field Probe Concept Utilizing a Geodesic Sphere and Quad-Rotor
2015-03-26
encompass the quad-rotor. This cage will behave like a faraday cage of sorts, shielding the quad-rotor’s RCS phenomenology from the radar’s antenna...test volume. Second, because the quad-rotor’s structural geometry is a cause for concern, a geodesic cage , in the shape of a sphere, will be built to...be the development of the geodesic cage that will encompass the quad-rotor along with an analysis of its scattering statistics as function of the
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.
Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.
2018-06-01
We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.
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 an...
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 in...
Sensitivity Analysis of Deviation Source for Fast Assembly Precision Optimization
Directory of Open Access Journals (Sweden)
Jianjun Tang
2014-01-01
Full Text Available Assembly precision optimization of complex product has a huge benefit in improving the quality of our products. Due to the impact of a variety of deviation source coupling phenomena, the goal of assembly precision optimization is difficult to be confirmed accurately. In order to achieve optimization of assembly precision accurately and rapidly, sensitivity analysis of deviation source is proposed. First, deviation source sensitivity is defined as the ratio of assembly dimension variation and deviation source dimension variation. Second, according to assembly constraint relations, assembly sequences and locating, deviation transmission paths are established by locating the joints between the adjacent parts, and establishing each part’s datum reference frame. Third, assembly multidimensional vector loops are created using deviation transmission paths, and the corresponding scalar equations of each dimension are established. Then, assembly deviation source sensitivity is calculated by using a first-order Taylor expansion and matrix transformation method. Finally, taking assembly precision optimization of wing flap rocker as an example, the effectiveness and efficiency of the deviation source sensitivity analysis method are verified.
Deviations in human gut microbiota
DEFF Research Database (Denmark)
Casén, C; Vebø, H C; Sekelja, M
2015-01-01
microbiome profiling. AIM: To develop and validate a novel diagnostic test using faecal samples to profile the intestinal microbiota and identify and characterise dysbiosis. METHODS: Fifty-four DNA probes targeting ≥300 bacteria on different taxonomic levels were selected based on ability to distinguish......, and potential clinically relevant deviation in the microbiome from normobiosis. This model was tested in different samples from healthy volunteers and IBS and IBD patients (n = 330) to determine the ability to detect dysbiosis. RESULTS: Validation confirms dysbiosis was detected in 73% of IBS patients, 70...
Energy Technology Data Exchange (ETDEWEB)
Zhang, H; Yan, L; Huang, K; Kong, F; Jin, J [Georgia Regents University, Augusta, GA (Georgia)
2016-06-15
Purpose: The shape of the Positron Emission Tomography (PET) image represents the heterogeneity of tumor growth in various directions, and thus could be associated with tumor malignancy. We have proposed a median geodesic distance (MGD) to represent the local complexity of the shape and use a normalized MGD (NMGD) to quantify the shape, and found a potential correlation of NMGD to survival in a 20-patient pilot study. This study was to verify the finding in a larger patient cohort. Methods: Geodesic distance of two vertices on a surface is defined as the shortest path on the surface connecting the two vertices. The MGD was calculated for each vertex on the surface to display the local complexity of the shape. The NMGD was determined as: NMGD = 100*standard deviation(MGDs)/mean(MGDs). We applied the NMGD to 40 NSCLC patients who were enrolled in prospective PET image protocols and received radiotherapy. Each patient had a pre-treatment PET scan with the resolution of 4mm*4mm*5mm. Tumors were contoured by a professional radiation oncologist and triangulation meshes were built up based on the contours. Results: The mean and standard deviation of NMGD was 6.4±3.0. The OS was 33.1±16.9 months for low NMGD group, and 15.4±15.6 months for the high NMGD group. The low NMGD group had significant better OS than the high NMGD group (p=0.0013). Conclusion: NMGD could be used as a shape biomarker to predict survival and the MGD could be combined with image texture in future to increase prediction accuracy. This study was supported by Award Number 1R01CA166948 from the NIH and National Cancer Institute.
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.
The generalized good cut equation
International Nuclear Information System (INIS)
Adamo, T M; Newman, E T
2010-01-01
The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.
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 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 the...
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 an...
48 CFR 1201.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Individual deviations... FEDERAL ACQUISITION REGULATIONS SYSTEM 70-Deviations From the FAR and TAR 1201.403 Individual deviations... Executive Service (SES) official or that of a Flag Officer, may authorize individual deviations (unless (FAR...
48 CFR 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 effect...
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 Procurement...
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 contracting...
Fröb, Markus B.
2018-02-01
We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.
Null geodesics and wave front singularities in the Gödel space-time
Kling, Thomas P.; Roebuck, Kevin; Grotzke, Eric
2018-01-01
We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.
Geodesic least squares regression for scaling studies in magnetic confinement fusion
International Nuclear Information System (INIS)
Verdoolaege, Geert
2015-01-01
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices
AdS/CFT prescription for angle-deficit space and winding geodesics
International Nuclear Information System (INIS)
Aref’eva, Irina Ya.; Khramtsov, Mikhail A.
2016-01-01
We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS_3 space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical bulk-boundary propagator for a scalar field in the space with conical defect and use it to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of ℤ_r-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.
International Nuclear Information System (INIS)
Yehia, Hamad M
2013-01-01
In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S 2 is constructed. (paper)
New perspectives for high accuracy SLR with second generation geodesic satellites
Lund, Glenn
1993-01-01
This paper reports on the accuracy limitations imposed by geodesic satellite signatures, and on the potential for achieving millimetric performances by means of alternative satellite concepts and an optimized 2-color system tradeoff. Long distance laser ranging, when performed between a ground (emitter/receiver) station and a distant geodesic satellite, is now reputed to enable short arc trajectory determinations to be achieved with an accuracy of 1 to 2 centimeters. This state-of-the-art accuracy is limited principally by the uncertainties inherent to single-color atmospheric path length correction. Motivated by the study of phenomena such as postglacial rebound, and the detailed analysis of small-scale volcanic and strain deformations, the drive towards millimetric accuracies will inevitably be felt. With the advent of short pulse (less than 50 ps) dual wavelength ranging, combined with adequate detection equipment (such as a fast-scanning streak camera or ultra-fast solid-state detectors) the atmospheric uncertainty could potentially be reduced to the level of a few millimeters, thus, exposing other less significant error contributions, of which by far the most significant will then be the morphology of the retroreflector satellites themselves. Existing geodesic satellites are simply dense spheres, several 10's of cm in diameter, encrusted with a large number (426 in the case of LAGEOS) of small cube-corner reflectors. A single incident pulse, thus, results in a significant number of randomly phased, quasi-simultaneous return pulses. These combine coherently at the receiver to produce a convolved interference waveform which cannot, on a shot to shot basis, be accurately and unambiguously correlated to the satellite center of mass. This paper proposes alternative geodesic satellite concepts, based on the use of a very small number of cube-corner retroreflectors, in which the above difficulties are eliminated while ensuring, for a given emitted pulse, the return
Cosmological models in globally geodesic coordinates. II. Near-field approximation
International Nuclear Information System (INIS)
Liu Hongya
1987-01-01
A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system
Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background
International Nuclear Information System (INIS)
Iftikhar, Sehrish; Sharif, M.
2015-01-01
This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole
Chiral equations and fiber bundles
International Nuclear Information System (INIS)
Mateos, T.; Becerril, R.
1992-01-01
Using the hypothesis g = g (lambda i ), the chiral equations (rhog, z g -1 ), z -bar + (rhog, z -barg -1 ), z = 0 are reduced to a Killing equation of a p-dimensional space V p , being lambda i lambda i (z, z-bar) 'geodesic' parameters of V p . Supposing that g belongs to a Lie group G, one writes the corresponding Lie algebra elements (F) in terms of the Killing vectors of V p and the generators of the subalgebra of F of dimension d = dimension of the Killing space. The elements of the subalgebras belong to equivalence classes which in the respective group form a principal fiber bundle. This is used to integrate the matrix g in terms of the complex variables z and z-bar ( Author)
The reinterpretation of standard deviation concept
Ye, Xiaoming
2017-01-01
Existing mathematical theory interprets the concept of standard deviation as the dispersion degree. Therefore, in measurement theory, both uncertainty concept and precision concept, which are expressed with standard deviation or times standard deviation, are also defined as the dispersion of measurement result, so that the concept logic is tangled. Through comparative analysis of the standard deviation concept and re-interpreting the measurement error evaluation principle, this paper points o...
Introducing the Mean Absolute Deviation "Effect" Size
Gorard, Stephen
2015-01-01
This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is easier to use and understand, and more tolerant of extreme…
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) of...
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 individual...
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. Individual...
48 CFR 3001.403 - Individual deviations.
2010-10-01
... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Individual deviations... from the FAR and HSAR 3001.403 Individual deviations. Unless precluded by law, executive order, or other regulation, the HCA is authorized to approve individual deviation (except with respect to (FAR) 48...
48 CFR 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. The...
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 the...
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. Individual...
The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view
Gallouët, Thomas; Vialard, François-Xavier
2018-04-01
The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.
The Standard Deviation of Launch Vehicle Environments
Yunis, Isam
2005-01-01
Statistical analysis is used in the development of the launch vehicle environments of acoustics, vibrations, and shock. The standard deviation of these environments is critical to accurate statistical extrema. However, often very little data exists to define the standard deviation and it is better to use a typical standard deviation than one derived from a few measurements. This paper uses Space Shuttle and expendable launch vehicle flight data to define a typical standard deviation for acoustics and vibrations. The results suggest that 3dB is a conservative and reasonable standard deviation for the source environment and the payload environment.
Large Deviations for Two-Time-Scale Diffusions, with Delays
International Nuclear Information System (INIS)
Kushner, Harold J.
2010-01-01
We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.
INDICATIVE MODEL OF DEVIATIONS IN PROJECT
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2016-02-01
Full Text Available The article shows the process of constructing the project deviations indicator model. It based on a conceptual model of project deviations integrated management (PDIM. During the project different causes (such as risks, changes, problems, crises, conflicts, stress lead to deviations of integrated project indicators - time, cost, quality, and content. For a more detailed definition of where in the project deviations occur and how they are dangerous for the whole project, it needs to develop an indicative model of project deviations. It allows identifying the most dangerous deviations that require PDIM. As a basis for evaluation of project's success has been taken famous model IPMA Delta. During the evaluation, IPMA Delta estimated project management competence of organization in three modules: I-Module ("Individuals" - a self-assessment personnel, P-module ("Projects" - self-assessment of projects and/or programs, and O-module ("Organization" - used to conduct interviews with selected people during auditing company. In the process of building an indicative model of deviations in the project, the first step is the assessment of project management in the organization by IPMA Delta. In the future, built cognitive map and matrix of system interconnections of the project, which conducted simulations and built a scale of deviations for the selected project. They determined a size and place of deviations. To identify the detailed causes of deviations in the project management has been proposed to use the extended system of indicators, which is based on indicators of project management model Project Excellence. The proposed indicative model of deviations in projects allows to estimate the size of variation and more accurately identify the place of negative deviations in the project and provides the project manager information for operational decision making for the management of deviations in the implementation of the project
Deviations from thermal equilibrium in plasmas
International Nuclear Information System (INIS)
Burm, K.T.A.L.
2004-01-01
A plasma system in local thermal equilibrium can usually be described with only two parameters. To describe deviations from equilibrium two extra parameters are needed. However, it will be shown that deviations from temperature equilibrium and deviations from Saha equilibrium depend on one another. As a result, non-equilibrium plasmas can be described with three parameters. This reduction in parameter space will ease the plasma describing effort enormously
2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds
Araya Quezada, Ignacio Jesus
In this thesis, we discuss two different contexts where the idea of gauge symmetry and duality is used to solve the dynamics of physical systems. The first of such contexts is 2T-physics in the worldline in d+2 dimensions, where the principle of Sp(2,R) gauge symmetry in phase space is used to relate different 1T systems in (d -- 1) + 1 dimensions, such as a free relativistic particle, and a relativistic particle in an arbitrary V(x2) potential. Because each 1T shadow system corresponds to a particular gauge of the underlying symmetry, there is a web of dualities relating them. The dualities between said systems amount to canonical transformations including time and energy, which allows the different systems to be described by different Hamiltonians, and consequently, to correspond to different dynamics in the (d -- 1)+1 phase space. The second context, corresponds to a Weyl invariant scalar-tensor theory of gravity, obtained as a direct prediction of 2T gravity, where the Weyl symmetry is used to obtain geodesically complete dynamics both in the context of cosmology and black hole (BH) backgrounds. The geodesic incompleteness of usual Einstein gravity, in the presence of singularities in spacetime, is related to the definition of the Einstein gauge, which fixes the sign and magnitude of the gravitational constant GN, and therefore misses the existence of antigravity patches, which are expected to arise generically just beyond gravitational singularities. The definition of the Einstein gauge can be generalized by incorporating a sign flip of the gravitational constant GN at the transitions between gravity and antigravity. This sign is a key aspect that allows us to define geodesically complete dynamics in cosmology and in BH backgrounds, particularly, in the case of the 4D Schwarzschild BH and the 2D stringy BH. The complete nature of particle geodesics in these BH backgrounds is exhibited explicitly at the classical level, and the extension of these results to the
Mean E×B shear effect on geodesic acoustic modes in Tokamaks
International Nuclear Information System (INIS)
Singh, Rameswar; Gurcan, Ozgur D.
2015-01-01
E × B shearing effect on geodesic acoustic mode (GAM) is investigated for the first time both as an initial value problem in the shearing frame and as an eigenvalue value problem in the lab frame. The nontrivial effects are that E × B shearing couples the standard GAM perturbations to their complimentary poloidal parities. The resulting GAM acquires an effective inertia increasing in time leading to GAM damping. Eigenmode analysis shows that GAMs are radially localized by E × B shearing with the mode width being inversely proportional and radial wave number directly proportional to the shearing rate for weak shear. (author)
Nonlocal analysis of the excitation of the geodesic acoustic mode by drift waves
DEFF Research Database (Denmark)
Guzdar, P.N.; Kleva, R.G.; Chakrabarti, N.
2009-01-01
The geodesic acoustic modes (GAMs) are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical...... of the edge region of tokamaks is presented in this paper. The continuum GAM modes with coupling to the drift waves can create discrete "global" unstable eigenmodes localized in the edge "pedestal" region of the plasma. Multiple resonantly driven unstable radial eigenmodes can coexist on the edge pedestal....
A geodesic atmospheric model with a quasi-Lagrangian vertical coordinate
International Nuclear Information System (INIS)
Heikes, Ross; Konor, Celal; Randall, David A
2006-01-01
The development of the Coupled Colorado State Model (CCoSM) is ultimately motivated by the need to predict and study climate change. All components of CCoSM innovatively blend unique design ideas and advanced computational techniques. The atmospheric model combines a geodesic horizontal grid with a quasi-Lagrangian vertical coordinate to improve the quality of simulations, particularly that of moisture and cloud distributions. Here we briefly describe the dynamical core, physical parameterizations and computational aspects of the atmospheric model, and present our preliminary numerical results. We also briefly discuss the rational behind our design choices and selection of computational techniques
Asymptotically shear-free and twist-free null geodesic congruences
International Nuclear Information System (INIS)
Kozameh, Carlos; Newman, Ezra T
2007-01-01
The Robinson-Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)
2016-11-15
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren
2010-01-01
, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...
Czech Academy of Sciences Publication Activity Database
Camilo de Souza, F.; Elfimov, A.; Galvão, R.M.O.; Krbec, Jaroslav; Seidl, Jakub; Stöckel, Jan; Hron, Martin; Havlíček, Josef; Mitošinková, Klára
2017-01-01
Roč. 381, č. 36 (2017), s. 3066-3070 ISSN 0375-9601 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 Institutional support: RVO:61389021 Keywords : Tokamak * Geodesic acoustic modes * Kinetic theory * Instability * Landau damping Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: 1.3 Physical sciences Impact factor: 1.772, year: 2016 http://www.sciencedirect.com/science/article/pii/S0375960117306989
Comparing Standard Deviation Effects across Contexts
Ost, Ben; Gangopadhyaya, Anuj; Schiman, Jeffrey C.
2017-01-01
Studies using tests scores as the dependent variable often report point estimates in student standard deviation units. We note that a standard deviation is not a standard unit of measurement since the distribution of test scores can vary across contexts. As such, researchers should be cautious when interpreting differences in the numerical size of…
FINDING STANDARD DEVIATION OF A FUZZY NUMBER
Fokrul Alom Mazarbhuiya
2017-01-01
Two probability laws can be root of a possibility law. Considering two probability densities over two disjoint ranges, we can define the fuzzy standard deviation of a fuzzy variable with the help of the standard deviation two random variables in two disjoint spaces.
Exploring Students' Conceptions of the Standard Deviation
delMas, Robert; Liu, Yan
2005-01-01
This study investigated introductory statistics students' conceptual understanding of the standard deviation. A computer environment was designed to promote students' ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an…
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 Individual...
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Deviations. 226.4 Section 226.4 Foreign Relations AGENCY FOR INTERNATIONAL DEVELOPMENT ADMINISTRATION OF ASSISTANCE AWARDS TO U.S. NON-GOVERNMENTAL ORGANIZATIONS General § 226.4 Deviations. The Office of Management and Budget (OMB) may grant exceptions for...
41 CFR 115-1.110 - Deviations.
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviations. 115-1.110 Section 115-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) ENVIRONMENTAL PROTECTION AGENCY 1-INTRODUCTION 1.1-Regulation System § 115-1.110 Deviations...
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviation. 105-1.110 Section 105-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.110 Deviation. (a...
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...
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Equations of motion for a (non-linear) scalar field model as derived from the field equations
International Nuclear Information System (INIS)
Kaniel, S.; Itin, Y.
2006-01-01
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Directory of Open Access Journals (Sweden)
N. Zarrinpanjeh
2017-09-01
Full Text Available Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.
Directory of Open Access Journals (Sweden)
DanFang Yan
Full Text Available OBJECTS: To introduce a new method for generating the clinical target volume (CTV from gross tumor volume (GTV using the geodesic distance calculation for glioma. METHODS: One glioblastoma patient was enrolled. The GTV and natural barriers were contoured on each slice of the computer tomography (CT simulation images. Then, a graphic processing unit based on a parallel Euclidean distance transform was used to generate the CTV considering natural barriers. Three-dimensional (3D visualization technique was applied to show the delineation results. Speed of operation and precision were compared between this new delineation method and the traditional method. RESULTS: In considering spatial barriers, the shortest distance from the point sheltered from these barriers equals the sum of the distance along the shortest path between the two points; this consists of several segments and evades the spatial barriers, rather than being the direct Euclidean distance between two points. The CTV was generated irregularly rather than as a spherical shape. The time required to generate the CTV was greatly reduced. Moreover, this new method improved inter- and intra-observer variability in defining the CTV. CONCLUSIONS: Compared with the traditional CTV delineation, this new method using geodesic distance calculation not only greatly shortens the time to modify the CTV, but also has better reproducibility.
Zarrinpanjeh, N.; Dadrassjavan, F.
2017-09-01
Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.
YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME
Energy Technology Data Exchange (ETDEWEB)
Yang Xiaolin; Wang Jiancheng, E-mail: yangxl@ynao.ac.cn [National Astronomical Observatories, Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011 (China)
2013-07-01
Following the work of Dexter and Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/{approx}yangxl/yxl.html.
YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME
International Nuclear Information System (INIS)
Yang Xiaolin; Wang Jiancheng
2013-01-01
Following the work of Dexter and Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/~yangxl/yxl.html.
Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe
2014-02-01
In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.
Entanglement transitions induced by large deviations
Bhosale, Udaysinh T.
2017-12-01
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
Karney, C. F. F.; Deakin, R. E.
2010-08-01
Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3
TERMINOLOGY MANAGEMENT FRAMEWORK DEVIATIONS IN PROJECTS
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2015-05-01
Full Text Available The article reviews new approaches to managing projects deviations (risks, changes, problems. By offering integrated control these parameters of the project and by analogy with medical terminological systems building a new system for managing terminological variations in the projects. With an improved method of triads system definitions are analyzed medical terms that make up terminological basis. Using the method of analogy proposed new definitions for managing deviations in projects. By using triad integrity built a new system triad in project management, which will subsequently also analogous to develop a new methodology of deviations in projects.
Transport Coefficients from Large Deviation Functions
Gao, Chloe Ya; Limmer, David T.
2017-01-01
We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate th...
An absolute deviation approach to assessing correlation.
Gorard, S.
2015-01-01
This paper describes two possible alternatives to the more traditional Pearson’s R correlation coefficient, both based on using the mean absolute deviation, rather than the standard deviation, as a measure of dispersion. Pearson’s R is well-established and has many advantages. However, these newer variants also have several advantages, including greater simplicity and ease of computation, and perhaps greater tolerance of underlying assumptions (such as the need for linearity). The first alter...
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
The large deviation approach to statistical mechanics
International Nuclear Information System (INIS)
Touchette, Hugo
2009-01-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
The large deviation approach to statistical mechanics
Touchette, Hugo
2009-07-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Jacobson, Daniel; Stratt, Richard M.
2014-05-01
Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.
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.
Light-cone observables and gauge-invariance in the geodesic light-cone formalism
Energy Technology Data Exchange (ETDEWEB)
Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich (Switzerland)
2017-06-01
The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.
Directory of Open Access Journals (Sweden)
Petarpa Boonserm
2018-05-01
Full Text Available Geodesics (by definition have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates.
Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole
International Nuclear Information System (INIS)
Iftikhar, Sehrish; Sharif, M.
2015-01-01
We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole
Vacuum solutions admitting a geodesic null congruence with shear proportional to expansion
International Nuclear Information System (INIS)
Kupeli, A.H.
1988-01-01
Algebraically general, nontwisting solutions for the vacuum to vacuum generalized Kerr--Schild (GKS) transformation are obtained. These solutions admit a geodesic null congruence with shear proportional to expansion. In the Newman--Penrose formalism, if l/sup μ/ is chosen to be the null vector of the GKS transformation, this property is stated as σ = arho and Da = 0. It is assumed that a is a constant, and the background is chosen as a pp-wave solution. For generic values of a, the GKS metrics consist of the Kasner solutions. For a = +- (1 +- (2)/sup 1/2/), there are solutions with less symmetries including special cases of the Kota--Perjes and Lukacs solutions
Analytic continuation of tgensor fields along geodesics by covariant Taylor series
International Nuclear Information System (INIS)
Tsirulev, A.N.
1995-01-01
It is shown that in a certain normal neighborhood of a submanifold-the analog of a normal neighborhood of a point-the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered
Quantum maps of geodesic flows on surfaces of constant negative curvature
International Nuclear Information System (INIS)
Bogomolny, E.B.; Carioli, M.
1992-01-01
The Selberg zeta function Z(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds Z(s) can be exactly rewritten as the Fredholm determinant det(1-T s ), where T s is the generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is presented, yielding a method to find not only the spectrum but also the eigenvalues of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically. (author) 15 refs., 10 figs
International Nuclear Information System (INIS)
Angelino, P; Bottino, A; Hatzky, R; Jolliet, S; Sauter, O; Tran, T M; Villard, L
2006-01-01
The mutual interactions of ion temperature gradient (ITG) driven modes, zonal flows and geodesic acoustic modes (GAM) in tokamak plasmas are investigated using a global nonlinear gyrokinetic formulation with totally unconstrained evolution of temperature gradient and profile. A series of numerical simulations with the same initial temperature and density profile specifications is performed using a sequence of ideal MHD equilibria differing only in the value of the total plasma current, in particular with identical magnetic shear profiles and shapes of magnetic surfaces. On top of a bursty or quasi-steady state behaviour the zonal flows oscillate at the GAM frequency. The amplitude of these oscillations increases with the value of the safety factor q, resulting in a less effective suppression of ITG turbulence by zonal flows at a lower plasma current. The turbulence-driven volume-averaged radial heat transport is found to scale inversely with the total plasma current
Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT
International Nuclear Information System (INIS)
Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi
2015-01-01
Purpose: This work aims to develop a robust and efficient method to track the fuzzy borders between liver and the abutted organs where automatic liver segmentation usually suffers, and to investigate its applications in automatic liver segmentation on noncontrast-enhanced planning computed tomography (CT) images. Methods: In order to track the fuzzy liver–chestwall and liver–heart borders where oversegmentation is often found, a starting point and an ending point were first identified on the coronal view images; the fuzzy border was then determined as a geodesic curve constructed by minimizing the gradient-weighted path length between these two points near the fuzzy border. The minimization of path length was numerically solved by fast-marching method. The resultant fuzzy borders were incorporated into the authors’ automatic segmentation scheme, in which the liver was initially estimated by a patient-specific adaptive thresholding and then refined by a geodesic active contour model. By using planning CT images of 15 liver patients treated with stereotactic body radiation therapy, the liver contours extracted by the proposed computerized scheme were compared with those manually delineated by a radiation oncologist. Results: The proposed automatic liver segmentation method yielded an average Dice similarity coefficient of 0.930 ± 0.015, whereas it was 0.912 ± 0.020 if the fuzzy border tracking was not used. The application of fuzzy border tracking was found to significantly improve the segmentation performance. The mean liver volume obtained by the proposed method was 1727 cm 3 , whereas it was 1719 cm 3 for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. Conclusions: The proposed method was shown to provide accurate segmentation for liver in the planning CT images where contrast agent is not applied. The authors’ results also clearly demonstrated
Transport Coefficients from Large Deviation Functions
Directory of Open Access Journals (Sweden)
Chloe Ya Gao
2017-10-01
Full Text Available We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green–Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
Transport Coefficients from Large Deviation Functions
Gao, Chloe; Limmer, David
2017-10-01
We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
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.
SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS
Kalpesh S. Tailor
2017-01-01
Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the c...
A robust standard deviation control chart
Schoonhoven, M.; Does, R.J.M.M.
2012-01-01
This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse
Evolutionary implications of genetic code deviations
International Nuclear Information System (INIS)
Chela Flores, J.
1986-07-01
By extending the standard genetic code into a temperature dependent regime, we propose a train of molecular events leading to alternative coding. The first few examples of these deviations have already been reported in some ciliated protozoans and Gram positive bacteria. A possible range of further alternative coding, still within the context of universality, is pointed out. (author)
48 CFR 201.404 - Class deviations.
2010-10-01
..., and the Defense Logistics Agency, may approve any class deviation, other than those described in 201...) Diminish any preference given small business concerns by the FAR or DFARS; or (D) Extend to requirements imposed by statute or by regulations of other agencies such as the Small Business Administration and the...
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…
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.
Stationary deviations from quasineutrality in plasma dynamics
International Nuclear Information System (INIS)
Sholin, G.V.; Trushin, S.A.
1985-01-01
The general assumption of quasineutrality of plasmas is broken in some cases. A self-consistent method is presented to solve the nonlinear differential equations of two-liquid hydrodynamics. The method is based on the theory of singularly perturbed differential equations of A.N. Tikhonov. The case of perpendicular magneto-acoustic wave of large amplitude is described. The rearrangement of the charges is related to the instability of root of the gendering system. (D.Gy.)
Note onset deviations as musical piece signatures.
Serrà, Joan; Özaslan, Tan Hakan; Arcos, Josep Lluis
2013-01-01
A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Note onset deviations as musical piece signatures.
Directory of Open Access Journals (Sweden)
Joan Serrà
Full Text Available A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Hearing protector performance and standard deviation.
Williams, W; Dillon, H
2005-01-01
The attenuation performance of a hearing protector is used to estimate the protected exposure level of the user. The aim is to reduce the exposed level to an acceptable value. Users should expect the attenuation to fall within a reasonable range of values around a norm. However, an analysis of extensive test data indicates that there is a negative relationship between attenuation performance and the standard deviation. This result is deduced using a variation in the method of calculating a single number rating of attenuation that is more amenable to drawing statistical inferences. As performance is typically specified as a function of the mean attenuation minus one or two standard deviations from the mean to ensure that greater than 50% of the wearer population are well protected, the implication of increasing standard deviation with decreasing attenuation found in this study means that a significant number of users are, in fact, experiencing over-protection. These users may be disinclined to use their hearing protectors because of an increased feeling of acoustic isolation. This problem is exacerbated in areas with lower noise levels.
Top Yukawa deviation in extra dimension
International Nuclear Information System (INIS)
Haba, Naoyuki; Oda, Kin-ya; Takahashi, Ryo
2009-01-01
We suggest a simple one-Higgs-doublet model living in the bulk of five-dimensional spacetime compactified on S 1 /Z 2 , in which the top Yukawa coupling can be smaller than the naive standard-model expectation, i.e. the top quark mass divided by the Higgs vacuum expectation value. If we find only single Higgs particle at the LHC and also observe the top Yukawa deviation, our scenario becomes a realistic candidate beyond the standard model. The Yukawa deviation comes from the fact that the wave function profile of the free physical Higgs field can become different from that of the vacuum expectation value, due to the presence of the brane-localized Higgs potentials. In the Brane-Localized Fermion scenario, we find sizable top Yukawa deviation, which could be checked at the LHC experiment, with a dominant Higgs production channel being the WW fusion. We also study the Bulk Fermion scenario with brane-localized Higgs potential, which resembles the Universal Extra Dimension model with a stable dark matter candidate. We show that both scenarios are consistent with the current electroweak precision measurements.
International Nuclear Information System (INIS)
Schubert, R.
1995-05-01
We investigate the behaviour of the remainder term R(E) in the Weyl formula {nvertical stroke E n ≤E}=Vol(M).E d/2 /[(4π) d/2 Γ(d/2+1)]+R(E) for the eigenvalues E n of a Schroedinger operator on a d-dimensional compact Riemannian manifold all of whose geodesics are closed. We show that R(E) is of the form E (d-1)/2 Θ(√E), where Θ(x) is an almost periodic function of Besicovitch class B 2 which has a limit distribution whose density is a box-shaped function. Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits. The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly. (orig.)
Sefton-Nash, E.; Williams, J.-P.; Greenhagen, B. T.; Aye, K.-M.; Paige, D. A.
2017-12-01
An approach is presented to efficiently produce high quality gridded data records from the large, global point-based dataset returned by the Diviner Lunar Radiometer Experiment aboard NASA's Lunar Reconnaissance Orbiter. The need to minimize data volume and processing time in production of science-ready map products is increasingly important with the growth in data volume of planetary datasets. Diviner makes on average >1400 observations per second of radiance that is reflected and emitted from the lunar surface, using 189 detectors divided into 9 spectral channels. Data management and processing bottlenecks are amplified by modeling every observation as a probability distribution function over the field of view, which can increase the required processing time by 2-3 orders of magnitude. Geometric corrections, such as projection of data points onto a digital elevation model, are numerically intensive and therefore it is desirable to perform them only once. Our approach reduces bottlenecks through parallel binning and efficient storage of a pre-processed database of observations. Database construction is via subdivision of a geodesic icosahedral grid, with a spatial resolution that can be tailored to suit the field of view of the observing instrument. Global geodesic grids with high spatial resolution are normally impractically memory intensive. We therefore demonstrate a minimum storage and highly parallel method to bin very large numbers of data points onto such a grid. A database of the pre-processed and binned points is then used for production of mapped data products that is significantly faster than if unprocessed points were used. We explore quality controls in the production of gridded data records by conditional interpolation, allowed only where data density is sufficient. The resultant effects on the spatial continuity and uncertainty in maps of lunar brightness temperatures is illustrated. We identify four binning regimes based on trades between the
Computerized liver volumetry on MRI by using 3D geodesic active contour segmentation.
Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji
2014-01-01
Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time.
Ben Slama, Amine; Mouelhi, Aymen; Sahli, Hanene; Manoubi, Sondes; Mbarek, Chiraz; Trabelsi, Hedi; Fnaiech, Farhat; Sayadi, Mounir
2017-07-01
The diagnostic of the vestibular neuritis (VN) presents many difficulties to traditional assessment methods This paper deals with a fully automatic VN diagnostic system based on nystagmus parameter estimation using a pupil detection algorithm. A geodesic active contour model is implemented to find an accurate segmentation region of the pupil. Hence, the novelty of the proposed algorithm is to speed up the standard segmentation by using a specific mask located on the region of interest. This allows a drastically computing time reduction and a great performance and accuracy of the obtained results. After using this fast segmentation algorithm, the obtained estimated parameters are represented in temporal and frequency settings. A useful principal component analysis (PCA) selection procedure is then applied to obtain a reduced number of estimated parameters which are used to train a multi neural network (MNN). Experimental results on 90 eye movement videos show the effectiveness and the accuracy of the proposed estimation algorithm versus previous work. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Alim Samat
2016-03-01
Full Text Available In order to deal with scenarios where the training data, used to deduce a model, and the validation data have different statistical distributions, we study the problem of transformed subspace feature transfer for domain adaptation (DA in the context of hyperspectral image classification via a geodesic Gaussian flow kernel based support vector machine (GFKSVM. To show the superior performance of the proposed approach, conventional support vector machines (SVMs and state-of-the-art DA algorithms, including information-theoretical learning of discriminative cluster for domain adaptation (ITLDC, joint distribution adaptation (JDA, and joint transfer matching (JTM, are also considered. Additionally, unsupervised linear and nonlinear subspace feature transfer techniques including principal component analysis (PCA, randomized nonlinear principal component analysis (rPCA, factor analysis (FA and non-negative matrix factorization (NNMF are investigated and compared. Experiments on two real hyperspectral images show the cross-image classification performances of the GFKSVM, confirming its effectiveness and suitability when applied to hyperspectral images.
Standard deviation of scatterometer measurements from space.
Fischer, R. E.
1972-01-01
The standard deviation of scatterometer measurements has been derived under assumptions applicable to spaceborne scatterometers. Numerical results are presented which show that, with sufficiently long integration times, input signal-to-noise ratios below unity do not cause excessive degradation of measurement accuracy. The effects on measurement accuracy due to varying integration times and changing the ratio of signal bandwidth to IF filter-noise bandwidth are also plotted. The results of the analysis may resolve a controversy by showing that in fact statistically useful scatterometer measurements can be made from space using a 20-W transmitter, such as will be used on the S-193 experiment for Skylab-A.
Wasserstein gradient flows from large deviations of many-particle limits
Duong, M.H.; Laschos, V.; Renger, D.R.M.
2013-01-01
We study the Fokker–Planck equation as the many-particle limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the path-space rate functional, which characterises the large deviations from the expected trajectories, in such a way that the free
Deviations from mass transfer equilibrium and mathematical modeling of mixer-settler contactors
International Nuclear Information System (INIS)
Beyerlein, A.L.; Geldard, J.F.; Chung, H.F.; Bennett, J.E.
1980-01-01
This paper presents the mathematical basis for the computer model PUBG of mixer-settler contactors which accounts for deviations from mass transfer equilibrium. This is accomplished by formulating the mass balance equations for the mixers such that the mass transfer rate of nuclear materials between the aqueous and organic phases is accounted for. 19 refs
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.
Computation of standard deviations in eigenvalue calculations
International Nuclear Information System (INIS)
Gelbard, E.M.; Prael, R.
1990-01-01
In Brissenden and Garlick (1985), the authors propose a modified Monte Carlo method for eigenvalue calculations, designed to decrease particle transport biases in the flux and eigenvalue estimates, and in corresponding estimates of standard deviations. Apparently a very similar method has been used by Soviet Monte Carlo specialists. The proposed method is based on the generation of ''superhistories'', chains of histories run in sequence without intervening renormalization of the fission source. This method appears to have some disadvantages, discussed elsewhere. Earlier numerical experiments suggest that biases in fluxes and eigenvalues are negligibly small, even for very small numbers of histories per generation. Now more recent experiments, run on the CRAY-XMP, tend to confirm these earlier conclusions. The new experiments, discussed in this paper, involve the solution of one-group 1D diffusion theory eigenvalue problems, in difference form, via Monte Carlo. Experiments covered a range of dominance ratios from ∼0.75 to ∼0.985. In all cases flux and eigenvalue biases were substantially smaller than one standard deviation. The conclusion that, in practice, the eigenvalue bias is negligible has strong theoretical support. (author)
Directory of Open Access Journals (Sweden)
İhsan Çaça
2004-01-01
Full Text Available We evaluated the correlation with success rates and deviation type and degree inhorizontal concomitant deviations. 104 horizontal concomitan strabismus cases whowere operated in our clinic between January 1994 – December 2000 were included in thestudy. 56 cases undergone recession-resection procedure in the same eye 19 cases twomuscle recession and one muscle resection, 20 cases two muscle recession, 9 cases onlyone muscle recession. 10 ± prism diopter deviation in postoperative sixth monthexamination was accepted as surgical success.Surgical success rate was 90% and 89.3% in the cases with deviation angle of 15-30and 31-50 prism diopter respectively. Success rate was 78.9% if the angle was more than50 prism diopter. According to strabismus type when surgical success rate examined; inalternan esotropia 88.33%, in alternan exotropia 84.6%, in monocular esotropia 88%and in monocular exotropia 83.3% success was fixed. Statistically significant differencewas not found between strabismus type and surgical success rate. The binocular visiongaining rate was found as 51.8% after the treatment of cases.In strabismus surgery, preoperative deviation angle was found to be an effectivefactor on the success rate.
The Raychaudhuri equation in homogeneous cosmologies
International Nuclear Information System (INIS)
Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A.
2014-01-01
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories
Transmission-type angle deviation microscopy
International Nuclear Information System (INIS)
Chiu, M.-H.; Lai, C.-W.; Tan, C.-T.; Lai, C.-F.
2008-01-01
We present a new microscopy technique that we call transmission angle deviation microscopy (TADM). It is based on common-path heterodyne interferometry and geometrical optics. An ultrahigh sensitivity surface plasmon resonance (SPR) angular sensor is used to expand dynamic measurement ranges and to improve the axial resolution in three-dimensional optical microscopy. When transmitted light is incident upon a specimen, the beam converges or diverges because of refractive and/or surface height variations. Advantages include high axial resolution (∼32 nm), nondestructive and noncontact measurement, and larger measurement ranges (± 80 μm) for a numerical aperture of 0.21in a transparent measurement medium. The technique can be used without conductivity and pretreatment
Investigating deviations from norms in court interpreting
DEFF Research Database (Denmark)
Dubslaff, Friedel; Martinsen, Bodil
Since Shlesinger (1989) discussed the applicability of translational norms to the field of interpreting, a number of scholars have advocated the use of this concept as a frame of reference in interpreting research (e.g. Harris 1990, Schjoldager 1994, 1995, Jansen 1995, Gile 1999, Garzone 2002). Due...... for the study, we intend to conduct interviews instead. The purpose of the study is to investigate deviations from translational norms in court interpreting. More specifically, we aim to identify and describe instances of deviant behaviour on the part of the interpreters, discuss signs of possible deviant...... speaking these languages. This example does not immediately indicate that Translation Studies might be able to contribute to, for example, an improvement of the training situation for the group of court interpreters mentioned above. However, in our opinion, there is reason to believe that TS can make...
Phylogenetic rooting using minimal ancestor deviation.
Tria, Fernando Domingues Kümmel; Landan, Giddy; Dagan, Tal
2017-06-19
Ancestor-descendent relations play a cardinal role in evolutionary theory. Those relations are determined by rooting phylogenetic trees. Existing rooting methods are hampered by evolutionary rate heterogeneity or the unavailability of auxiliary phylogenetic information. Here we present a rooting approach, the minimal ancestor deviation (MAD) method, which accommodates heterotachy by using all pairwise topological and metric information in unrooted trees. We demonstrate the performance of the method, in comparison to existing rooting methods, by the analysis of phylogenies from eukaryotes and prokaryotes. MAD correctly recovers the known root of eukaryotes and uncovers evidence for the origin of cyanobacteria in the ocean. MAD is more robust and consistent than existing methods, provides measures of the root inference quality and is applicable to any tree with branch lengths.
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...
14 CFR 21.609 - Approval for deviation.
2010-01-01
... deviation. (a) Each manufacturer who requests approval to deviate from any performance standard of a TSO shall show that the standards from which a deviation is requested are compensated for by factors or... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Approval for deviation. 21.609 Section 21...
International Nuclear Information System (INIS)
Hoegl, A.
1996-01-01
This study investigates how, from a legal point of view, deviations in radiation protection measurements should be treated in comparisons between measured results and limits stipulated by nuclear legislation or goods transport regulations. A case-by-case distinction is proposed which is based on the legal concequences of the respective measurement. Commentaries on nuclear law contain no references to the legal assessment of deviating measurements in radiation protection. The examples quoted in legal commentaries on civil and criminal proceedings of the way in which errors made in measurements for speed control and determinations of the alcohol content in the blood are to be taken into account, and a commentary on ozone legislation, are examined for analogies with radiation protection measurements. Leading cases in the nuclear field are evaluated in the light of the requirements applying in case of deviations in measurements. The final section summarizes the most important findings and conclusions. (orig.) [de
VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)
Karney, C. F. F.; Deakin, R. E.
2010-06-01
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).
CT liver volumetry using geodesic active contour segmentation with a level-set algorithm
Suzuki, Kenji; Epstein, Mark L.; Kohlbrenner, Ryan; Obajuluwa, Ademola; Xu, Jianwu; Hori, Masatoshi; Baron, Richard
2010-03-01
Automatic liver segmentation on CT images is challenging because the liver often abuts other organs of a similar density. Our purpose was to develop an accurate automated liver segmentation scheme for measuring liver volumes. We developed an automated volumetry scheme for the liver in CT based on a 5 step schema. First, an anisotropic smoothing filter was applied to portal-venous phase CT images to remove noise while preserving the liver structure, followed by an edge enhancer to enhance the liver boundary. By using the boundary-enhanced image as a speed function, a fastmarching algorithm generated an initial surface that roughly estimated the liver shape. A geodesic-active-contour segmentation algorithm coupled with level-set contour-evolution refined the initial surface so as to more precisely fit the liver boundary. The liver volume was calculated based on the refined liver surface. Hepatic CT scans of eighteen prospective liver donors were obtained under a liver transplant protocol with a multi-detector CT system. Automated liver volumes obtained were compared with those manually traced by a radiologist, used as "gold standard." The mean liver volume obtained with our scheme was 1,520 cc, whereas the mean manual volume was 1,486 cc, with the mean absolute difference of 104 cc (7.0%). CT liver volumetrics based on an automated scheme agreed excellently with "goldstandard" manual volumetrics (intra-class correlation coefficient was 0.95) with no statistically significant difference (p(F<=f)=0.32), and required substantially less completion time. Our automated scheme provides an efficient and accurate way of measuring liver volumes.
On the geodesic incompleteness of spacetimes containing marginally (outer) trapped surfaces
International Nuclear Information System (INIS)
Costa e Silva, I P
2012-01-01
In a recent paper, Eichmair et al (2012 arXiv:1204.0278v1) have proved a Gannon–Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. A natural question is whether the corresponding incomplete geodesics could still be complete in a possible non-globally hyperbolic extension of spacetime. In this paper, some variants of their result are given with weaker causality assumptions, thus suggesting that the answer is generically negative, at least if the putative extension has no closed timelike curves. We consider first marginally trapped surfaces (MTS) in chronological spacetimes, introducing the natural notion of a generic MTS, a notion also applicable to MOTS. In particular, a Hawking–Penrose-type singularity theorem is proven in chronological spacetimes with dimension n ⩾ 3 containing a generic MTS. Such surfaces naturally arise as cross-sections of quasi-local generalizations of black hole horizons, such as dynamical and trapping horizons, and we discuss some natural conditions which ensure the existence of MTS in initial data sets. Nevertheless, much of the more recent literature has focused on MOTS rather than MTS as quasi-local substitutes for the description of black holes, as they are arguably more natural and easier to handle in a number of situations. It is therefore pertinent to ask to what extent one can deduce the existence of singularities in the presence of MOTS alone. We address this issue and show that singularities indeed arise in the presence of generic MOTS, but under slightly stronger causal conditions than those in the case of MTS (specifically, for causally simple spacetimes). On the other hand, we show that with additional conditions on the MOTS itself, namely that it is either the boundary of a compact spatial region, or strictly stable in a suitable sense, a Penrose–Hawking-type singularity theorem can still be established for
Constraints on deviations from ΛCDM within Horndeski gravity
Energy Technology Data Exchange (ETDEWEB)
Bellini, Emilio; Cuesta, Antonio J. [ICCUB, University of Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona (Spain); Jimenez, Raul; Verde, Licia, E-mail: emilio.bellini@icc.ub.edu, E-mail: ajcuesta@icc.ub.edu, E-mail: rauljimenez@g.harvard.edu, E-mail: liciaverde@icc.ub.edu [Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona (Spain)
2016-02-01
Recent anomalies found in cosmological datasets such as the low multipoles of the Cosmic Microwave Background or the low redshift amplitude and growth of clustering measured by e.g., abundance of galaxy clusters and redshift space distortions in galaxy surveys, have motivated explorations of models beyond standard ΛCDM. Of particular interest are models where general relativity (GR) is modified on large cosmological scales. Here we consider deviations from ΛCDM+GR within the context of Horndeski gravity, which is the most general theory of gravity with second derivatives in the equations of motion. We adopt a parametrization in which the four additional Horndeski functions of time α{sub i}(t) are proportional to the cosmological density of dark energy Ω{sub DE}(t). Constraints on this extended parameter space using a suite of state-of-the art cosmological observations are presented for the first time. Although the theory is able to accommodate the low multipoles of the Cosmic Microwave Background and the low amplitude of fluctuations from redshift space distortions, we find no significant tension with ΛCDM+GR when performing a global fit to recent cosmological data and thus there is no evidence against ΛCDM+GR from an analysis of the value of the Bayesian evidence ratio of the modified gravity models with respect to ΛCDM, despite introducing extra parameters. The posterior distribution of these extra parameters that we derive return strong constraints on any possible deviations from ΛCDM+GR in the context of Horndeski gravity. We illustrate how our results can be applied to a more general frameworks of modified gravity models.
GEODESIC MONITORING OF VERTICAL MOVEMENT OF JSC «GRODNO AZOT» BUILDINGS USING DIGITAL DNA 03 LEVEL
Directory of Open Access Journals (Sweden)
V. I. Mikhailov
2010-01-01
Full Text Available The paper presents peculiar features and methodology pertaining to application of digital DNA 03 level for monitoring vertical movement of load-carrying structures in the workshops and foundations of various capacities, exhaust pipes and granulation towers having height from 100 to150 meters. The proposed methods presuppose usage of the results of engineering and geological investigations and highly accurate geodesic measurements considered in the process of hydro- and pneumatic tests of an isothermic storage of liquid ammonia and a production “Ammonia” shop taken as an example.
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.
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
He, Nana; Zhang, Xiaolong; Zhao, Juanjuan; Zhao, Huilan; Qiang, Yan
2017-07-01
While the popular thin layer scanning technology of spiral CT has helped to improve diagnoses of lung diseases, the large volumes of scanning images produced by the technology also dramatically increase the load of physicians in lesion detection. Computer-aided diagnosis techniques like lesions segmentation in thin CT sequences have been developed to address this issue, but it remains a challenge to achieve high segmentation efficiency and accuracy without much involvement of human manual intervention. In this paper, we present our research on automated segmentation of lung parenchyma with an improved geodesic active contour model that is geodesic active contour model based on similarity (GACBS). Combining spectral clustering algorithm based on Nystrom (SCN) with GACBS, this algorithm first extracts key image slices, then uses these slices to generate an initial contour of pulmonary parenchyma of un-segmented slices with an interpolation algorithm, and finally segments lung parenchyma of un-segmented slices. Experimental results show that the segmentation results generated by our method are close to what manual segmentation can produce, with an average volume overlap ratio of 91.48%.
Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity
Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek
2014-07-01
We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.
3D asthenopia in horizontal deviation.
Kim, Seung-Hyun; Suh, Young-Woo; Yun, Cheol-Min; Yoo, Eun-Joo; Yeom, Ji-Hyun; Cho, Yoonae A
2013-05-01
This study was conducted to investigate the asthenopic symptoms in patients with exotropia and esotropia while watching stereoscopic 3D (S3D) television (TV). A total 77 subjects who more than 9 years of age were enrolled in this study. We divided them into three groups; Thirty-four patients with exodeviation (Exo group), 11 patients with esodeviation (Eso group) and 32 volunteers with normal binocular vision (control group). The S3D images were shown to all patients with S3D high-definition TV for a period of 20 min. Best corrected visual acuity, refractive errors, angle of strabismus, stereopsis test and history of strabismus surgery, were evaluated. After watching S3D TV for 20 min, a survey of subjective symptoms was conducted with a questionnaire to evaluate the degree of S3D perception and asthenopic symptoms such as headache, dizziness and ocular fatigue while watching 3D TV. The mean amounts of deviation in the Exo group and Eso group were 11.2 PD and 7.73PD, respectively. Mean stereoacuity was 102.7 arc sec in the the Exo group and 1389.1 arc sec in the Eso group. In the control group, it was 41.9 arc sec. Twenty-nine patients in the Exo group showed excellent stereopsis (≤60 arc sec at near), but all 11 subjects of the Eso group showed 140 arc sec or worse and showed more decreased 3D perception than the Exo and the control group (p Kruskal-Wallis test). The Exo group reported more eye fatigue (p Kruskal-Wallis test) than the Eso and the control group. However, the scores of ocular fatigue in the patients who had undergone corrective surgery were less than in the patients who had not in the Exo group (p Kruskal-Wallis test) and the amount of exodeviation was not correlated with the asthenopic symptoms (dizziness, r = 0.034, p = 0.33; headache, r = 0.320, p = 0.119; eye fatigue, r = 0.135, p = 0.519, Spearman rank correlation test, respectively). Symptoms of 3D asthenopia were related to the presence of exodeviation but not to esodeviation. This may
9 CFR 318.308 - Deviations in processing.
2010-01-01
...) Deviations in processing (or process deviations) must be handled according to: (1)(i) A HACCP plan for canned...) of this section. (c) [Reserved] (d) Procedures for handling process deviations where the HACCP plan... accordance with the following procedures: (a) Emergency stops. (1) When retort jams or breakdowns occur...
7 CFR 400.204 - Notification of deviation from standards.
2010-01-01
... 7 Agriculture 6 2010-01-01 2010-01-01 false Notification of deviation from standards. 400.204... Contract-Standards for Approval § 400.204 Notification of deviation from standards. A Contractor shall advise the Corporation immediately if the Contractor deviates from the requirements of these standards...
A Visual Model for the Variance and Standard Deviation
Orris, J. B.
2011-01-01
This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.
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...
41 CFR 109-1.110-50 - Deviation procedures.
2010-07-01
... best interest of the Government; (3) If applicable, the name of the contractor and identification of... background information which will contribute to a full understanding of the desired deviation. (b)(1... authorized to grant deviations to the DOE-PMR. (d) Requests for deviations from the FPMR will be coordinated...
Deviations of Lambert-Beer???s law affect corneal refractive parameters after refractive surgery
Jim??nez Cuesta, Jos?? Ram??n; Rodr??guez-Mar??n, Francisco; Gonz??lez Anera, Rosario; Jim??nez del Barco Jaldo, Luis Miguel
2006-01-01
We calculate whether deviations of Lambert-Beer???s law, which regulates depth ablation during corneal ablation, significantly influence corneal refractive parameters after refractive surgery and whether they influence visual performance. For this, we compute a point-to-point correction on the cornea while assuming a non-linear (including a quadratic term) fit for depth ablation. Post-surgical equations for refractive parameters using a non-linear fit show significant differences with respect...
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Kawase, H.; Nakano, K.
2015-12-01
We investigated the characteristics of strong ground motions separated from acceleration Fourier spectra and acceleration response spectra of 5% damping calculated from weak and moderate ground motions observed by K-NET, KiK-net, and the JMA Shindokei Network in Japan using the generalized spectral inversion method. The separation method used the outcrop motions at YMGH01 as reference where we extracted site responses due to shallow weathered layers. We include events with JMA magnitude equal to or larger than 4.5 observed from 1996 to 2011. We find that our frequency-dependent Q values are comparable to those of previous studies. From the corner frequencies of Fourier source spectra, we calculate Brune's stress parameters and found a clear magnitude dependence, in which smaller events tend to spread over a wider range while maintaining the same maximum value. We confirm that this is exactly the case for several mainshock-aftershock sequences. The average stress parameters for crustal earthquakes are much smaller than those of subduction zone, which can be explained by their depth dependence. We then compared the strong motion characteristics based on the acceleration response spectra and found that the separated characteristics of strong ground motions are different, especially in the lower frequency range less than 1Hz. These differences comes from the difference between Fourier spectra and response spectra found in the observed data; that is, predominant components in high frequency range of Fourier spectra contribute to increase the response in lower frequency range with small Fourier amplitude because strong high frequency component acts as an impulse to a Single-Degree-of-Freedom system. After the separation of the source terms for 5% damping response spectra we can obtain regression coefficients with respect to the magnitude, which lead to a new GMPE as shown in Fig.1 on the left. Although stress drops for inland earthquakes are 1/7 of the subduction-zone earthquakes, we can see linear regression works quite well. After this linear regression we correlate residuals as a function of Brune's stress parameters of corresponding events as shown in Fig.1 on the right for the case of 1Hz. We found quite good linear correlation, which makes aleatoric uncertainty 40 to 60 % smaller than the original.
International Nuclear Information System (INIS)
Matsyuk, R.Ya.
1985-01-01
The problem on the existence of the invariant third-order Euler-Poisson equations in the pseudo-Euclidean space is investigated. The locally variational problem is determined by the Lagrangian density over the space of the second-order jets. The one - parameter family of the invariant third-order Euler-Poisson equations is groved to be the only one in the three-dimensional pseudo-Euclidean space. No invariant third-order Euler-Poisson equations exist in the four-dimensional pseudo-Euclidean space. It is shown that the Mathisson equation and the equation of geodesic circles in particular cases may be considered in the context of the Ostrogradiskij mechanics and the Kavaguchi geometry
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
International Nuclear Information System (INIS)
Yue, Ning J.; Kim, Sung; Jabbour, Salma; Narra, Venkat; Haffty, Bruce G.
2007-01-01
verification and were used to determine potential target deviations. To derive the detected CTV geometry from the planning CTV based on the locations of the gold markers, the CTV was approximated with an elastic semirigid body model. The derived CTV geometry and shape were confirmed with CBCT imaging. The evaluation results and the related mathematical equations and computational algorithm are presented. It is concluded that the proposed strategy is potentially useful in establishing objective criteria for the necessity of correction of the target deviations
Tomaschitz, R
1989-01-01
We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.
International Nuclear Information System (INIS)
Vermare, L.; Hennequin, P.; Gürcan, Ö.D.
2012-01-01
This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the additional heating power is varied, the frequency is found to scale with C s /R. The MUltiple SIgnal Classification (MUSIC) algorithm is employed to access the temporal evolution of the perpendicular velocity of density fluctuations. The method is presented in some detail, and is validated and compared against standard methods, such as the conventional fast Fourier transform method, using a synthetic signal. It stands out as a powerful data analysis method to follow the Doppler frequency with a high temporal resolution, which is important in order to extract the dynamics of GAMs. (paper)
Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type
International Nuclear Information System (INIS)
Bialy, Misha; Mironov, Andrey E
2011-01-01
In this paper, we deal with the classical question of the existence of polynomials in momenta integrals for geodesic flows on the 2-torus. For the quasilinear system on the coefficients of the polynomial integral, we investigate the region (so-called elliptic region) where two of the eigenvalues are complex conjugate. We show that for quartic integrals the other two eigenvalues are real and necessarily genuinely nonlinear. This observation, together with the property of the system to be rich (semi-Hamiltonian), enables us to classify elliptic regions completely. We prove that on these regions the integral is always reducible. The case of complex-conjugate eigenvalues for the system corresponding to the integral of degree 3 is done similarly. These results show that if new integrable examples exist, they can be found only within the region of hyperbolicity of the quasilinear system
Geodesically complete BTZ-type solutions of 2 + 1 Born–Infeld gravity
International Nuclear Information System (INIS)
Bazeia, D; Losano, L; Olmo, Gonzalo J; Rubiera-Garcia, D
2017-01-01
We study Born–Infeld gravity coupled to a static, non-rotating electric field in 2 + 1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom. (paper)
International Nuclear Information System (INIS)
Tomaschitz, R.
1989-01-01
We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)
Wang, Chun; Zheng, Yi; Chang, Hua-Hua
2014-01-01
With the advent of web-based technology, online testing is becoming a mainstream mode in large-scale educational assessments. Most online tests are administered continuously in a testing window, which may post test security problems because examinees who take the test earlier may share information with those who take the test later. Researchers have proposed various statistical indices to assess the test security, and one most often used index is the average test-overlap rate, which was further generalized to the item pooling index (Chang & Zhang, 2002, 2003). These indices, however, are all defined as the means (that is, the expected proportion of common items among examinees) and they were originally proposed for computerized adaptive testing (CAT). Recently, multistage testing (MST) has become a popular alternative to CAT. The unique features of MST make it important to report not only the mean, but also the standard deviation (SD) of test overlap rate, as we advocate in this paper. The standard deviation of test overlap rate adds important information to the test security profile, because for the same mean, a large SD reflects that certain groups of examinees share more common items than other groups. In this study, we analytically derived the lower bounds of the SD under MST, with the results under CAT as a benchmark. It is shown that when the mean overlap rate is the same between MST and CAT, the SD of test overlap tends to be larger in MST. A simulation study was conducted to provide empirical evidence. We also compared the security of MST under the single-pool versus the multiple-pool designs; both analytical and simulation studies show that the non-overlapping multiple-pool design will slightly increase the security risk.
International Nuclear Information System (INIS)
Barack, Leor; Sago, Norichika
2011-01-01
We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass μ is much smaller than the black hole mass M, and explore post-geodesic corrections of O(μ/M). Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the O(μ/M) conservative correction to the periastron advance of the orbit, as a function of the (gauge-dependent) semilatus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit ''redshift'' invariant. We compute the O(μ/M) conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak-field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.
Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements
Ming-Hung Chiu; Jia-Ze Shen; Jian-Ming Huang
2016-01-01
We proposed heterodyne angle deviation interferometry (HADI) for angle deviation measurements. The phase shift of an angular sensor (which can be a metal film or a surface plasmon resonance (SPR) prism) is proportional to the deviation angle of the test beam. The method has been demonstrated in bubble and speaker’s vibration measurements in this paper. In the speaker’s vibration measurement, the voltage from the phase channel of a lock-in amplifier includes the vibration level and frequency. ...
Large deviations for noninteracting infinite-particle systems
International Nuclear Information System (INIS)
Donsker, M.D.; Varadhan, S.R.S.
1987-01-01
A large deviation property is established for noninteracting infinite particle systems. Previous large deviation results obtained by the authors involved a single I-function because the cases treated always involved a unique invariant measure for the process. In the context of this paper there is an infinite family of invariant measures and a corresponding infinite family of I-functions governing the large deviations
Quantum uncertainty relation based on the mean deviation
Sharma, Gautam; Mukhopadhyay, Chiranjib; Sazim, Sk; Pati, Arun Kumar
2018-01-01
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplica...
Two examples of non strictly convex large deviations
De Marco, Stefano; Jacquier, Antoine; Roome, Patrick
2016-01-01
We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Perception of midline deviations in smile esthetics by laypersons.
Ferreira, Jamille Barros; Silva, Licínio Esmeraldo da; Caetano, Márcia Tereza de Oliveira; Motta, Andrea Fonseca Jardim da; Cury-Saramago, Adriana de Alcantara; Mucha, José Nelson
2016-01-01
To evaluate the esthetic perception of upper dental midline deviation by laypersons and if adjacent structures influence their judgment. An album with 12 randomly distributed frontal view photographs of the smile of a woman with the midline digitally deviated was evaluated by 95 laypersons. The frontal view smiling photograph was modified to create from 1 mm to 5 mm deviations in the upper midline to the left side. The photographs were cropped in two different manners and divided into two groups of six photographs each: group LCN included the lips, chin, and two-thirds of the nose, and group L included the lips only. The laypersons performed the rate of each smile using a visual analog scale (VAS). Wilcoxon test, Student's t-test and Mann-Whitney test were applied, adopting a 5% level of significance. Laypersons were able to perceive midline deviations starting at 1 mm. Statistically significant results (p< 0.05) were found for all multiple comparisons of the values in photographs of group LCN and for almost all comparisons in photographs of group L. Comparisons between the photographs of groups LCN and L showed statistically significant values (p< 0.05) when the deviation was 1 mm. Laypersons were able to perceive the upper dental midline deviations of 1 mm, and above when the adjacent structures of the smiles were included. Deviations of 2 mm and above when the lips only were included. The visualization of structures adjacent to the smile demonstrated influence on the perception of midline deviation.
Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation
Wasserman, Nicholas H.; Casey, Stephanie; Champion, Joe; Huey, Maryann
2017-01-01
This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator--not just a descriptive statistic for the variation (spread) in data--is related to teachers' instruction regarding standard deviation, particularly…
Moderate deviations principles for the kernel estimator of ...
African Journals Online (AJOL)
Abstract. The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of condence regions for the regression function. Resume. L'objectif de ...
Generation of deviation parameters for amino acid singlets, doublets ...
Indian Academy of Sciences (India)
We present a new method, secondary structure prediction by deviation parameter (SSPDP) for predicting the secondary structure of proteins from amino acid sequence. Deviation parameters (DP) for amino acid singlets, doublets and triplets were computed with respect to secondary structural elements of proteins based on ...
38 CFR 36.4304 - Deviations; changes of identity.
2010-07-01
... identity. 36.4304 Section 36.4304 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS... Deviations; changes of identity. A deviation of more than 5 percent between the estimates upon which a... change in the identity of the property upon which the original appraisal was based, will invalidate the...
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Towards a large deviation theory for strongly correlated systems
International Nuclear Information System (INIS)
Ruiz, Guiomar; Tsallis, Constantino
2012-01-01
A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N→∞) limit yielding Gaussian distributions. The probability of n≠N/2 out of N throws is governed by e −Nr , r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q,γ) are studied, the (N→∞) limit yielding Q-Gaussians (Q→1 recovers a Gaussian). Its large deviations are governed by e q −Nr q (∝1/N 1/(q−1) , q>1), q=(Q−1)/(γ[3−Q])+1. This illustration opens the door towards a large-deviation foundation of nonextensive statistical mechanics. -- Highlights: ► We introduce the formalism of relative entropy for a single random binary variable and its q-generalization. ► We study a model of N strongly correlated binary random variables and their large-deviation probabilities. ► Large-deviation probability of strongly correlated model exhibits a q-exponential decay whose argument is proportional to N, as extensivity requires. ► Our results point to a q-generalized large deviation theory and suggest a large-deviation foundation of nonextensive statistical mechanics.
Limiting values of large deviation probabilities of quadratic statistics
Jeurnink, Gerardus A.M.; Kallenberg, W.C.M.
1990-01-01
Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation
45 CFR 63.19 - Budget revisions and minor deviations.
2010-10-01
... 45 Public Welfare 1 2010-10-01 2010-10-01 false Budget revisions and minor deviations. 63.19 Section 63.19 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION GRANT PROGRAMS... Budget revisions and minor deviations. Pursuant to § 74.102(d) of this title, paragraphs (b)(3) and (b)(4...
Refraction in Terms of the Deviation of the Light.
Goldberg, Fred M.
1985-01-01
Discusses refraction in terms of the deviation of light. Points out that in physics courses where very little mathematics is used, it might be more suitable to describe refraction entirely in terms of the deviation, rather than by introducing Snell's law. (DH)
The centripetal force law and the equation of motion for a particle on a curved hypersurface
International Nuclear Information System (INIS)
Hu, L.D.; Lian, D.K.; Liu, Q.H.
2016-01-01
It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable. (orig.)
From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage
Adams, S.; Dirr, N.; Peletier, M.A.; Zimmer, J.
2011-01-01
We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial
International Nuclear Information System (INIS)
Kraehenbuehl, Y.
1983-01-01
Oscillatory phase-slip solution of a set of integrodifferential equations describing time-dependent processes in dirty superconductors in the Ginzburg-Landau regime are found numerically very near Tsub(c). Deviations from local equilibrium improve the agreement with observed V-I curves. (orig.)
[The crooked nose: correction of dorsal and caudal septal deviations].
Foda, H M T
2010-09-01
The deviated nose represents a complex cosmetic and functional problem. Septal surgery plays a central role in the successful management of the externally deviated nose. This study included 800 patients seeking rhinoplasty to correct external nasal deviations; 71% of these suffered from variable degrees of nasal obstruction. Septal surgery was necessary in 736 (92%) patients, not only to improve breathing, but also to achieve a straight, symmetric external nose. A graduated surgical approach was adopted to allow correction of the dorsal and caudal deviations of the nasal septum without weakening its structural support to the nasal dorsum or nasal tip. The approach depended on full mobilization of deviated cartilage, followed by straightening of the cartilage and its fixation in the corrected position by using bony splinting grafts through an external rhinoplasty approach.
Comment on ''Modified photon equation of motion as a test for the principle of equivalence''
International Nuclear Information System (INIS)
Nityananda, R.
1992-01-01
In a recent paper, a modification of the geodesic equation was proposed for spinning photons containing a spin-curvature coupling term. The difference in arrival times of opposite circular polarizations starting simultaneously from a source was computed, obtaining a result linear in the coupling parameter. It is pointed out here that this linear term violates causality and, more generally, Fermat's principle, implying calculational errors. Even if these are corrected, there is a violation of covariance in the way the photon spin was introduced. Rectifying this makes the effect computed vanish entirely
Entropy Measures as Geometrical Tools in the Study of Cosmology
Directory of Open Access Journals (Sweden)
Gilbert Weinstein
2017-12-01
Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.
Large deviations in the presence of cooperativity and slow dynamics
Whitelam, Stephen
2018-06-01
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative or when its basic time scale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change in shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition but do not necessarily do so.
POSITIVE SOLUTIONS TO TWO TYPES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.
Management of Contract Waivers and Deviations for Defense Systems
National Research Council Canada - National Science Library
1998-01-01
This report is the fourth and final in a series of reports resulting from our audit of management of contract waivers and deviations for Defense systems and summarizes our overall evaluation. Report...
New g-2 measurement deviates further from Standard Model
2004-01-01
"The latest result from an international collaboration of scientists investigating how the spin of a muon is affected as this type of subatomic particle moves through a magnetic field deviates further than previous measurements from theoretical predictions" (1 page).
A Note on Standard Deviation and Standard Error
Hassani, Hossein; Ghodsi, Mansoureh; Howell, Gareth
2010-01-01
Many students confuse the standard deviation and standard error of the mean and are unsure which, if either, to use in presenting data. In this article, we endeavour to address these questions and cover some related ambiguities about these quantities.
Prosthodontic management of mandibular deviation using palatal ramp appliance
Directory of Open Access Journals (Sweden)
Prince Kumar
2012-08-01
Full Text Available Segmental resection of the mandible generally results in deviation of the mandible to the defective side. This loss of continuity of the mandible destroys the balance of the lower face and leads to decreased mandibular function by deviation of the residual segment toward the surgical site. Prosthetic methods advocated to reduce or eliminate mandibular deviation include intermaxillary fixation, removable mandibular guide flange, palatal ramp, implant-supported prosthesis and palatal guidance restorations which may be useful in reducing mandibular deviation and improving masticatory performance and efficiency. These methods and restorations would be combined with a well organized mandibular exercise regimen. This clinical report describes the rehabilitation following segmental mandibulectomy using palatal ramp prosthesis.
Collapsing radiating stars with various equations of state
Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.
2017-06-01
We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.
Working covariance model selection for generalized estimating equations.
Carey, Vincent J; Wang, You-Gan
2011-11-20
We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.
Lipschitz Metrics for a Class of Nonlinear Wave Equations
Bressan, Alberto; Chen, Geng
2017-12-01
The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.
Influence of asymmetrical drawing radius deviation in micro deep drawing
Heinrich, L.; Kobayashi, H.; Shimizu, T.; Yang, M.; Vollertsen, F.
2017-09-01
Nowadays, an increasing demand for small metal parts in electronic and automotive industries can be observed. Deep drawing is a well-suited technology for the production of such parts due to its excellent qualities for mass production. However, the downscaling of the forming process leads to new challenges in tooling and process design, such as high relative deviation of tool geometry or blank displacement compared to the macro scale. FEM simulation has been a widely-used tool to investigate the influence of symmetrical process deviations as for instance a global variance of the drawing radius. This study shows a different approach that allows to determine the impact of asymmetrical process deviations on micro deep drawing. In this particular case the impact of an asymmetrical drawing radius deviation and blank displacement on cup geometry deviation was investigated for different drawing ratios by experiments and FEM simulation. It was found that both variations result in an increasing cup height deviation. Nevertheless, with increasing drawing ratio a constant drawing radius deviation has an increasing impact, while blank displacement results in a decreasing offset of the cups geometry. This is explained by different mechanisms that result in an uneven cup geometry. While blank displacement leads to material surplus on one side of the cup, an unsymmetrical radius deviation on the other hand generates uneven stretching of the cups wall. This is intensified for higher drawing ratios. It can be concluded that the effect of uneven radius geometry proves to be of major importance for the production of accurately shaped micro cups and cannot be compensated by intentional blank displacement.
The Analysis of a Deviation of Investment and Corporate Governance
Shoichi Hisa
2008-01-01
Investment of firms is affected by not only fundamentals factors, but liquidity constraint, ownership or corporate structure. Information structure between manager and owner is a significant factor to decide the level of investment, and deviation of investment from optimal condition. The reputation model between manager and owner suggest that the separate of ownership and management may induce the deviation of investment, and indicate that governance structure is important to reduce it. In th...
Deviation from local thermodynamic equilibrium in a cesium-seeded argon plasma
International Nuclear Information System (INIS)
Stefanov, B.; Zarkova, L.
1985-11-01
The possibility of deviations from local thermodynamic equilibrium of a cesium seeded argon plasma has been analyzed. A four level model of cesium has been employed. Overpopulations of the ground state and the first excited state as well as the corresponding reduction of the electron density are calculated for cylindrical discharge structures by solving stationary rate equations. Numerical results are presented. These results indicate that in a large regime of plasma conditions the LTE assumption is valid for electron temperatures larger than 3000 K. (orig.)
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Biancalani, A.; Bottino, A.; Ehrlacher, C.; Grandgirard, V.; Merlo, G.; Novikau, I.; Qiu, Z.; Sonnendrücker, E.; Garbet, X.; Görler, T.; Leerink, S.; Palermo, F.; Zarzoso, D.
2017-06-01
The linear properties of the geodesic acoustic modes (GAMs) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, and safety factor), electro-magnetic effects, collisions, and the presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the Lagrangian (particle-in-cell) code ORB5, the Eulerian code GENE, and semi-Lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.
International Nuclear Information System (INIS)
Mourragui, Mustapha; Orlandi, Enza
2013-01-01
A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long-range potential parametrized by β⩾0 and evolve according to an exclusion rule. It is shown that the empirical particle density under the diffusive scaling solves a quasilinear integro-differential evolution equation with Dirichlet boundary conditions. The associated dynamical large deviation principle is proved. Furthermore, when β is small enough, it is also demonstrated that the empirical particle density obeys a law of large numbers with respect to the stationary measures (hydrostatic). The macroscopic particle density solves a non-local, stationary, transport equation. (paper)
Effect of nasal deviation on quality of life.
de Lima Ramos, Sueli; Hochman, Bernardo; Gomes, Heitor Carvalho; Abla, Luiz Eduardo Felipe; Veiga, Daniela Francescato; Juliano, Yara; Dini, Gal Moreira; Ferreira, Lydia Masako
2011-07-01
Nasal deviation is a common complaint in otorhinolaryngology and plastic surgery. This condition not only causes impairment of nasal function but also affects quality of life, leading to psychological distress. The subjective assessment of quality of life, as an important aspect of outcomes research, has received increasing attention in recent decades. Quality of life is measured using standardized questionnaires that have been tested for reliability, validity, and sensitivity. The aim of this study was to evaluate health-related quality of life, self-esteem, and depression in patients with nasal deviation. Sixty patients were selected for the study. Patients with nasal deviation (n = 32) were assigned to the study group, and patients without nasal deviation (n = 28) were assigned to the control group. The diagnosis of nasal deviation was made by digital photogrammetry. Quality of life was assessed using the Medical Outcomes Study 36-Item Short Form Health Survey questionnaire; the Rosenberg Self-Esteem/Federal University of São Paulo, Escola Paulista de Medicina Scale; and the 20-item Self-Report Questionnaire. There were significant differences between groups in the physical functioning and general health subscales of the Medical Outcomes Study 36-Item Short Form Health Survey (p < 0.05). Depression was detected in 11 patients (34.4 percent) in the study group and in two patients in the control group, with a significant difference between groups (p < 0.05). Nasal deviation is an aspect of rhinoplasty of which the surgeon should be aware so that proper psychological diagnosis can be made and suitable treatment can be planned because psychologically the patients with nasal deviation have significantly worse quality of life and are more prone to depression. Risk, II.(Figure is included in full-text article.).
Deviations from Newton's law in supersymmetric large extra dimensions
International Nuclear Information System (INIS)
Callin, P.; Burgess, C.P.
2006-01-01
Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case
Performance of Phonatory Deviation Diagrams in Synthesized Voice Analysis.
Lopes, Leonardo Wanderley; da Silva, Karoline Evangelista; da Silva Evangelista, Deyverson; Almeida, Anna Alice; Silva, Priscila Oliveira Costa; Lucero, Jorge; Behlau, Mara
2018-05-02
To analyze the performance of a phonatory deviation diagram (PDD) in discriminating the presence and severity of voice deviation and the predominant voice quality of synthesized voices. A speech-language pathologist performed the auditory-perceptual analysis of the synthesized voice (n = 871). The PDD distribution of voice signals was analyzed according to area, quadrant, shape, and density. Differences in signal distribution regarding the PDD area and quadrant were detected when differentiating the signals with and without voice deviation and with different predominant voice quality. Differences in signal distribution were found in all PDD parameters as a function of the severity of voice disorder. The PDD area and quadrant can differentiate normal voices from deviant synthesized voices. There are differences in signal distribution in PDD area and quadrant as a function of the severity of voice disorder and the predominant voice quality. However, the PDD area and quadrant do not differentiate the signals as a function of severity of voice disorder and differentiated only the breathy and rough voices from the normal and strained voices. PDD density is able to differentiate only signals with moderate and severe deviation. PDD shape shows differences between signals with different severities of voice deviation. © 2018 S. Karger AG, Basel.
Complexity analysis based on generalized deviation for financial markets
Li, Chao; Shang, Pengjian
2018-03-01
In this paper, a new modified method is proposed as a measure to investigate the correlation between past price and future volatility for financial time series, known as the complexity analysis based on generalized deviation. In comparison with the former retarded volatility model, the new approach is both simple and computationally efficient. The method based on the generalized deviation function presents us an exhaustive way showing the quantization of the financial market rules. Robustness of this method is verified by numerical experiments with both artificial and financial time series. Results show that the generalized deviation complexity analysis method not only identifies the volatility of financial time series, but provides a comprehensive way distinguishing the different characteristics between stock indices and individual stocks. Exponential functions can be used to successfully fit the volatility curves and quantify the changes of complexity for stock market data. Then we study the influence for negative domain of deviation coefficient and differences during the volatile periods and calm periods. after the data analysis of the experimental model, we found that the generalized deviation model has definite advantages in exploring the relationship between the historical returns and future volatility.
Deviations from the Gutenberg–Richter law on account of a random distribution of block sizes
Energy Technology Data Exchange (ETDEWEB)
Sibiryakov, B. P., E-mail: sibiryakovbp@ipgg.sbras.ru [Trofimuk Institute of Oil and Gas Geology and Geophysics SB RAS, Novosibirsk, 630090 (Russian Federation); Novosibirsk State University, Novosibirsk, 630090 (Russian Federation)
2015-10-27
This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations are nonautomatically transformed into differential ones. It is impossible to consider an infinitesimal volume of a body, to which the major conservation laws could be applied, because the minimum representative volume of the body must contain at least a few elementary microstructures. The corresponding equations of motion are equations of infinite order, solutions of which include, along with usual sound waves, unusual waves with abnormally low velocities without a lower limit. It is shown that in such media weak perturbations can increase or decrease outside the limits. The number of complex roots of the corresponding dispersion equation, which can be interpreted as the number of unstable solutions, depends on the specific surface of cracks and is an almost linear dependence on a logarithmic scale, as in the seismological Gutenberg–Richter law. If the distance between one pore (crack) to another one is a random value with some distribution, we must write another dispersion equation and examine different scenarios depending on the statistical characteristics of the random distribution. In this case, there are sufficient deviations from the Gutenberg–Richter law and this theoretical result corresponds to some field and laboratory observations.
Fokker-Planck equation in mirror research
International Nuclear Information System (INIS)
Post, R.F.
1983-01-01
Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror
Mean-deviation analysis in the theory of choice.
Grechuk, Bogdan; Molyboha, Anton; Zabarankin, Michael
2012-08-01
Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered. © 2012 Society for Risk Analysis.
Minimizing Hexapod Robot Foot Deviations Using Multilayer Perceptron
Directory of Open Access Journals (Sweden)
Vytautas Valaitis
2015-12-01
Full Text Available Rough-terrain traversability is one of the most valuable characteristics of walking robots. Even despite their slower speeds and more complex control algorithms, walking robots have far wider usability than wheeled or tracked robots. However, efficient movement over irregular surfaces can only be achieved by eliminating all possible difficulties, which in many cases are caused by a high number of degrees of freedom, feet slippage, frictions and inertias between different robot parts or even badly developed inverse kinematics (IK. In this paper we address the hexapod robot-foot deviation problem. We compare the foot-positioning accuracy of unconfigured inverse kinematics and Multilayer Perceptron-based (MLP methods via theory, computer modelling and experiments on a physical robot. Using MLP-based methods, we were able to significantly decrease deviations while reaching desired positions with the hexapod's foot. Furthermore, this method is able to compensate for deviations of the robot arising from any possible reason.
Effect of density deviations of concrete on its attenuation efficiency
International Nuclear Information System (INIS)
Szymendera, L.; Wincel, K.; Blociszewski, S.; Kordyasz, D.; Sobolewska, I.
In the work, the influence of concrete density deviation on shield thickness and total dose ratio outside the reactor shield, has--on the basis of numerical analysis--been considered. It has been noticed the possibility of introducing flexible corrections--without additional shielding calculation--to the design thickness of the shield. It has been also found that in common cases of shield design, where any necessity of minimizing the shield thickness does not exist, the tendency to minimize the value of this deviation is hardly substantiable
Deviation from Covered Interest Rate Parity in Korea
Directory of Open Access Journals (Sweden)
Seungho Lee
2003-06-01
Full Text Available This paper tested the factors which cause deviation from covered interest rate parity (CIRP in Korea, using regression and VAR models. The empirical evidence indicates that the difference between the swap rate and interest rate differential exists and is greatly affected by variables which represent the currency liquidity situation of foreign exchange banks. In other words, the deviation from CIRP can easily occur due to the lack of foreign exchange liquidity of banks in a thin market, despite few capital constraints, small transaction costs, and trivial default risk in Korea.
Approaching nanometre accuracy in measurement of the profile deviation of a large plane mirror
International Nuclear Information System (INIS)
Müller, Andreas; Hofmann, Norbert; Manske, Eberhard
2012-01-01
The interferometric nanoprofilometer (INP), developed at the Institute of Process Measurement and Sensor Technology at the Ilmenau University of Technology, is a precision device for measuring the profile deviations of plane mirrors with a profile length of up to 250 mm at the nanometre scale. As its expanded uncertainty of U(l) = 7.8 nm at a confidence level of p = 95% (k = 2) was mainly influenced by the uncertainty of the straightness standard (3.6 nm) and the uncertainty caused by the signal and demodulation errors of the interferometer signals (1.2 nm), these two sources of uncertainty have been the subject of recent analyses and modifications. To measure the profile deviation of the standard mirror we performed a classic three-flat test using the INP. The three-flat test consists of a combination of measurements between three different test flats. The shape deviations of the three flats can then be determined by applying a least-squares solution of the resulting equation system. The results of this three-flat test showed surprisingly good consistency, enabling us to correct this systematic error in profile deviation measurements and reducing the uncertainty component of the standard mirror to 0.4 nm. Another area of research is the signal and demodulation error arising during the interpretation of the interferometer signals. In the case of the interferometric nanoprofilometer, the special challenge is that the maximum path length differences are too small during the scan of the entire profile deviation over perfectly aligned 250 mm long mirrors for proper interpolation and correction since they do not yet cover even half of an interference fringe. By applying a simple method of weighting to the interferometer data the common ellipse fitting could be performed successfully and the demodulation error was greatly reduced. The remaining uncertainty component is less than 0.5 nm. In summary we were successful in greatly reducing two major systematic errors. The
48 CFR 552.252-6 - Authorized Deviations in Clauses.
2010-10-01
... published in the General Services Administration Acquisition Regulation (48 CFR chapter 5). (2) This... published in the General Services Administration Acquisition Regulation by the addition of “(DEVIATION (FAR... ADMINISTRATION CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Text of Provisions and Clauses 552...
A Positional Deviation Sensor for Training of Robots
Directory of Open Access Journals (Sweden)
Fredrik Dessen
1988-04-01
Full Text Available A device for physically guiding a robot manipulator through its task is described. It consists of inductive, contact-free positional deviation sensors. The sensor will be used in high performance sensory control systems. The paper describes problems concerning multi-dimensional, non-linear measurement functions and the design of the servo control system.
Large deviations for Gaussian processes in Hoelder norm
International Nuclear Information System (INIS)
Fatalov, V R
2003-01-01
Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields
Patterns of deviation in Niyi Osundare's poetry | Dick | Mgbakoigba ...
African Journals Online (AJOL)
Log in or Register to get access to full text downloads. ... A critical stylistic study of the poetry of Niyi Osundare from Nigeria reveals that he has made an exemplary ... deviate from norms and conventions of language thereby creating aesthetics ...
International asset pricing under segmentation and PPP deviations
Chaieb, I.; Errunza, V.
2007-01-01
We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of
9 CFR 381.308 - Deviations in processing.
2010-01-01
...) must be handled according to: (1)(i) A HACCP plan for canned product that addresses hazards associated... (d) of this section. (c) [Reserved] (d) Procedures for handling process deviations where the HACCP... accordance with the following procedures: (a) Emergency stops. (1) When retort jams or breakdowns occur...
Semiparametric Bernstein–von Mises for the error standard deviation
Jonge, de R.; Zanten, van J.H.
2013-01-01
We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a
Semiparametric Bernstein-von Mises for the error standard deviation
de Jonge, R.; van Zanten, H.
2013-01-01
We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein-von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a
Robust Confidence Interval for a Ratio of Standard Deviations
Bonett, Douglas G.
2006-01-01
Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple…
Sample-path large deviations in credit risk
Leijdekker, V.J.G.; Mandjes, M.R.H.; Spreij, P.J.C.
2011-01-01
The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a
Analysis of form deviation in non-isothermal glass molding
Kreilkamp, H.; Grunwald, T.; Dambon, O.; Klocke, F.
2018-02-01
Especially in the market of sensors, LED lighting and medical technologies, there is a growing demand for precise yet low-cost glass optics. This demand poses a major challenge for glass manufacturers who are confronted with the challenge arising from the trend towards ever-higher levels of precision combined with immense pressure on market prices. Since current manufacturing technologies especially grinding and polishing as well as Precision Glass Molding (PGM) are not able to achieve the desired production costs, glass manufacturers are looking for alternative technologies. Non-isothermal Glass Molding (NGM) has been shown to have a big potential for low-cost mass manufacturing of complex glass optics. However, the biggest drawback of this technology at the moment is the limited accuracy of the manufactured glass optics. This research is addressing the specific challenges of non-isothermal glass molding with respect to form deviation of molded glass optics. Based on empirical models, the influencing factors on form deviation in particular form accuracy, waviness and surface roughness will be discussed. A comparison with traditional isothermal glass molding processes (PGM) will point out the specific challenges of non-isothermal process conditions. Furthermore, the underlying physical principle leading to the formation of form deviations will be analyzed in detail with the help of numerical simulation. In this way, this research contributes to a better understanding of form deviations in non-isothermal glass molding and is an important step towards new applications demanding precise yet low-cost glass optics.
Linguistics deviation, a tool for teaching English grammar: evidence ...
African Journals Online (AJOL)
We have always advocated that those teaching the Use of English must seek out novel ways of teaching the grammar of English to take out the drudgery of the present approach. Here, we proposed using Linguistic deviation as a tool for teaching English grammar. This approach will produce students who are both strong in ...
Process Measurement Deviation Analysis for Flow Rate due to Miscalibration
Energy Technology Data Exchange (ETDEWEB)
Oh, Eunsuk; Kim, Byung Rae; Jeong, Seog Hwan; Choi, Ji Hye; Shin, Yong Chul; Yun, Jae Hee [KEPCO Engineering and Construction Co., Deajeon (Korea, Republic of)
2016-10-15
An analysis was initiated to identify the root cause, and the exemption of high static line pressure correction to differential pressure (DP) transmitters was one of the major deviation factors. Also the miscalibrated DP transmitter range was identified as another major deviation factor. This paper presents considerations to be incorporated in the process flow measurement instrumentation calibration and the analysis results identified that the DP flow transmitter electrical output decreased by 3%. Thereafter, flow rate indication decreased by 1.9% resulting from the high static line pressure correction exemption and measurement range miscalibration. After re-calibration, the flow rate indication increased by 1.9%, which is consistent with the analysis result. This paper presents the brief calibration procedures for Rosemount DP flow transmitter, and analyzes possible three cases of measurement deviation including error and cause. Generally, the DP transmitter is required to be calibrated with precise process input range according to the calibration procedure provided for specific DP transmitter. Especially, in case of the DP transmitter installed in high static line pressure, it is important to correct the high static line pressure effect to avoid the inherent systematic error for Rosemount DP transmitter. Otherwise, failure to notice the correction may lead to indicating deviation from actual value.
On asymptotically efficient simulation of large deviation probabilities.
Dieker, A.B.; Mandjes, M.R.H.
2005-01-01
ABSTRACT: Consider a family of probabilities for which the decay is governed by a large deviation principle. To find an estimate for a fixed member of this family, one is often forced to use simulation techniques. Direct Monte Carlo simulation, however, is often impractical, particularly if the
Linear Estimation of Standard Deviation of Logistic Distribution ...
African Journals Online (AJOL)
The paper presents a theoretical method based on order statistics and a FORTRAN program for computing the variance and relative efficiencies of the standard deviation of the logistic population with respect to the Cramer-Rao lower variance bound and the best linear unbiased estimators (BLUE\\'s) when the mean is ...
The one-shot deviation principle for sequential rationality
DEFF Research Database (Denmark)
Hendon, Ebbe; Whitta-Jacobsen, Hans Jørgen; Sloth, Birgitte
1996-01-01
We present a decentralization result which is useful for practical and theoretical work with sequential equilibrium, perfect Bayesian equilibrium, and related equilibrium concepts for extensive form games. A weak consistency condition is sufficient to obtain an analogy to the well known One-Stage......-Stage-Deviation Principle for subgame perfect equilibrium...
Importance sampling large deviations in nonequilibrium steady states. I
Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.
2018-03-01
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.
Importance sampling large deviations in nonequilibrium steady states. I.
Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T
2018-03-28
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Weight of fitness deviation governs strict physical chaos in replicator dynamics.
Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar
2018-03-01
Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.
Energy Technology Data Exchange (ETDEWEB)
Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan, E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: jan.schee@fpf.slu.cz, E-mail: bobir.toshmatov@fpf.slu.cz, E-mail: jan.hladik@fpf.slu.cz, E-mail: jan.novotny@fpf.slu.cz [Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic)
2017-06-01
We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.
Dynamics of relative motion of test particles in general relativity
International Nuclear Information System (INIS)
Bazanski, S.L.
1977-01-01
Several variational principles which lead to the first and the second geodesic deviation equations, recently formulated by the author and used for the description of the relative motion of test particles in general relativity are presented. Relations between these principles are investigated and exhibited. The Hamilton-Jacobi equation is also studied for these generalized deviations and the conservation laws appearing here are discussed
International Nuclear Information System (INIS)
Peletier, Mark A.; Redig, Frank; Vafayi, Kiamars
2014-01-01
We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter m (BEP(m)), a Generalized Brownian Energy Process, and the Kipnis-Marchioro-Presutti (KMP) process. The hydrodynamic limit of each of these three processes is a parabolic equation, the linear heat equation in the case of the BEP(m) and the KMP, and a nonlinear heat equation for the Generalized Brownian Energy Process with parameter a (GBEP(a)). We prove the hydrodynamic limit rigorously for the BEP(m), and give a formal derivation for the GBEP(a). We then formally derive the pathwise large-deviation rate functional for the empirical measure of the three processes. These rate functionals imply gradient-flow structures for the limiting linear and nonlinear heat equations. We contrast these gradient-flow structures with those for processes describing the diffusion of mass, most importantly the class of Wasserstein gradient-flow systems. The linear and nonlinear heat-equation gradient-flow structures are each driven by entropy terms of the form −log ρ; they involve dissipation or mobility terms of order ρ 2 for the linear heat equation, and a nonlinear function of ρ for the nonlinear heat equation
Solar radiation pressure and deviations from Keplerian orbits
Energy Technology Data Exchange (ETDEWEB)
Kezerashvili, Roman Ya. [Physics Department, New York City College of Technology, the City University of New York, Brooklyn, NY 11201 (United States); Vazquez-Poritz, Justin F. [Physics Department, New York City College of Technology, City University of New York, Brooklyn, NY 11201 (United States)], E-mail: jporitz@gmail.com
2009-05-04
Newtonian gravity and general relativity give exactly the same expression for the period of an object in circular orbit around a static central mass. However, when the effects of the curvature of spacetime and solar radiation pressure are considered simultaneously for a solar sail propelled satellite, there is a deviation from Kepler's third law. It is shown that solar radiation pressure affects the period of this satellite in two ways: by effectively decreasing the solar mass, thereby increasing the period, and by enhancing the effects of other phenomena, potentially rendering some of them detectable. In particular, we consider deviations from Keplerian orbits due to spacetime curvature, frame dragging from the rotation of the sun, the oblateness of the sun, a possible net electric charge of the sun, and a very small positive cosmological constant.
Moderate Deviation Analysis for Classical Communication over Quantum Channels
Chubb, Christopher T.; Tan, Vincent Y. F.; Tomamichel, Marco
2017-11-01
We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altŭg and Wagner as well as Polyanskiy and Verdú. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks.
Beat the Deviations in Estimating Maximum Power of Thermoelectric Modules
DEFF Research Database (Denmark)
Gao, Junling; Chen, Min
2013-01-01
Under a certain temperature difference, the maximum power of a thermoelectric module can be estimated by the open-circuit voltage and the short-circuit current. In practical measurement, there exist two switch modes, either from open to short or from short to open, but the two modes can give...... different estimations on the maximum power. Using TEG-127-2.8-3.5-250 and TEG-127-1.4-1.6-250 as two examples, the difference is about 10%, leading to some deviations with the temperature change. This paper analyzes such differences by means of a nonlinear numerical model of thermoelectricity, and finds out...... that the main cause is the influence of various currents on the produced electromotive potential. A simple and effective calibration method is proposed to minimize the deviations in specifying the maximum power. Experimental results validate the method with improved estimation accuracy....
Deviation from the superparamagnetic behaviour of fine-particle systems
Malaescu, I
2000-01-01
Studies concerning superparamagnetic behaviour of fine magnetic particle systems were performed using static and radiofrequency measurements, in the range 1-60 MHz. The samples were: a ferrofluid with magnetite particles dispersed in kerosene (sample A), magnetite powder (sample B) and the same magnetite powder dispersed in a polymer (sample C). Radiofrequency measurements indicated a maximum in the imaginary part of the complex magnetic susceptibility, for each of the samples, at frequencies with the magnitude order of tens of MHz, the origin of which was assigned to Neel-type relaxation processes. The static measurements showed a Langevin-type dependence of magnetisation M and of susceptibility chi, on the magnetic field for sample A. For samples B and C deviations from this type of dependence were found. These deviations were analysed qualitatively and explained in terms of the interparticle interactions, dispersion medium influence and surface effects.
OBSERVABLE DEVIATIONS FROM HOMOGENEITY IN AN INHOMOGENEOUS UNIVERSE
Energy Technology Data Exchange (ETDEWEB)
Giblin, John T. Jr. [Department of Physics, Kenyon College, 201 N College Road Gambier, OH 43022 (United States); Mertens, James B.; Starkman, Glenn D. [CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106 (United States)
2016-12-20
How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedmann–Lemaître–Robertson–Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe, and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer’s sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects, with implications for using real observables in an inhomogeneous universe such as our own.
OBSERVABLE DEVIATIONS FROM HOMOGENEITY IN AN INHOMOGENEOUS UNIVERSE
International Nuclear Information System (INIS)
Giblin, John T. Jr.; Mertens, James B.; Starkman, Glenn D.
2016-01-01
How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedmann–Lemaître–Robertson–Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe, and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer’s sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects, with implications for using real observables in an inhomogeneous universe such as our own.
Complex service recovery processes: how to avoid triple deviation
Edvardsson, Bo; Tronvoll, Bård; Höykinpuro, Ritva
2011-01-01
Purpose – This article seeks to develop a new framework to outline factors that influence the resolution of unfavourable service experiences as a result of double deviation. The focus is on understanding and managing complex service recovery processes. Design/methodology/approach – An inductive, explorative and narrative approach was selected. Data were collected in the form of narratives from the field through interviews with actors at various levels in organisations as well as with custo...
OSMOSIS: A CAUSE OF APPARENT DEVIATIONS FROM DARCY'S LAW.
Olsen, Harold W.
1985-01-01
This review of the existing evidence shows that osmosis causes intercepts in flow rate versus hydraulic gradient relationships that are consistent with the observed deviations from Darcy's law at very low gradients. Moreover, it is suggested that a natural cause of osmosis in laboratory samples could be chemical reactions such as those involved in aging effects. This hypothesis is analogous to the previously proposed occurrence of electroosmosis in nature generated by geochemical weathering reactions. Refs.
Semiparametric Bernstein–von Mises for the error standard deviation
Jonge, de, R.; Zanten, van, J.H.
2013-01-01
We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regr...
Geometry of river networks. I. Scaling, fluctuations, and deviations
International Nuclear Information System (INIS)
Dodds, Peter Sheridan; Rothman, Daniel H.
2001-01-01
This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary, suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of a subbasin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density, and provide observations and explanations of deviations from scaling. We show that fluctuations about scaling are substantial, and grow with system size. We find strong deviations from scaling at small scales which can be explained by the existence of a linear network structure. At intermediate scales, we find slow drifts in exponent values, indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations, and will not be improved by increases in network resolution
[Deviation in psychosexual development in the pre-puberty children].
Liavshina, G Kh
2002-01-01
Psychosexual health of 308 children, aged 2-11 years, as well as that of their families, was studied. Deviations in psychosexual development were found in 34.6% of the children examined. The following types were detected: difficulties in formation of gender-determined behavior features--64.4%, precocious psychosexual development--13.7%, delayed psychosexual development--12.3%, obsessive masturbation--9.6%. Risk factors for deviant psychosexual development were found.
Direct training of robots using a positional deviation sensor
Dessen, Fredrik
1988-01-01
A device and system for physically guiding a manipulator through its task is described. The device consists of inductive, contact-free positional deviation sensors, enabling the rcbot to track a motion marker. Factors limiting the tracking performance are the kinematics of the sensor device and the bartdwidth of the servo system. Means for improving it includes the use of optimal motion coordination and force and velocity feedback. This enables real-time manual training o...
The Kerr/fluid duality and the singularity of solutions to the fluid equation
International Nuclear Information System (INIS)
Fujisawa, Ippei; Nakayama, Ryuichi
2016-01-01
An equation for a viscous incompressible fluid on a spheroidal surface that is dual to the perturbation around the near-near-horizon extreme Kerr (near-NHEK) black hole is derived. It is also shown that an expansion scalar θ of a congruence of null geodesics on the perturbed horizon of the perturbed near-NHEK spacetime, which is dual to a viscous incompressible fluid, is not in general positive semidefinite, even if initial conditions on the velocity are smooth. Unless the initial conditions are appropriately adjusted, caustics of null congruence will occur on the perturbed horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime, which is dual to a viscous incompressible fluid on S 2 . An initial condition that θ be positive semidefinite at any point on S 2 is a necessary condition for the existence of smooth solutions to the incompressible Navier-Stokes equation on S 2
Wavelength selection method with standard deviation: application to pulse oximetry.
Vazquez-Jaccaud, Camille; Paez, Gonzalo; Strojnik, Marija
2011-07-01
Near-infrared spectroscopy provides useful biological information after the radiation has penetrated through the tissue, within the therapeutic window. One of the significant shortcomings of the current applications of spectroscopic techniques to a live subject is that the subject may be uncooperative and the sample undergoes significant temporal variations, due to his health status that, from radiometric point of view, introduce measurement noise. We describe a novel wavelength selection method for monitoring, based on a standard deviation map, that allows low-noise sensitivity. It may be used with spectral transillumination, transmission, or reflection signals, including those corrupted by noise and unavoidable temporal effects. We apply it to the selection of two wavelengths for the case of pulse oximetry. Using spectroscopic data, we generate a map of standard deviation that we propose as a figure-of-merit in the presence of the noise introduced by the living subject. Even in the presence of diverse sources of noise, we identify four wavelength domains with standard deviation, minimally sensitive to temporal noise, and two wavelengths domains with low sensitivity to temporal noise.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Weight of fitness deviation governs strict physical chaos in replicator dynamics
Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar
2018-03-01
Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.
Large deviations and mixing for dissipative PDEs with unbounded random kicks
Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.
2018-02-01
We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.
Quality Assessment of Vertical Angular Deviations for Photometer Calibration Benches
International Nuclear Information System (INIS)
Ribeiro, A Silva; Santos, A Costa; E Sousa, J Alves; Forbes, A B
2015-01-01
Lighting, both natural and electric, constitutes one of the most important aspects of the life of human beings, allowing us to see and perform our daily tasks in outdoor and indoor environments. The safety aspects of lighting are self-evident in areas such as road lighting, urban lighting and also indoor lighting. The use of photometers to measure lighting levels requires traceability obtained in accredited laboratories, which must provide an associated uncertainty. It is therefore relevant to study the impact of known uncertainty sources like the vertical angular deviation of photometer calibration benches, in order to define criteria to its quality assessment
Efficient characterisation of large deviations using population dynamics
Brewer, Tobias; Clark, Stephen R.; Bradford, Russell; Jack, Robert L.
2018-05-01
We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. We use the simple symmetric exclusion process with periodic boundary conditions as a prototypical example and investigate the convergence of the results with respect to the algorithmic parameters, focussing on the dynamical phase transition between homogeneous and inhomogeneous states, where convergence is relatively difficult to achieve. We discuss how the performance of the algorithm can be optimised, and how it can be efficiently exploited on parallel computing platforms.
Distribution of standard deviation of an observable among superposed states
International Nuclear Information System (INIS)
Yu, Chang-shui; Shao, Ting-ting; Li, Dong-mo
2016-01-01
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.
Distribution of standard deviation of an observable among superposed states
Yu, Chang-shui; Shao, Ting-ting; Li, Dong-mo
2016-10-01
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.
Distribution of Standard deviation of an observable among superposed states
Yu, Chang-shui; Shao, Ting-ting; Li, Dong-mo
2016-01-01
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of in...
Fluctuations and large deviations in non-equilibrium systems
Indian Academy of Sciences (India)
When ρa = ρb = r, the steady state is a Bernoulli measure where all the ... where the function F(x) is the monotone solution of the differential equation ρ(x) = F + .... quantity is conserved (numbers of particles, energy, momentum..) would also be.
Deviation-based spam-filtering method via stochastic approach
Lee, Daekyung; Lee, Mi Jin; Kim, Beom Jun
2018-03-01
In the presence of a huge number of possible purchase choices, ranks or ratings of items by others often play very important roles for a buyer to make a final purchase decision. Perfectly objective rating is an impossible task to achieve, and we often use an average rating built on how previous buyers estimated the quality of the product. The problem of using a simple average rating is that it can easily be polluted by careless users whose evaluation of products cannot be trusted, and by malicious spammers who try to bias the rating result on purpose. In this letter we suggest how trustworthiness of individual users can be systematically and quantitatively reflected to build a more reliable rating system. We compute the suitably defined reliability of each user based on the user's rating pattern for all products she evaluated. We call our proposed method as the deviation-based ranking, since the statistical significance of each user's rating pattern with respect to the average rating pattern is the key ingredient. We find that our deviation-based ranking method outperforms existing methods in filtering out careless random evaluators as well as malicious spammers.
Rodny, Marek; Nolz, Reinhard
2017-04-01
Evapotranspiration (ET) is a fundamental component of the hydrological cycle, but challenging to be quantified. Lysimeter facilities, for example, can be installed and operated to determine ET, but they are costly and represent only point measurements. Therefore, lysimeter data are traditionally used to develop, calibrate, and validate models that allow calculating reference evapotranspiration (ET0) based on meteorological data, which can be measured more easily. The standardized form of the well-known FAO Penman-Monteith equation (ASCE-EWRI) is recommended as a standard procedure for estimating ET0 and subsequently plant water requirements. Applied and validated under different climatic conditions, the Penman-Monteith equation is generally known to deliver proper results. On the other hand, several studies documented deviations between measured and calculated ET0 depending on environmental conditions. Potential reasons are, for example, differing or varying surface characteristics of the lysimeter and the location where the weather instruments are placed. Advection of sensible heat (transport of dry and hot air from surrounding areas) might be another reason for deviating ET-values. However, elaborating causal processes is complex and requires comprehensive data of high quality and specific analysis techniques. In order to assess influencing factors, we correlated differences between measured and calculated ET0 with pre-selected meteorological parameters and related system parameters. Basic data were hourly ET0-values from a weighing lysimeter (ET0_lys) with a surface area of 2.85 m2 (reference crop: frequently irrigated grass), weather data (air and soil temperature, relative humidity, air pressure, wind velocity, and solar radiation), and soil water content in different depths. ET0_ref was calculated in hourly time steps according to the standardized procedure after ASCE-EWRI (2005). Deviations between both datasets were calculated as ET0_lys-ET0_ref and
Non-linear neutron star oscillations viewed as deviations from an equilibrium state
International Nuclear Information System (INIS)
Sperhake, U
2002-01-01
A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)
International Nuclear Information System (INIS)
Clara, Rene A.; Gomez Marigliano, Ana C.; Solimo, Horacio N.
2007-01-01
Density and viscosity measurements for pure chloroform and methyl isobutyl ketone at T = (283.15, 293.15, 303.15, and 313.15) K as well as for the binary system {x 1 chloroform + (1 - x 1 ) methyl isobutyl ketone} at the same temperatures were made over the whole concentration range. The experimental results were fitted to empirical equations, which permit the calculation of these properties over the whole concentration and temperature ranges studied. Data of the binary mixture were further used to calculate the excess molar volume and viscosity deviation. The (vapour + liquid) equilibrium (VLE) at T = 303.15 K for this binary system was also measured in order to calculate the activity coefficients and the excess molar Gibbs energy. This binary system shows no azeotrope and negative deviations from ideal behaviour. The excess or deviation properties were fitted to the Redlich-Kister polynomial relation to obtain their coefficients and standard deviations
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Energy Technology Data Exchange (ETDEWEB)
Parekh, V [The Johns Hopkins University, Computer Science. Baltimore, MD (United States); Jacobs, MA [The Johns Hopkins University School of Medicine, Dept of Radiology and Oncology. Baltimore, MD (United States)
2016-06-15
Purpose: Multiparametric radiological imaging is used for diagnosis in patients. Potentially extracting useful features specific to a patient’s pathology would be crucial step towards personalized medicine and assessing treatment options. In order to automatically extract features directly from multiparametric radiological imaging datasets, we developed an advanced unsupervised machine learning algorithm called the multidimensional imaging radiomics-geodesics(MIRaGe). Methods: Seventy-six breast tumor patients underwent 3T MRI breast imaging were used for this study. We tested the MIRaGe algorithm to extract features for classification of breast tumors into benign or malignant. The MRI parameters used were T1-weighted, T2-weighted, dynamic contrast enhanced MR imaging (DCE-MRI) and diffusion weighted imaging(DWI). The MIRaGe algorithm extracted the radiomics-geodesics features (RGFs) from multiparametric MRI datasets. This enable our method to learn the intrinsic manifold representations corresponding to the patients. To determine the informative RGF, a modified Isomap algorithm(t-Isomap) was created for a radiomics-geodesics feature space(tRGFS) to avoid overfitting. Final classification was performed using SVM. The predictive power of the RGFs was tested and validated using k-fold cross validation. Results: The RGFs extracted by the MIRaGe algorithm successfully classified malignant lesions from benign lesions with a sensitivity of 93% and a specificity of 91%. The top 50 RGFs identified as the most predictive by the t-Isomap procedure were consistent with the radiological parameters known to be associated with breast cancer diagnosis and were categorized as kinetic curve characterizing RGFs, wash-in rate characterizing RGFs, wash-out rate characterizing RGFs and morphology characterizing RGFs. Conclusion: In this paper, we developed a novel feature extraction algorithm for multiparametric radiological imaging. The results demonstrated the power of the MIRa
International Nuclear Information System (INIS)
Parekh, V; Jacobs, MA
2016-01-01
Purpose: Multiparametric radiological imaging is used for diagnosis in patients. Potentially extracting useful features specific to a patient’s pathology would be crucial step towards personalized medicine and assessing treatment options. In order to automatically extract features directly from multiparametric radiological imaging datasets, we developed an advanced unsupervised machine learning algorithm called the multidimensional imaging radiomics-geodesics(MIRaGe). Methods: Seventy-six breast tumor patients underwent 3T MRI breast imaging were used for this study. We tested the MIRaGe algorithm to extract features for classification of breast tumors into benign or malignant. The MRI parameters used were T1-weighted, T2-weighted, dynamic contrast enhanced MR imaging (DCE-MRI) and diffusion weighted imaging(DWI). The MIRaGe algorithm extracted the radiomics-geodesics features (RGFs) from multiparametric MRI datasets. This enable our method to learn the intrinsic manifold representations corresponding to the patients. To determine the informative RGF, a modified Isomap algorithm(t-Isomap) was created for a radiomics-geodesics feature space(tRGFS) to avoid overfitting. Final classification was performed using SVM. The predictive power of the RGFs was tested and validated using k-fold cross validation. Results: The RGFs extracted by the MIRaGe algorithm successfully classified malignant lesions from benign lesions with a sensitivity of 93% and a specificity of 91%. The top 50 RGFs identified as the most predictive by the t-Isomap procedure were consistent with the radiological parameters known to be associated with breast cancer diagnosis and were categorized as kinetic curve characterizing RGFs, wash-in rate characterizing RGFs, wash-out rate characterizing RGFs and morphology characterizing RGFs. Conclusion: In this paper, we developed a novel feature extraction algorithm for multiparametric radiological imaging. The results demonstrated the power of the MIRa
Image contrast enhancement based on a local standard deviation model
International Nuclear Information System (INIS)
Chang, Dah-Chung; Wu, Wen-Rong
1996-01-01
The adaptive contrast enhancement (ACE) algorithm is a widely used image enhancement method, which needs a contrast gain to adjust high frequency components of an image. In the literature, the gain is usually inversely proportional to the local standard deviation (LSD) or is a constant. But these cause two problems in practical applications, i.e., noise overenhancement and ringing artifact. In this paper a new gain is developed based on Hunt's Gaussian image model to prevent the two defects. The new gain is a nonlinear function of LSD and has the desired characteristic emphasizing the LSD regions in which details are concentrated. We have applied the new ACE algorithm to chest x-ray images and the simulations show the effectiveness of the proposed algorithm
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
Deviations from scale invariance near a general conformal background
International Nuclear Information System (INIS)
Babichenko, A.; Elitzur, S.
1994-01-01
Deviations from scale invariance resulting from small perturbations of a general two-dimensional conformal field theory are studied. They are expressed in terms of β-functions for the renormalization of general couplings under a local change of scale. The β-functions for a homogeneous background are given perturbatively in terms of the data of the original conformal theory without any specific assumptions on its nature. The renormalization of couplings to primary operators and to first descendents is considered as well as that of couplings of a dilatonic type which involve explicit dependence on world sheet curvature. The first descendent couplings are interpreted as gauge degrees of freedom in the string field action and the corresponding gauge transformation is spelled out. (orig.)
Standard deviation of luminance distribution affects lightness and pupillary response.
Kanari, Kei; Kaneko, Hirohiko
2014-12-01
We examined whether the standard deviation (SD) of luminance distribution serves as information of illumination. We measured the lightness of a patch presented in the center of a scrambled-dot pattern while manipulating the SD of the luminance distribution. Results showed that lightness decreased as the SD of the surround stimulus increased. We also measured pupil diameter while viewing a similar stimulus. The pupil diameter decreased as the SD of luminance distribution of the stimuli increased. We confirmed that these results were not obtained because of the increase of the highest luminance in the stimulus. Furthermore, results of field measurements revealed a correlation between the SD of luminance distribution and illuminance in natural scenes. These results indicated that the visual system refers to the SD of the luminance distribution in the visual stimulus to estimate the scene illumination.
Total focusing method (TFM) robustness to material deviations
Painchaud-April, Guillaume; Badeau, Nicolas; Lepage, Benoit
2018-04-01
The total focusing method (TFM) is becoming an accepted nondestructive evaluation method for industrial inspection. What was a topic of discussion in the applied research community just a few years ago is now being deployed in critical industrial applications, such as inspecting welds in pipelines. However, the method's sensitivity to unexpected parametric changes (material and geometric) has not been rigorously assessed. In this article, we investigate the robustness of TFM in relation to unavoidable deviations from modeled nominal inspection component characteristics, such as sound velocities and uncertainties about the parts' internal and external diameters. We also review TFM's impact on the standard inspection modes often encountered in industrial inspections, and we present a theoretical model supported by empirical observations to illustrate the discussion.
Deviations from uniform power law scaling in nonstationary time series
Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.
1997-01-01
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
The Effects of Marginal Deviations on Behavioral Development.
Caprara, Gian Vittorio; Dodge, Kenneth A; Pastorelli, Concetta; Zelli, Arnaldo
2006-01-01
This investigation was conceptually framed within the theory of marginal deviations (Caprara & Zimbardo, 1996) and sought evidence for the general hypothesis that some children who initially show marginal behavioral problems may, over time, develop more serious problems depending partly on other personal and behavioral characteristics. To this end, the findings of two studies conducted, respectively, with American elementary school children and Italian middle school students are reviewed. These two studies show that hyperactivity, cognitive difficulties, low special preference, and lack of prosocial behavior increase a child's risk for growth in aggressive behavior over several school years. More importantly, they also show that equivalent levels of these risk factors have a greater impact on the development of children who, early on, were marginally aggressive.
Mod-ϕ convergence normality zones and precise deviations
Féray, Valentin; Nikeghbali, Ashkan
2016-01-01
The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy’s continuity theorem. This monograph focuses on this characteristic function approach and presents a renormalization theory called mod-ϕ convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models related to classical probability, combinatorics, non-commutative random variables, as well as geometric and number-theoretical objects. Intended for researchers in probability theory, the text is carefully well-written and well-structured, containing a great amount of detail and interesting examples. .
The response to prism deviations in human infants.
Riddell, P M; Horwood, A M; Houston, S M; Turner, J E
1999-09-23
Previous research has suggested that infants are unable to make a corrective eye movement in response to a small base-out prism placed in front of one eye before 14-16 weeks [1]. Three hypotheses have been proposed to explain this early inability, and each of these makes different predictions for the time of onset of a response to a larger prism. The first proposes that infants have a 'degraded sensory capacity' and so require a larger retinal disparity (difference in the position of the image on the retina of each eye) to stimulate disparity detectors [2]. This predicts that infants might respond at an earlier age than previously reported [1] when tested using a larger prism. The second hypothesis proposes that infants learn to respond to larger retinal disparities through practice with small disparities [3]. According to this theory, using a larger prism will not result in developmentally earlier responses, and may even delay the response. The third hypothesis proposes that the ability to respond to prismatic deviation depends on maturational factors indicated by the onset of stereopsis (the ability to detect depth in an image on the basis of retinal disparity cues only) [4] [5], predicting that the size of the prism is irrelevant. To differentiate between these hypotheses, we tested 192 infants ranging from 2 to 52 weeks of age using a larger prism. Results showed that 63% of infants of 5-8 weeks of age produced a corrective eye movement in response to placement of a prism in front of the eye when in the dark. Both the percentage of infants who produced a response, and the speed of the response, increased with age. These results suggest that infants can make corrective eye movements in response to large prismatic deviations before 14-16 weeks of age. This, in combination with other recent results [6], discounts previous hypotheses.
The gait standard deviation, a single measure of kinematic variability.
Sangeux, Morgan; Passmore, Elyse; Graham, H Kerr; Tirosh, Oren
2016-05-01
Measurement of gait kinematic variability provides relevant clinical information in certain conditions affecting the neuromotor control of movement. In this article, we present a measure of overall gait kinematic variability, GaitSD, based on combination of waveforms' standard deviation. The waveform standard deviation is the common numerator in established indices of variability such as Kadaba's coefficient of multiple correlation or Winter's waveform coefficient of variation. Gait data were collected on typically developing children aged 6-17 years. Large number of strides was captured for each child, average 45 (SD: 11) for kinematics and 19 (SD: 5) for kinetics. We used a bootstrap procedure to determine the precision of GaitSD as a function of the number of strides processed. We compared the within-subject, stride-to-stride, variability with the, between-subject, variability of the normative pattern. Finally, we investigated the correlation between age and gait kinematic, kinetic and spatio-temporal variability. In typically developing children, the relative precision of GaitSD was 10% as soon as 6 strides were captured. As a comparison, spatio-temporal parameters required 30 strides to reach the same relative precision. The ratio stride-to-stride divided by normative pattern variability was smaller in kinematic variables (the smallest for pelvic tilt, 28%) than in kinetic and spatio-temporal variables (the largest for normalised stride length, 95%). GaitSD had a strong, negative correlation with age. We show that gait consistency may stabilise only at, or after, skeletal maturity. Copyright © 2016 Elsevier B.V. All rights reserved.
Extremes of 2d Coulomb gas: universal intermediate deviation regime
Lacroix-A-Chez-Toine, Bertrand; Grabsch, Aurélien; Majumdar, Satya N.; Schehr, Grégory
2018-01-01
In this paper, we study the extreme statistics in the complex Ginibre ensemble of N × N random matrices with complex Gaussian entries, but with no other symmetries. All the N eigenvalues are complex random variables and their joint distribution can be interpreted as a 2d Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential v(r) \\propto r2 . We study the statistics of the eigenvalue with the largest modulus r\\max in the complex plane. The typical and large fluctuations of r\\max around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this ‘intermediate deviation function’ (IDF) and show that it is universal, i.e. independent of the confining potential v(r) as long as it is spherically symmetric and increases faster than \\ln r2 for large r with an unbounded support. If the confining potential v(r) has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as v(r) ∼ \\ln r2 for r \\gg 1 with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.
Evaluating deviations in prostatectomy patients treated with IMRT.
Sá, Ana Cravo; Peres, Ana; Pereira, Mónica; Coelho, Carina Marques; Monsanto, Fátima; Macedo, Ana; Lamas, Adrian
2016-01-01
To evaluate the deviations in prostatectomy patients treated with IMRT in order to calculate appropriate margins to create the PTV. Defining inappropriate margins can lead to underdosing in target volumes and also overdosing in healthy tissues, increasing morbidity. 223 CBCT images used for alignment with the CT planning scan based on bony anatomy were analyzed in 12 patients treated with IMRT following prostatectomy. Shifts of CBCT images were recorded in three directions to calculate the required margin to create PTV. The mean and standard deviation (SD) values in millimetres were -0.05 ± 1.35 in the LR direction, -0.03 ± 0.65 in the SI direction and -0.02 ± 2.05 the AP direction. The systematic error measured in the LR, SI and AP direction were 1.35 mm, 0.65 mm, and 2.05 mm with a random error of 2.07 mm; 1.45 mm and 3.16 mm, resulting in a PTV margin of 4.82 mm; 2.64 mm, and 7.33 mm, respectively. With IGRT we suggest a margin of 5 mm, 3 mm and 8 mm in the LR, SI and AP direction, respectively, to PTV1 and PTV2. Therefore, this study supports an anisotropic margin expansion to the PTV being the largest expansion in the AP direction and lower in SI.
Deviation from the Knudsen law on quantum gases
International Nuclear Information System (INIS)
Babac, Gulru
2014-01-01
Gas flow in micro/nano scale systems has been generally studied for the Maxwell gases. In the limits of very low temperature and very confined domains, the Maxwellian approximation can break down and the quantum character of the gases becomes important. In these cases, Knudsen law, which is one of the important equations to analyze rarefied gas flows is invalid and should be reanalyzed for quantum gases. In this work, the availability of quantum gas conditions in the high Knudsen number cases is discussed and Knudsen law is analyzed for quantum gases
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Amplification biases: possible differences among deviating gene expressions
Directory of Open Access Journals (Sweden)
Piumi Francois
2008-01-01
Full Text Available Abstract Background Gene expression profiling has become a tool of choice to study pathological or developmental questions but in most cases the material is scarce and requires sample amplification. Two main procedures have been used: in vitro transcription (IVT and polymerase chain reaction (PCR, the former known as linear and the latter as exponential. Previous reports identified enzymatic pitfalls in PCR and IVT protocols; however the possible differences between the sequences affected by these amplification defaults were only rarely explored. Results Screening a bovine cDNA array dedicated to embryonic stages with embryonic (n = 3 and somatic tissues (n = 2, we proceeded to moderate amplifications starting from 1 μg of total RNA (global PCR or IVT one round. Whatever the tissue, 16% of the probes were involved in deviating gene expressions due to amplification defaults. These distortions were likely due to the molecular features of the affected sequences (position within a gene, GC content, hairpin number but also to the relative abundance of these transcripts within the tissues. These deviating genes mainly encoded housekeeping genes from physiological or cellular processes (70% and constituted 2 subsets which did not overlap (molecular features, signal intensities, gene ID. However, the differential expressions identified between embryonic stages were both reliable (minor intersect with biased expressions and relevant (biologically validated. In addition, the relative expression levels of those genes were biologically similar between amplified and unamplified samples. Conclusion Conversely to the most recent reports which challenged the use of intense amplification procedures on minute amounts of RNA, we chose moderate PCR and IVT amplifications for our gene profiling study. Conclusively, it appeared that systematic biases arose even with moderate amplification procedures, independently of (i the sample used: brain, ovary or embryos, (ii
New experimental proposals for testing Dirac equation
International Nuclear Information System (INIS)
Camacho, Abel; Macias, Alfredo
2004-01-01
The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by-product of this quest the possible modifications that some field equations, for instance, the motion equation of spin-1/2-particles, have already been considered. In the present Letter a modified Dirac equation, whose extra term embraces a second-order time derivative, is taken as mainstay, and three different experimental proposals to detect it are put forward. The novelty in these ideas is that two of them do not fall within the extant approaches in this context, to wit, red-shift, atomic interferometry, or Hughes-Drever type-like experiments
WKB theory of large deviations in stochastic populations
Assaf, Michael; Meerson, Baruch
2017-06-01
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics—such as those determining population extinction, fixation or switching between different states—are presently in a focus of attention of statistical physicists. We review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation allows one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and multiple, but also briefly consider populations on heterogeneous networks and spatial populations. The spatial setting also allows one to study large fluctuations of the speed of biological invasions. Finally, we briefly discuss possible directions of future work.
Vertical dispersion generated by correlated closed orbit deviations
International Nuclear Information System (INIS)
Kewisch, J.; Limberg, T.; Rossbach, J.; Willeke, F.
1986-02-01
Vertical displacement of quadrupole magnets is one of the main causes of a vertical dispersion in a flat storage ring and thus a major contributor to the height of an electron beam. Computer simulations of the beam height in the HERA electron ring give a value of the ratio ε z /ε x of more than 10 percent. This large value occurs even for an rms value of the quadrupole vertical displacements Δz as small as 0.01 mm. Such a vertical emittance is much larger than one expects on the base of a theoretical estimate and it is clearly necessary to investigate the origin of the disagreements especially since the beam height has such an important influence on the machine performance. The key to the understanding of this discrepancy lies in the correlations of the closed orbit deviations at different position of the machine. This is investigated in the next section and in the section which follows we derive the expression for the rms value of dispersion and the vertical emittance. Finally the theoretical results are compared with computer simulations. (orig.)
Large-deviation properties of resilience of power grids
International Nuclear Information System (INIS)
Dewenter, Timo; Hartmann, Alexander K
2015-01-01
We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks, and in addition, the topology of the British transmission power grid. The three ensembles are Erdős–Rényi random graphs, Erdős–Rényi random graphs with a fixed number of links, and spatial networks where the nodes are embedded in a two-dimensional plane. We numerically investigate the probability density functions (pdfs) down to the tails to gain insight into very resilient and very vulnerable networks. This is achieved via large-deviation techniques, which allow us to study very rare values that occur with probability densities below 10 −160 . We find that the right tail of the pdfs towards larger backup capacities follows an exponential with a strong curvature. This is confirmed by the rate function, which approaches a limiting curve for increasing network sizes. Very resilient networks are basically characterized by a small diameter and a large power sign ratio. In addition, networks can be made typically more resilient by adding more links. (paper)
Phage display peptide libraries: deviations from randomness and correctives
Ryvkin, Arie; Ashkenazy, Haim; Weiss-Ottolenghi, Yael; Piller, Chen; Pupko, Tal; Gershoni, Jonathan M
2018-01-01
Abstract Peptide-expressing phage display libraries are widely used for the interrogation of antibodies. Affinity selected peptides are then analyzed to discover epitope mimetics, or are subjected to computational algorithms for epitope prediction. A critical assumption for these applications is the random representation of amino acids in the initial naïve peptide library. In a previous study, we implemented next generation sequencing to evaluate a naïve library and discovered severe deviations from randomness in UAG codon over-representation as well as in high G phosphoramidite abundance causing amino acid distribution biases. In this study, we demonstrate that the UAG over-representation can be attributed to the burden imposed on the phage upon the assembly of the recombinant Protein 8 subunits. This was corrected by constructing the libraries using supE44-containing bacteria which suppress the UAG driven abortive termination. We also demonstrate that the overabundance of G stems from variant synthesis-efficiency and can be corrected using compensating oligonucleotide-mixtures calibrated by mass spectroscopy. Construction of libraries implementing these correctives results in markedly improved libraries that display random distribution of amino acids, thus ensuring that enriched peptides obtained in biopanning represent a genuine selection event, a fundamental assumption for phage display applications. PMID:29420788
Standard deviation and standard error of the mean.
Lee, Dong Kyu; In, Junyong; Lee, Sangseok
2015-06-01
In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results.
Clonal status and clinicopathological observation of cervical minimal deviation adenocarcinoma
Directory of Open Access Journals (Sweden)
Lan Miao
2010-04-01
Full Text Available Abstract Background Minimal deviation adenocarcinoma (MDA of the uterine cervix is defined as an extremely well differentiated variant of cervical adenocarcinoma, with well-formed glands that resemble benign glands but show distinct nuclear anaplasia or evidence of stromal invasion. Thus, MDA is difficult to differentiate from other cervical hyperplastic lesions. Monoclonality is a major characteristic of most tumors, whereas normal tissue and reactive hyperplasia are polyclonal. Methods The clinicopathological features and clonality of MDA were investigated using laser microdissection and a clonality assay based on the polymorphism of androgen receptor (AR and X-chromosomal inactivation mosaicism in female somatic tissues. Results The results demonstrated that the glands were positive for CEA, Ki-67, and p53 and negative for estrogen receptor (ER, progesterone receptor (PR, and high-risk human papilloma virus (HPV DNA. The index of proliferation for Ki-67 was more than 50%. However, the stromal cells were positive for ER, PR, vimentin, and SM-actin. The clonal assay showed that MDA was monoclonal. Thus, our findings indicate that MDA is a true neoplasm but is not associated with high-risk HPV. Conclusions Diagnosis of MDA depends mainly on its clinical manifestations, the pathological feature that MDA glands are located deeper than the lower level of normal endocervical glands, and immunostaining.
Channel Deviation-Based Power Control in Body Area Networks.
Van, Son Dinh; Cotton, Simon L; Smith, David B
2018-05-01
Internet enabled body area networks (BANs) will form a core part of future remote health monitoring and ambient assisted living technology. In BAN applications, due to the dynamic nature of human activity, the off-body BAN channel can be prone to deep fading caused by body shadowing and multipath fading. Using this knowledge, we present some novel practical adaptive power control protocols based on the channel deviation to simultaneously prolong the lifetime of wearable devices and reduce outage probability. The proposed schemes are both flexible and relatively simple to implement on hardware platforms with constrained resources making them inherently suitable for BAN applications. We present the key algorithm parameters used to dynamically respond to the channel variation. This allows the algorithms to achieve a better energy efficiency and signal reliability in everyday usage scenarios such as those in which a person undertakes many different activities (e.g., sitting, walking, standing, etc.). We also profile their performance against traditional, optimal, and other existing schemes for which it is demonstrated that not only does the outage probability reduce significantly, but the proposed algorithms also save up to average transmit power compared to the competing schemes.
WKB theory of large deviations in stochastic populations
International Nuclear Information System (INIS)
Assaf, Michael; Meerson, Baruch
2017-01-01
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics—such as those determining population extinction, fixation or switching between different states—are presently in a focus of attention of statistical physicists. We review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation allows one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and multiple, but also briefly consider populations on heterogeneous networks and spatial populations. The spatial setting also allows one to study large fluctuations of the speed of biological invasions. Finally, we briefly discuss possible directions of future work. (topical review)
Obtaining TEM images with a uniform deviation parameter
International Nuclear Information System (INIS)
Eades, Alwyn
2006-01-01
In transmission electron microscopes made during the last quarter of a century, it has been impossible to take images in which the diffraction contrast conditions are uniform across the field of view. This is inconvenient when, for example, imaging dislocations at a relatively low magnification. The problem arises because modern microscopes use immersion lenses in which the sample sits in a high magnetic field. The resulting helical trajectories of the electrons at the sample plane mean that it is not possible to make a beam that is parallel at the sample. Results of a method to overcome this problem are presented. It is shown that a simple modification to the microscope (which, on a computer-controlled microscope, could be implemented in software) can be used to produce images in which the deviation parameter is essentially constant across many microns of image. By a happy accident, this method can be used, not only to correct for the helicity imparted by immersion lenses, but also to correct for buckling of the sample (up to a point)
Large deviations of the maximum eigenvalue in Wishart random matrices
International Nuclear Information System (INIS)
Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol
2007-01-01
We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions
Large deviations of the maximum eigenvalue in Wishart random matrices
Energy Technology Data Exchange (ETDEWEB)
Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)
2007-04-20
We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.
Large-deviation theory for diluted Wishart random matrices
Castillo, Isaac Pérez; Metz, Fernando L.
2018-03-01
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.
Gait Deviations in Children with Autism Spectrum Disorders: A Review
Directory of Open Access Journals (Sweden)
Deirdre Kindregan
2015-01-01
Full Text Available In recent years, it has become clear that children with autism spectrum disorders (ASDs have difficulty with gross motor function and coordination, factors which influence gait. Knowledge of gait abnormalities may be useful for assessment and treatment planning. This paper reviews the literature assessing gait deviations in children with ASD. Five online databases were searched using keywords “gait” and “autism,” and 11 studies were found which examined gait in childhood ASD. Children with ASD tend to augment their walking stability with a reduced stride length, increased step width and therefore wider base of support, and increased time in the stance phase. Children with ASD have reduced range of motion at the ankle and knee during gait, with increased hip flexion. Decreased peak hip flexor and ankle plantar flexor moments in children with ASD may imply weakness around these joints, which is further exhibited by a reduction in ground reaction forces at toe-off in children with ASD. Children with ASD have altered gait patterns to healthy controls, widened base of support, and reduced range of motion. Several studies refer to cerebellar and basal ganglia involvement as the patterns described suggest alterations in those areas of the brain. Further research should compare children with ASD to other clinical groups to improve assessment and treatment planning.
Wind power limit calculation basedon frequency deviation using Matlab
International Nuclear Information System (INIS)
Santos Fuentefria, Ariel; Salgado Duarte, Yorlandis; MejutoFarray, Davis
2017-01-01
The utilization of the wind energy for the production of electricity it’s a technology that has promoted itself in the last years, like an alternative before the environmental deterioration and the scarcity of the fossil fuels. When the power generation of wind energy is integrated into the electrical power systems, maybe take place problems in the frequency stability due to, mainly, the stochastic characteristic of the wind and the impossibility of the wind power control on behalf of the dispatchers. In this work, is make an analysis of frequency deviation when the wind power generation rise in an isolated electrical power system. This analysis develops in a computerized frame with the construction of an algorithm using Matlab, which allowed to make several simulations in order to obtain the frequency behavior for different loads and wind power conditions. Besides, it was determined the wind power limit for minimum, medium and maximum load. The results show that the greatest values on wind power are obtained in maximum load condition. However, the minimum load condition limit the introduction of wind power into the system. (author)
Deviations from excitation equilibrium in optically thick mercury arc plasmas
International Nuclear Information System (INIS)
Karabourniotis, D.; Couris, S.; Damelincourt, J.J.
1989-01-01
Up to date mercury arcs at pressure greater than 1 atm have been investigated as plasma systems in local thermodynamic equilibrium (LTE) state. These studies have been motivated by the applications of mercury arcs, e.g., in the lighting industry. The LTE-assumption simplifies the use of spectroscopic diagnostics and the performance of species-concentration calculations. A high pressure mercury arc of about 1 atm had been considered in two possibilities: excitation and gas temperatures are the same, the electron temperature is higher and excitation and electron temperatures are the same, the gas temperature is lower. Recent measurements in mercury arcs reveal the existence of severe departures from thermal equilibrium and suggest the absence of excitation equilibrium in the axis and in the periphery in such an arc. The deviation from equilibrium leads to complicated distributions, such that the system cannot be described correctly by any single temperature. This becomes quite complicated when plasma inhomogeneity and strong reabsorption of the radiation are present
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Liouville's equation and radiative acceleration in general relativity
International Nuclear Information System (INIS)
Keane, A.J.
1999-01-01
spacetimes. In the case of the Schwarzschild spacetime we find a solution of the Liouville equation which is invariant under the Killing vector symmetries and we adopt this as our model radiation field. Once a particular solution has been chosen the radiation field has been specified completely throughout the spacetime. In chapter 4 we investigate null and timelike geodesics in the Schwarzschild spacetime. Studying the null geodesics allows us to determine the viewing angles, that is, the (semi) angular size of the compact object as viewed by a stationary observer at an arbitrary point in the spacetime. The timelike geodesics are the trajectories of the (massive) test particles subject to no external radiation force and therefore constitute a limiting case of the radiative acceleration results. Given the radiation field one can calculate the radiation pressure force and because of special relativistic effects, the radiation pressure force experienced by the particle becomes velocity dependent. In chapter 5 we integrate the equations of motion for the case of purely radial motion in the Thomson limit. In this case we can obtain a tractable analytic expression for the solution in phase space, which can be compared with the high frequency case. In this chapter we consider a relativistic critical luminosity of a compact object, i.e. a relativistic Eddington luminosity. We also introduce and discuss terminal velocities and saturation velocities associated with a particular compact object. The terminal velocity of a radiation field is the 3-velocity required to annul the radiation pressure force on the test particle, neglecting the influence of any gravitational force on the particle. The saturation velocity is defined in the same way except the gravitational force is included. The saturation velocities are of course highly frequency dependent and provide important information about the dynamics of the system. In chapter 6 we discuss the Compton differential cross-section for
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Deviations from the Boltzmann distribution in vibrationally excited gas flows
International Nuclear Information System (INIS)
Offenhaeuser, F.; Frohn, A.
1986-01-01
A new model for the exchange of vibrational energy in one-dimensional flows of CO 2 -H 2 O-N 2 -O 2 -He gas mixtures is presented. In contrast to previous models, the assumption of local Boltzmann distributions for the vibrational degrees of freedom is not required. This generalization was achieved by the assumption that the molecules are harmonic oscillators with one or more degrees of freedom represented by finite numbers of energy levels. The population densities of these energy levels are coupled by a set of rate equations. It is shown that in some cases of molecular gas flow the Boltzmann distribution for the vibrational degrees of freedom may be disturbed. 12 references
Outcomes of minimally invasive strabismus surgery for horizontal deviation.
Merino, P; Blanco Domínguez, I; Gómez de Liaño, P
2016-02-01
To study the outcomes of minimally invasive strabismus surgery (MISS) for treating horizontal deviation Case Series of the first 26 consecutive patients operated on using the MISS technique in our hospital from February 2010 to March 2014. A total of 40 eyes were included: 26 patients (mean age: 7.7 years old ± 4.9); 34.61%: male. A total of 43 muscles were operated on: 20 medial, and 23 lateral recti; 28 recessions (range: 3-7.5mm), 6 resections (6-7 mm), and 9 plications (6.5-7.5 mm) were performed. No significant difference was found (P>0.05) for visual acuity at postoperative day 1, and 6 months after surgery. A mild hyperaemia was observed in 29.27%, moderate in 48.78%, and severe in 21.95% at postoperative day 1 and in 63.41%, 31.70% and 4.87%, respectively, at 4 days after surgery. The complications observed were 4 intraoperative conjunctival haemorrhages, 1 scleral perforation, and 2 Tenon's prolapses. A conversion from MISS to a fornix approach was necessary in 1 patient because of bad visualization. The operating time range decreased from 30 to 15 minutes. The MISS technique has obtained good results in horizontal strabismus surgery. The conjunctival inflammation was mild in most of the cases at postoperative day 4. The visual acuity was stable during follow-up, and operating time decreased after a 4-year learning curve. Copyright © 2015 Sociedad Española de Oftalmología. Published by Elsevier España, S.L.U. All rights reserved.
Petrothermal heat extraction using a single deviated well (Horstberg, revisited)
Ghergut, Julia; Behrens, Horst; Vogt, Esther; Bartetzko, Anne; Sauter, Martin
2013-04-01
The single-well tracer test conducted (Behrens et al. 2006) in conjunction with waterfrac experiments at Horstberg is re-examined with a view at four basic issues: why single-well? why fracturing? why tracers? does this only work at Horstberg, or can it work almost anywhere else in the Northern-German sedimentary basin? Heat and tracer transport within a composite reservoir (impermeable matrix + waterfrac + permeable layer), as accessed by a single deviated well, turn out to fit into a surprisingly simple description, as the plain (arithmetic) sum of certain petrothermal-type and aquifer-type contributions, whose weighting relative to each other can vary from site to site, depending upon stratigraphy and upon wellbore geometry. At Horstberg, within the particular formations tested ('Volpriehausen', 'Detfurth', 'Solling', comprising mainly claystone and sandstone layers), thermal lifetime results to be petrothermally-dominated, while tracer residence times prove to be 'aquifer'-dominated. Despite this disparity, the reservoir's thermal lifetime can reliably be predicted from tracer test results. What cannot be determined from waterfrac flow-path tracing is the very waterfrac's aperture. Aperture uncertainty, however, does not impede upon thermal lifetime predictability. The results of the semi-analytical approach are confirmed by numerical simulations using a FE model that includes more details of hydrogeological heterogeneity for the Horstberg site. They are complemented by a parameter sensitivity analysis. ACKNOWLEDGEMENT: This study is funded by MWK Niedersachsen (Lower-Saxony's Science and Culture Ministry) and by Baker Hughes (Celle) within task unit G6 of the Collaborative Research Project 'gebo' ('Geothermal Energy and High-Performance Drilling').
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Sea Surface Height Deviation, Aviso, 0.25 degrees, Global, Science Quality
National Oceanic and Atmospheric Administration, Department of Commerce — Aviso Sea Surface Height Deviation is the deviation from the mean geoid as measured from 1993 - 1995. This is Science Quality data.
Ambitwistor strings and the scattering equations at one loop
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Casali, Eduardo; Skinner, David [Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2014-04-15
Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo-He-Yuan formulæ for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulæ in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang-Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non-separating and separating degenerations.
Large deviations for Markov chains in the positive quadrant
Energy Technology Data Exchange (ETDEWEB)
Borovkov, A A; Mogul' skii, A A [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2001-10-31
The paper deals with so-called N-partially space-homogeneous time-homogeneous Markov chains X(y,n), n=0,1,2,..., X(y,0)=y, in the positive quadrant. These Markov chains are characterized by the following property of the transition probabilities P(y,A)=P(X(y,1) element of A): for some N{>=}0 the measure P(y,dx) depends only on x{sub 2}, y{sub 2}, and x{sub 1}-y{sub 1} in the domain x{sub 1}>N, y{sub 1}>N, and only on x{sub 1}, y{sub 1}, and x{sub 2}-y{sub 2} in the domain x{sub 2}>N, y{sub 2}>N. For such chains the asymptotic behaviour is found for a fixed set B as s{yields}{infinity}, |x|{yields}{infinity}, and n{yields}{infinity}. Some other conditions on the growth of parameters are also considered, for example, |x-y|{yields}{infinity}, |y|{yields}{infinity}. A study is made of the structure of the most probable trajectories, which give the main contribution to this asymptotics, and a number of other results pertaining to the topic are established. Similar results are obtained for the narrower class of 0-partially homogeneous ergodic chains under less restrictive moment conditions on the transition probabilities P(y,dx). Moreover, exact asymptotic expressions for the probabilities P(X(0,n) element of x+B) are found for 0-partially homogeneous ergodic chains under some additional conditions. The interest in partially homogeneous Markov chains in positive octants is due to the mathematical aspects (new and interesting problems arise in the framework of general large deviation theory) as well as applied issues, for such chains prove to be quite accurate mathematical models for numerous basic types of queueing and communication networks such as the widely known Jackson networks, polling systems, or communication networks associated with the ALOHA algorithm. There is a vast literature dealing with the analysis of these objects. The present paper is an attempt to find the extent to which an asymptotic analysis is possible for Markov chains of this type in their general
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Illusory shadow person causing paradoxical gaze deviations during temporal lobe seizures
Zijlmans, M.; van Eijsden, P.; Ferrier, C. H.; Kho, K. H.; van Rijen, P. C.; Leijten, F. S. S.
Generally, activation of the frontal eye field during seizures can cause versive (forced) gaze deviation, while non-versive head deviation is hypothesised to result from ictal neglect after inactivation of the ipsilateral temporoparietal area. Almost all non-versive head deviations occurring during
7 CFR 400.174 - Notification of deviation from financial standards.
2010-01-01
... 7 Agriculture 6 2010-01-01 2010-01-01 false Notification of deviation from financial standards... Agreement-Standards for Approval; Regulations for the 1997 and Subsequent Reinsurance Years § 400.174 Notification of deviation from financial standards. An insurer must immediately advise FCIC if it deviates from...
1 CFR 21.14 - Deviations from standard organization of the Code of Federal Regulations.
2010-01-01
... 1 General Provisions 1 2010-01-01 2010-01-01 false Deviations from standard organization of the... CODIFICATION General Numbering § 21.14 Deviations from standard organization of the Code of Federal Regulations. (a) Any deviation from standard Code of Federal Regulations designations must be approved in advance...
48 CFR 1352.219-71 - Notification to delay performance (Deviation).
2010-10-01
... performance (Deviation). 1352.219-71 Section 1352.219-71 Federal Acquisition Regulations System DEPARTMENT OF....219-71 Notification to delay performance (Deviation). As prescribed in 48 CFR 1319.811-3(b), insert the following clause: Notification To Delay Performance (Deviation) (APR 2010) The contractor shall...
Hazards and preventive measures of well deviation in well construction of in-situ leaching
International Nuclear Information System (INIS)
Zou Wenjie; Chen Shihe
2006-01-01
Whether the in-situ leaching method is successful depends on the quality of borehole engineering to a great extent. There are lots of factors that affect the quality, and the well deviation is one of notable problems. The hazards and causes of the well deviation are analyzed. The preventive measures and the methods of rectifying the deviation are put forward. (authors)
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)
2010-05-15
Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F{<=}f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less
International Nuclear Information System (INIS)
Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi
2010-01-01
Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F≤f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less completion time
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
Patil, Sujata S.; Mirgane, Sunil R.; Arbad, Balasaheb R.
2014-01-01
Densities and viscosities for the four binary liquid mixtures of methyl acrylate, ethyl acrylate, butyl acrylate and methyl methacrylate with hexane-1-ol at temperatures 303.15 and 313.15 K and at atmospheric pressure were measured over the entire composition range. These values were used to calculate excess molar volumes and deviation in viscosities which were fitted to Redlich–Kister polynomial equation. Recently proposed Jouyban Acree model was also used to correlate the experimental value...
Scaphoid and lunate movement in different ranges of carpal radioulnar deviation.
Tang, Jin Bo; Xu, Jing; Xie, Ren Guo
2011-01-01
We aimed to investigate scaphoid and lunate movement in radial deviation and in slight and moderate ulnar deviation ranges in vivo. We obtained computed tomography scans of the right wrists from 20° radial deviation to 40° ulnar deviation in 20° increments in 6 volunteers. The 3-dimensional bony structures of the wrist, including the distal radius and ulna, were reconstructed with customized software. The changes in position of the scaphoid and lunate along flexion-extension motion (FEM), radioulnar deviation (RUD), and supination-pronation axes in 3 parts--radial deviation and slight and moderate ulnar deviation--of the carpal RUD were calculated and analyzed. During carpal RUD, scaphoid and lunate motion along 3 axes--FEM, RUD, and supination-pronation--were the greatest in the middle third of the measured RUD (from neutral position to 20° ulnar deviation) and the smallest in radial deviation. Scaphoid motion along the FEM, RUD, and supination-pronation axes in the middle third was about half that in the entire motion range. In the middle motion range, lunate movement along the FEM and RUD axes was also the greatest. During carpal RUD, the greatest scaphoid and lunate movement occurs in the middle of the arc--slight ulnar deviation--which the wrist frequently adopts to accomplish major hand actions. At radial deviation, scaphoid and lunate motion is the smallest. Copyright © 2011 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either