Singularities of affine fibrations in the regularity theory of Fourier integral operators

International Nuclear Information System (INIS)

Ruzhansky, M V

2000-01-01

We consider regularity properties of Fourier integral operators in various function spaces. The most interesting case is the L p spaces, for which survey of recent results is given. For example, sharp orders are known for operators satisfying the so-called smooth factorization condition. Here this condition is analyzed in both real and complex settings. In the letter case, conditions for the continuity of Fourier integral operators are related to singularities of affine fibrations in C n (or subsets of C n ) specified by the kernels of Jacobi matrices of holomorphic maps. Singularities of such fibrations are analyzed in this paper in the general case. In particular, it is shown that if the dimension n or the rank of the Jacobi matrix is small, then all singularities of an affine fibration are removable. The fibration associated with a Fourier integral operator is given by the kernels of the Hessian of the phase function of the operator. On the basis of an analysis of singularities for operators commuting with translations we show in a number of cases that the factorization condition is satisfied, which leads to L p estimates for operators. In other cases, examples are given in which the factorization condition fails. The results are applied to deriving L p estimates for solutions of the Cauchy problem for hyperbolic partial differential operators

Timelike naked singularity

International Nuclear Information System (INIS)

Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis

2004-01-01

We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture

On preconditioning techniques for dense linear systems arising from singular boundary integral equations

Energy Technology Data Exchange (ETDEWEB)

Chen, Ke [Univ. of Liverpool (United Kingdom)

1996-12-31

We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.

Coloured phase singularities

International Nuclear Information System (INIS)

Berry, M.V.

2002-01-01

For illumination with white light, the spectra near a typical isolated phase singularity (nodal point of the component wavelengths) can be described by a universal function of position, up to linear distortion and a weak dependence on the spectrum of the source. The appearance of the singularity when viewed by a human observer is predicted by transforming the spectrum to trichromatic variables and chromaticity coordinates, and then rendering the colours, scaled to constant luminosity, on a computer monitor. The pattern far from the singularity is a white that depends on the source temperature, and the centre of the pattern is flanked by intensely coloured 'eyes', one orange and one blue, separated by red, and one of the eyes is surrounded by a bright white circle. Only a small range of possible colours appears near the singularity; in particular, there is no green. (author)

The index of Fourier integral operators on manifolds with conical singularities

International Nuclear Information System (INIS)

Nazaikinskii, Vladimir E; Sternin, B Yu; Schulze, B-W

2001-01-01

We describe homogeneous canonical transformations of the cotangent bundle of a manifold with conical singular points and compute the index of an elliptic Fourier integral operator obtained by the quantization of such a transformation. The answer involves the index of an elliptic Fourier integral operator on a smooth manifold and the residues of the conormal symbol

Singular integral equations boundary problems of function theory and their application to mathematical physics

CERN Document Server

Muskhelishvili, N I

2011-01-01

Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem

Weak-noise limit of a piecewise-smooth stochastic differential equation.

Science.gov (United States)

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Quantum dress for a naked singularity

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Marc Casals

2016-09-01

Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.

Energy conditions and spacetime singularities

International Nuclear Information System (INIS)

Tipler, F.J.

1978-01-01

In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete

Holder continuity of bounded weak solutions to generalized parabolic p-Laplacian equations II: singular case

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Sukjung Hwang

2015-11-01

Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1weak solution is locally Holder continuous with some degree of commonality between degenerate and singular types. By using geometric characters, our proof does not rely on any of alternatives which is based on the size of solutions.

On weakly singular and fully nonlinear travelling shallow capillary–gravity waves in the critical regime

Energy Technology Data Exchange (ETDEWEB)

Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)

2017-05-25

In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.

Singularities of Type-Q ABS Equations

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James Atkinson

2011-07-01

Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.

Solving differential equations for Feynman integrals by expansions near singular points

Science.gov (United States)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Singular and Marcinkiewicz integrals with H1 kernels on product spaces

International Nuclear Information System (INIS)

Chen, Jiecheng; Wang, Meng; Fan, Dashan

2008-08-01

In this paper we shall prove that for Ω is part of H 1 (S n-1 x S m-1 ), which satisfies the cancellation condition ∫ S n-1 Ω(x ' , y ' )dx ' = ∫ S m-1 Ω(x ' , y ' )dy ' = 0 (A(x ' , y ' ) is part of S n-1 x S m-1 , the Calderon-Zygmund singular integral operator T Ω , its maximal operator T Ω * and the Marcinkiewicz integral operator μ Ω are bounded on L p (R n x R m for 1 < p < ∞. (author)

Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

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Gemechis File

2012-01-01

Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

Science.gov (United States)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Band structure of an electron in a kind of periodic potentials with singularities

Science.gov (United States)

Hai, Kuo; Yu, Ning; Jia, Jiangping

2018-06-01

Noninteracting electrons in some crystals may experience periodic potentials with singularities and the governing Schrödinger equation cannot be defined at the singular points. The band structure of a single electron in such a one-dimensional crystal has been calculated by using an equivalent integral form of the Schrödinger equation. Both the perturbed and exact solutions are constructed respectively for the cases of a general singular weak-periodic system and its an exactly solvable version, Kronig-Penney model. Any one of them leads to a special band structure of the energy-dependent parameter, which results in an effective correction to the previous energy-band structure and gives a new explanation for forming the band structure. The used method and obtained results could be a valuable aid in the study of energy bands in solid-state physics, and the new explanation may trigger investigation to different physical mechanism of electron band structures.

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Science.gov (United States)

Boukraa, S.; Hassani, S.; Maillard, J.-M.

2012-12-01

Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard-Fuchs systems of two-variables ‘above’ Calabi-Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ(n), corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ(3) and χ(4), that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ(n)s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi-Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non-holonomic anisotropic full

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

International Nuclear Information System (INIS)

Boukraa, S; Hassani, S; Maillard, J-M

2012-01-01

Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard–Fuchs systems of two-variables ‘above’ Calabi–Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ (n) , corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ (3) and χ (4) , that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ (n) s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi–Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non

Integrated Giant Magnetoresistance Technology for Approachable Weak Biomagnetic Signal Detections.

Science.gov (United States)

Shen, Hui-Min; Hu, Liang; Fu, Xin

2018-01-07

With the extensive applications of biomagnetic signals derived from active biological tissue in both clinical diagnoses and human-computer-interaction, there is an increasing need for approachable weak biomagnetic sensing technology. The inherent merits of giant magnetoresistance (GMR) and its high integration with multiple technologies makes it possible to detect weak biomagnetic signals with micron-sized, non-cooled and low-cost sensors, considering that the magnetic field intensity attenuates rapidly with distance. This paper focuses on the state-of-art in integrated GMR technology for approachable biomagnetic sensing from the perspective of discipline fusion between them. The progress in integrated GMR to overcome the challenges in weak biomagnetic signal detection towards high resolution portable applications is addressed. The various strategies for 1/ f noise reduction and sensitivity enhancement in integrated GMR technology for sub-pT biomagnetic signal recording are discussed. In this paper, we review the developments of integrated GMR technology for in vivo/vitro biomagnetic source imaging and demonstrate how integrated GMR can be utilized for biomagnetic field detection. Since the field sensitivity of integrated GMR technology is being pushed to fT/Hz 0.5 with the focused efforts, it is believed that the potential of integrated GMR technology will make it preferred choice in weak biomagnetic signal detection in the future.

(Weakly) three-dimensional caseology

International Nuclear Information System (INIS)

Pomraning, G.C.

1996-01-01

The singular eigenfunction technique of Case for solving one-dimensional planar symmetry linear transport problems is extended to a restricted class of three-dimensional problems. This class involves planar geometry, but with forcing terms (either boundary conditions or internal sources) which are weakly dependent upon the transverse spatial variables. Our analysis involves a singular perturbation about the classic planar analysis, and leads to the usual Case discrete and continuum modes, but modulated by weakly dependent three-dimensional spatial functions. These functions satisfy parabolic differential equations, with a different diffusion coefficient for each mode. Representative one-speed time-independent transport problems are solved in terms of these generalised Case eigenfunctions. Our treatment is very heuristic, but may provide an impetus for more rigorous analysis. (author)

The dominant balance at cosmological singularities

International Nuclear Information System (INIS)

Cotsakis, Spiros; Barrow, John D

2007-01-01

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity

On Borel singularities in quantum field theory

International Nuclear Information System (INIS)

Chadha, S.; Olesen, P.

1977-10-01

The authors consider the effective one-loop Lagrangian in a constant electric field. It is shown that perturbation theory behaves as n factorial giving rise to singularities in the Borel plane. Comparing with the known exact result it is shown how to integrate these singularities. It is suggested that renormalons in QED and QCD should be integrated in a similar way. A speculation is made on a possible interpretation of this integration. (Auth.)

Quantum healing of classical singularities in power-law spacetimes

Energy Technology Data Exchange (ETDEWEB)

Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)

2007-07-07

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.

Dark energy and dark matter perturbations in singular universes

International Nuclear Information System (INIS)

Denkiewicz, Tomasz

2015-01-01

We discuss the evolution of density perturbations of dark matter and dark energy in cosmological models which admit future singularities in a finite time. Up to now geometrical tests of the evolution of the universe do not differentiate between singular universes and ΛCDM scenario. We solve perturbation equations using the gauge invariant formalism. The analysis shows that the detailed reconstruction of the evolution of perturbations within singular cosmologies, in the dark sector, can exhibit important differences between the singular universes models and the ΛCDM cosmology. This is encouraging for further examination and gives hope for discriminating between those models with future galaxy weak lensing experiments like the Dark Energy Survey (DES) and Euclid or CMB observations like PRISM and CoRE

Painleve singularity analysis applied to charged particle dynamics during reconnection

International Nuclear Information System (INIS)

Larson, J.W.

1992-01-01

For a plasma in the collisionless regime, test-particle modelling can lend some insight into the macroscopic behavior of the plasma, e.g. conductivity and heating. A common example for which this technique is used is a system with electric and magnetic fields given by B = δyx + zy + yz and E = εz, where δ, γ, and ε are constant parameters. This model can be used to model plasma behavior near neutral lines, (γ = 0), as well as current sheets (γ = 0, δ = 0). The integrability properties of the particle motion in such fields might affect the plasma's macroscopic behavior, and the author has asked the question open-quotes For what values of δ, γ, and ε is the system integrable?close quotes To answer this question, the author has employed Painleve singularity analysis, which is an examination of the singularity properties of a test particle's equations of motion in the complex time plane. This analysis has identified two field geometries for which the system's particle dynamics are integrable in terms of the second Painleve transcendent: the circular O-line case and the case of the neutral sheet configuration. These geometries yield particle dynamics that are integrable in the Liouville sense (i.e., there exist the proper number of integrals in involution) in an extended phase space which includes the time as a canonical coordinate, and this property is also true for nonzero γ. The singularity property tests also identified a large, dense set of X-line and O-line field geometries that yield dynamics that may possess the weak Painleve property. In the case of the X-line geometries, this result shows little relevance to the physical nature of the system, but the existence of a dense set of elliptical O-line geometries with this property may be related to the fact that for ε positive, one can construct asymptotic solutions in the limit t → ∞

A Good $\\lambda$ Estimate for Multilinear Commutator of Singular Integral on Spaces of Homogeneous Type

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Zhang Qian

2011-04-01

Full Text Available In this paper, a good $\\lambda$ estimate for the multilinear commutator associated to the singular integral operator on the spaces of homogeneous type is obtained. Under this result, we get the$(L^p(X,L^q(X$-boundedness of the multilinear commutator.

New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

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Snezhana Georgieva Gocheva-Ilieva

2013-01-01

Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.

Sporadic simple groups and quotient singularities

International Nuclear Information System (INIS)

Cheltsov, I A; Shramov, C A

2013-01-01

We show that if a faithful irreducible representation of a central extension of a sporadic simple group with centre contained in the commutator subgroup gives rise to an exceptional (resp. weakly exceptional but not exceptional) quotient singularity, then that simple group is the Hall-Janko group (resp. the Suzuki group)

Mapping local singularities using magnetic data to investigate the volcanic rocks of the Qikou depression, Dagang oilfield, eastern China

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G. Chen

2013-07-01

Full Text Available The spatial structural characteristics of geological anomaly, including singularity and self-similarity, can be analysed using fractal or multifractal modelling. Here we apply the multifractal methods to potential fields to demonstrate that singularities can characterise geological bodies, including rock density and magnetic susceptibility. In addition to enhancing weak gravity and magnetic anomalies with respect to either strong or weak background levels, the local singularity index (α ≈ 2 can be used to delineate the edges of geological bodies. Two models were established to evaluate the effectiveness of mapping singularities for extracting weak anomalies and delineating edges of buried geological bodies. The Qikou depression of the Dagang oilfield in eastern China has been chosen as a study area for demonstrating the extraction of weak anomalies of volcanic rocks, using the singularity mapping technique to analyse complex magnetic anomalies caused by complex geological background. The results have shown that the singularities of magnetic data mapped in the paper are associated with buried volcanic rocks, which have been verified by both drilling and seismic survey, and the S–N and E–W faults in the region. The targets delineated for deeply seated faults and volcanic rocks in the Qikou depression should be further investigated for the potential application in undiscovered oil and gas reservoirs exploration.

Singularly perturbed volterra integro-differential equations | Bijura ...

African Journals Online (AJOL)

Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

On the behaviour of Navier–Stokes equations near a possible singular point

International Nuclear Information System (INIS)

Kang, Kyungkeun; Lee, Jihoon

2010-01-01

We show that if a singularity of suitable weak solutions to Navier–Stokes equations occurs, then either p or at least two of ∂ i v i , i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂ r v r is not bounded both below and above near a singular point, if it exists

An Exact Solution of the Binary Singular Problem

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Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

The Geometry of Black Hole Singularities

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Ovidiu Cristinel Stoica

2014-01-01

Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

Singularities in the nonisotropic Boltzmann equation

International Nuclear Information System (INIS)

Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

1987-09-01

We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

Weakly oval electron lense

International Nuclear Information System (INIS)

Daumenov, T.D.; Alizarovskaya, I.M.; Khizirova, M.A.

2001-01-01

The method of the weakly oval electrical field getting generated by the axially-symmetrical field is shown. Such system may be designed with help of the cylindric form coaxial electrodes with the built-in quadrupole duplet. The singularity of the indicated weakly oval lense consists of that it provides the conducting both mechanical and electronic adjustment. Such lense can be useful for elimination of the near-axis astigmatism in the electron-optical system

Singularity confinement for maps with the Laurent property

International Nuclear Information System (INIS)

Hone, A.N.W.

2007-01-01

The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: The iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities

Non-singular spiked harmonic oscillator

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Guardiola, R.

1990-01-01

A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

Science.gov (United States)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type

International Nuclear Information System (INIS)

Iakovlev, Serguei I.

2006-01-01

In L 2 (R) we consider a family of self adjoint operators of the Friedrichs model: A m =|t| m +V. Here |t| m is the operator of multiplication by the corresponding function of the independent variable t element of R, and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel ν(t,x) satisfying some smoothness condition. These absolute type operators have one singular point of order m>0. Conditions on the kernel ν(t,x) are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity. The sharpness of these conditions is confirmed by counterexamples

Multi-particle phase space integration with arbitrary set of singularities in CompHEP

International Nuclear Information System (INIS)

Kovalenko, D.N.; Pukhov, A.E.

1997-01-01

We describe an algorithm of multi-particle phase space integration for collision and decay processes realized in CompHEP package version 3.2. In the framework of this algorithm it is possible to regularize an arbitrary set of singularities caused by virtual particle propagators. The algorithm is based on the method of the recursive representation of kinematics and on the multichannel Monte Carlo approach. CompHEP package is available by WWW: http://theory.npi.msu.su/pukhov/comphep. html (orig.)

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

International Nuclear Information System (INIS)

Levanony, Dana; Ori, Amos

2010-01-01

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

Science.gov (United States)

Levanony, Dana; Ori, Amos

2010-05-01

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Shocks and finite-time singularities in Hele-Shaw flow

Energy Technology Data Exchange (ETDEWEB)

Teodorescu, Razvan [Los Alamos National Laboratory; Wiegmann, P [UNIV OF MONTREAL; Lee, S-y [UNIV OF CHICAGO

2008-01-01

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

Science.gov (United States)

Liu, Jian-Guo; Xu, Xiangsheng

2018-04-01

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

Naked singularity formation in Brans-Dicke theory

Energy Technology Data Exchange (ETDEWEB)

Ziaie, Amir Hadi; Atazadeh, Khedmat [Department of Physics, Shahid Beheshti University, Evin, Tehran 19839 (Iran, Islamic Republic of); Tavakoli, Yaser, E-mail: am.ziaie@mail.sbu.ac.i, E-mail: k-atazadeh@sbu.ac.i, E-mail: tavakoli@ubi.p [Departamento de Fisica, Universidade da Beira Interior, Rua Marques d' Avila e Bolama, 6200 Covilha (Portugal)

2010-04-07

Gravitational collapse of the Brans-Dicke scalar field with non-zero potential in the presence of matter fluid obeying the barotropic equation of state, p = wrho, is studied. Utilizing the concept of the expansion parameter, it is seen that the cosmic censorship conjecture may be violated for w=-1/3 and w=-2/3 which correspond to the cosmic string and domain wall, respectively. We have shown that physically, it is the rate of collapse that governs the formation of a black hole or a naked singularity as the final fate of dynamical evolution and only for these two cases can the singularity be naked as the collapse end state. Also the weak energy condition is satisfied by the collapsing configuration.

One Critical Case in Singularly Perturbed Control Problems

Science.gov (United States)

Sobolev, Vladimir

2017-02-01

The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.

Papapetrou's naked singularity is a strong curvature singularity

International Nuclear Information System (INIS)

Hollier, G.P.

1986-01-01

Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Weak cosmic censorship: as strong as ever.

Science.gov (United States)

Hod, Shahar

2008-03-28

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.

A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

Energy Technology Data Exchange (ETDEWEB)

Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)

2017-12-15

We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

Nature of protein family signatures: insights from singular value analysis of position-specific scoring matrices.

Directory of Open Access Journals (Sweden)

Akira R Kinjo

Full Text Available Position-specific scoring matrices (PSSMs are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.

CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

International Nuclear Information System (INIS)

Benzley, S.E.; Beisinger, Z.E.

1981-01-01

1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

Conformally-flat, non-singular static metric in infinite derivative gravity

Science.gov (United States)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Singular perturbation techniques in the gravitational self-force problem

International Nuclear Information System (INIS)

Pound, Adam

2010-01-01

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.

Papapetrou's naked singularity is a strong curvature singularity

Energy Technology Data Exchange (ETDEWEB)

Hollier, G.P.

1986-11-01

Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.

A novel strategy for signal denoising using reweighted SVD and its applications to weak fault feature enhancement of rotating machinery

Science.gov (United States)

Zhao, Ming; Jia, Xiaodong

2017-09-01

Singular value decomposition (SVD), as an effective signal denoising tool, has been attracting considerable attention in recent years. The basic idea behind SVD denoising is to preserve the singular components (SCs) with significant singular values. However, it is shown that the singular values mainly reflect the energy of decomposed SCs, therefore traditional SVD denoising approaches are essentially energy-based, which tend to highlight the high-energy regular components in the measured signal, while ignoring the weak feature caused by early fault. To overcome this issue, a reweighted singular value decomposition (RSVD) strategy is proposed for signal denoising and weak feature enhancement. In this work, a novel information index called periodic modulation intensity is introduced to quantify the diagnostic information in a mechanical signal. With this index, the decomposed SCs can be evaluated and sorted according to their information levels, rather than energy. Based on that, a truncated linear weighting function is proposed to control the contribution of each SC in the reconstruction of the denoised signal. In this way, some weak but informative SCs could be highlighted effectively. The advantages of RSVD over traditional approaches are demonstrated by both simulated signals and real vibration/acoustic data from a two-stage gearbox as well as train bearings. The results demonstrate that the proposed method can successfully extract the weak fault feature even in the presence of heavy noise and ambient interferences.

The design of high performance weak current integrated amplifier

International Nuclear Information System (INIS)

Chen Guojie; Cao Hui

2005-01-01

A design method of high performance weak current integrated amplifier using ICL7650 operational amplifier is introduced. The operating principle of circuits and the step of improving amplifier's performance are illustrated. Finally, the experimental results are given. The amplifier has programmable measurement range of 10 -9 -10 -12 A, automatic zero-correction, accurate measurement, and good stability. (authors)

Distribution of flux vacua around singular points in Calabi-Yau moduli space

International Nuclear Information System (INIS)

Eguchi, Tohru; Tachikawa, Yuji

2006-01-01

We study the distribution of type-IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P 1 , Argyres-Douglas point etc, using the Ashok-Douglas density det (R+ω). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in a compact Calabi-Yau manifold

Can we observationally test the weak cosmic censorship conjecture?

International Nuclear Information System (INIS)

Kong, Lingyao; Malafarina, Daniele; Bambi, Cosimo

2014-01-01

In general relativity, gravitational collapse of matter fields ends with the formation of a spacetime singularity, where the matter density becomes infinite and standard physics breaks down. According to the weak cosmic censorship conjecture, singularities produced in the gravitational collapse cannot be seen by distant observers and must be hidden within black holes. The validity of this conjecture is still controversial and at present we cannot exclude that naked singularities can be created in our Universe from regular initial data. In this paper, we study the radiation emitted by a collapsing cloud of dust and check whether it is possible to distinguish the birth of a black hole from the one of a naked singularity. In our simple dust model, we find that the properties of the radiation emitted in the two scenarios is qualitatively similar. That suggests that observational tests of the cosmic censorship conjecture may be very difficult, even in principle. (orig.)

Can we observationally test the weak cosmic censorship conjecture?

Energy Technology Data Exchange (ETDEWEB)

Kong, Lingyao; Malafarina, Daniele; Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China)

2014-08-15

In general relativity, gravitational collapse of matter fields ends with the formation of a spacetime singularity, where the matter density becomes infinite and standard physics breaks down. According to the weak cosmic censorship conjecture, singularities produced in the gravitational collapse cannot be seen by distant observers and must be hidden within black holes. The validity of this conjecture is still controversial and at present we cannot exclude that naked singularities can be created in our Universe from regular initial data. In this paper, we study the radiation emitted by a collapsing cloud of dust and check whether it is possible to distinguish the birth of a black hole from the one of a naked singularity. In our simple dust model, we find that the properties of the radiation emitted in the two scenarios is qualitatively similar. That suggests that observational tests of the cosmic censorship conjecture may be very difficult, even in principle. (orig.)

Spectral curves in gauge/string dualities: integrability, singular sectors and regularization

International Nuclear Information System (INIS)

Konopelchenko, Boris; Alonso, Luis Martínez; Medina, Elena

2013-01-01

We study the moduli space of the spectral curves y 2 = W′(z) 2 + f(z) which characterize the vacua of N=1 U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential W(z). The integrable structure of the Whitham equations is used to determine the spectral curves from their moduli. An alternative characterization of the spectral curves in terms of critical points of a family of polynomial solutions W to Euler–Poisson–Darboux equations is provided. The equations for these critical points are a generalization of the planar limit equations for one-cut random matrix models. Moreover, singular spectral curves with higher order branch points turn out to be described by degenerate critical points of W. As a consequence we propose a multiple scaling limit method of regularization and show that, in the simplest cases, it leads to the Painlevè-I equation and its multi-component generalizations. (paper)

Naked singularities are not singular in distorted gravity

Energy Technology Data Exchange (ETDEWEB)

Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)

2014-07-15

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Naked singularities are not singular in distorted gravity

Science.gov (United States)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Naked singularities are not singular in distorted gravity

International Nuclear Information System (INIS)

Garattini, Remo; Majumder, Barun

2014-01-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity

Computation at a coordinate singularity

Science.gov (United States)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar

Power quality and integration of wind farms in weak grids in India

Energy Technology Data Exchange (ETDEWEB)

Soerensen, P.; Hauge Madsen, P. [Risoe National Lab., Roskilde (Denmark). Wind Energy and Atmospheric Physics Dept.; Vikkelsoe, A.; Koelbaek Jensen, K. [Danske Elvaerkers Forening Udredningsafdelingen (DEFU), Lyngby (Denmark); Fathima, K.A.; Unnikrishnan, A.K.

2000-04-01

This is the final report of a joint Danish and Indian project' Power Quality and Integration of Wind Farms in Weak Grids'. The power quality issues have been studied and analysed with the Indian conditions as a case. On the basis of meetings with Danish wind turbine industry, Indian electricity boards, nodal agencies, wind turbine industry and authorities, the critical power quality as-pects in India have been identified. Measurements on selected wind farms and wind turbines have quantified the power quality, and analyses of power quality issues, especially reactive power compensation, have been performed. Based on measurements and analyses, preliminary recommendations for grid integration of wind turbines in weak grids have been formulated. (au)

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

Energy Technology Data Exchange (ETDEWEB)

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence RI 02912 (United States)

2016-03-14

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

International Nuclear Information System (INIS)

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

2016-01-01

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

Modelling of fluid flow in fractured porous media by the singular integral equations method

International Nuclear Information System (INIS)

Vu, M.N.

2012-01-01

This thesis aims to develop a method for numerical modelling of fluid flow through fractured porous media and for determination of their effective permeability by taking advantage of recent results based on formulation of the problem by Singular Integral Equations. In parallel, it was also an occasion to continue on the theoretical development and to obtain new results in this area. The governing equations for flow in such materials are reviewed first and mass conservation at the fracture intersections is expressed explicitly. Using the theory of potential, the general potential solutions are proposed in the form of a singular integral equation that describes the steady-state flow in and around several fractures embedded in an infinite porous matrix under a far-field pressure condition. These solutions represent the pressure field in the whole body as functions of the infiltration in the fractures, which fully take into account the fracture interaction and intersections. Closed-form solutions for the fundamental problem of fluid flow around a single fracture are derived, which are considered as the benchmark problems to validate the numerical solutions. In particular, the solution obtained for the case of an elliptical disc-shaped crack obeying to the Poiseuille law has been compared to that obtained for ellipsoidal inclusions with Darcy law.The numerical programs have been developed based on the singular integral equations method to resolve the general potential equations. These allow modeling the fluid flow through a porous medium containing a great number of fractures. Besides, this formulation of the problem also allows obtaining a semi-analytical infiltration solution over a single fracture depending on the matrice permeability, the fracture conductivity and the fracture geometry. This result is the important key to up-scaling the effective permeability of a fractured porous medium by using different homogenisation schemes. The results obtained by the self

Generalized Parton Distributions and their Singularities

Energy Technology Data Exchange (ETDEWEB)

Anatoly Radyushkin

2011-04-01

A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\\beta)/\\beta$ rather than with the usual parton density $f(\\beta)$. This results in a non-integrable singularity at $\\beta=0$ exaggerated by the fact that $f(\\beta)$'s, on their own, have a singular $\\beta^{-a}$ Regge behavior for small $\\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x,\\xi)$ that are finite and continuous at the "border point'' $x=\\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\\beta, \\alpha)$ into the "plus'' part $[f(\\beta,\\alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x,x)$ with the $D$-term function $D(\\alpha)$.

Anomalous singularities in the complex Kohn variational principle of quantum scattering theory

International Nuclear Information System (INIS)

Lucchese, R.R.

1989-01-01

Variational principles for symmetric complex scattering matrices (e.g., the S matrix or the T matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied

Algorithms in Singular

Directory of Open Access Journals (Sweden)

Hans Schonemann

1996-12-01

Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].

Singular Linear Differential Equations in Two Variables

NARCIS (Netherlands)

Braaksma, B.L.J.; Put, M. van der

2008-01-01

The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

Gap asymptotics in a weakly bent leaky quantum wire

Czech Academy of Sciences Publication Activity Database

Exner, Pavel; Kondej, S.

2015-01-01

Roč. 48, č. 49 (2015), s. 495301 ISSN 1751-8113 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : singular Schroedinger operators * delta interaction * leaky quantum wires * weak perturbation * asymptotic expansion Subject RIV: BE - Theoretical Physics Impact factor: 1.933, year: 2015

Singular instantons in Eddington-inspired-Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Arroja, Frederico; Chen, Che-Yu; Chen, Pisin; Yeom, Dong-han, E-mail: arroja@phys.ntu.edu.tw, E-mail: b97202056@gmail.com, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan (China)

2017-03-01

In this work, we investigate O (4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.

Educational process their different contents, singularities to the sculpture the Formation integral in university students

Directory of Open Access Journals (Sweden)

Laura Margarita Fernández-Martínez

2018-03-01

Full Text Available Presently article is approached important relating theoretical the in artistic education, that facilitate the formation integral in university students, the educational process their different contents, singularities to the sculpture artistic manifestation, with which one works methodologically. However, it is necessary to establish a methodological theoretical position in this respect to be able to evidence the relationship education-culture the understanding of the artistic education in that relationship and their contribution to the formation integral. From the didactic point of view, it is sustained in the basics of the teaching-learning process, related with the Didactics of the Superior Education and in the analysis and valuation of the components of the process of teaching learning where the dynamics of the relationships is revealed among these that it is constituted in a dialectical process where starting from the created conditions the fellow appropriates of the necessary tools for interaction with the reality.

Introduction to singularities

CERN Document Server

Ishii, Shihoko

2014-01-01

This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...

Bellman-Krein formula for an integral equation with kernel of the type k(x,y)=k(x - y) x- y sup(-α)

International Nuclear Information System (INIS)

Youssef, M.Y.A.; El Walik, S.A.

1976-08-01

With the aid of the Bellman-Krein formula for the resolvent, it is shown how to solve the integral equation with kernel of the type k(x,y)=k(x - y) x - ysup(-α), 0<α< n, i.e. the kernel with weak singularity

Surface Plasmon Singularities

Directory of Open Access Journals (Sweden)

Gabriel Martínez-Niconoff

2012-01-01

Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.

Lecture notes on mean curvature flow, barriers and singular perturbations

CERN Document Server

Bellettini, Giovanni

2013-01-01

The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.

Constructing Current Singularity in a 3D Line-tied Plasma

Science.gov (United States)

Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

2018-01-01

We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

OpenAIRE

Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane; Natarajan, S.; Rabczuk, T.

2013-01-01

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient ...

Quantum evolution across singularities

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg

2008-01-01

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space)

Integrability and the conformal field theory of the Higgs branch

International Nuclear Information System (INIS)

Sax, Olof Ohlsson; Sfondrini, Alessandro; Bogdan, Stefański Jr.

2015-01-01

In the context of the AdS 3 /CFT 2 correspondence, we investigate the Higgs branch CFT 2 . Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT 2 spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS 3 side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT 2 side of the correspondence.

Wentzel-Bardeen singularity in coupled Luttinger liquids: Transport properties

International Nuclear Information System (INIS)

Martin, T.

1994-01-01

The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated elections coupled to low energy acoustic phonons in one dimension. The exponents of various response functions are calculated, and their striking sensitivity to the Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons the equivalent of a phase diagram is established. By increasing the filling factor towards half filling the WB singularity is approached. This in turn suppresses antiferromagnetic fluctuations and drives the system towards the superconducting regime, via a new intermediate (metallic) phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions

A singularity extraction technique for computation of antenna aperture fields from singular plane wave spectra

DEFF Research Database (Denmark)

Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel

2008-01-01

An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...

Singular stochastic differential equations

CERN Document Server

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.

Loop quantum cosmology and singularities.

Science.gov (United States)

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

Weak convergence of the function-indexed integrated periodogram for infinite variance processes

DEFF Research Database (Denmark)

Can, Umut; Mikosch, Thomas Valentin; Samorodnitsky, Gennady

2010-01-01

constitute α-stable processes which have representations as infinite Fourier series with i.i.d. α-stable coefficients. The cases α ∈ (0, 1) and α ∈ [1, 2) are dealt with by rather different methods and under different assumptions on the classes of functions. For example, in contrast to the case α ∈ (0, 1......In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric α-stable innovations. Under suitable summability conditions on the series of the Fourier coefficients of the index functions, we show that the weak limits...

Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model

DEFF Research Database (Denmark)

Brøns, Morten; Desroches, Mathieu; Krupa, Martin

2015-01-01

In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...

A Connection between Singular Stochastic Control and Optimal Stopping

International Nuclear Information System (INIS)

Espen Benth, Fred; Reikvam, Kristin

2003-01-01

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions

Integration of singularity and zonality methods for prospectivity map of blind mineralization

Directory of Open Access Journals (Sweden)

samaneh safari

2016-12-01

Full Text Available Singularity based on fractal and multifractal is a technique for detection of depletion and enrichment for geochemical exploration, while the index of vertical geochemical zonality (Vz of Pb.Zn/Cu.Ag is a practical method for exploration of blind porphyry copper mineralization. In this study, these methods are combined for recognition, delineation, and enrichment of Vz in Jebal- Barez in the south of Iran. The studied area is located in the Shar-E-Babak–Bam ore field in the southern part of the Central Iranian volcano–plutonic magmatic arc. The region has a semiarid climate, mountainous topography, and poor vegetation cover. Seven hundreds samples of stream sedimentary were taken from the region. Geochemical data subset represent a total drainage basin area. Samples are analyzed for Cu, Zn, Ag, Pb, Au, W, As, Hg, Ba, Bi by atomic absorption method. Prospectivity map for blind mineralization is represented in this area. The results are in agreement with previous studies which have been focused in this region. Kerver is detected as the main blind mineralization in Jebal- Barz which had been previously intersected by drilled borehole for exploration purposes. In this research, it has been demonstrated that employing the singularity of geochemical zonality anomalies method, as opposed to using singularity of elements, improves mapping of mineral prospectivity.

Singularities in minimax optimization of networks

DEFF Research Database (Denmark)

Madsen, Kaj; Schjær-Jacobsen, Hans

1976-01-01

A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the li......A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used...

Volume-preserving normal forms of Hopf-zero singularity

International Nuclear Information System (INIS)

Gazor, Majid; Mokhtari, Fahimeh

2013-01-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto–Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple. (paper)

Volume-preserving normal forms of Hopf-zero singularity

Science.gov (United States)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

Coupled singular and non singular thermoelastic system and double lapalce decomposition methods

OpenAIRE

Hassan Gadain; Hassan Gadain

2016-01-01

In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples

Naked singularity, firewall, and Hawking radiation.

Science.gov (United States)

Zhang, Hongsheng

2017-06-21

Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

International Nuclear Information System (INIS)

Kirsch, W.; Martinelli, F.

1983-01-01

We consider the integrated density of states (IDS) rhosub(infinite)(lambda) of random Hamiltonian Hsub#betta#=-δ+Vsub#betta#, Vsub#betta# being a random field on Rsup(d) which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDSvertical stroke#betta#vertical stroke - 1 rho(lambda,Hsub(lambda)(#betta#)), #betta#is contained inRsup(d), around the thermodynamic limit rhosub(infinite)(lambda) is bounded from above by exp[-kvertical stroke#betta#vertical stroke], k>0. In this case rhosub(infinite)(lambda) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitz-type of singularity of rhosub(infinite)(lambda) as lambda->0 + in the case where Vsub#betta# is non-negative. More precisely we prove the following bound: rhosub(infinite)(lambda) 0 + k>0. This last result is then discussed in some examples. (orig.)

Finite-time future singularities in modified Gauss-Bonnet and F(R,G) gravity and singularity avoidance

International Nuclear Information System (INIS)

Bamba, Kazuharu; Odintsov, Sergei D.; Sebastiani, Lorenzo; Zerbini, Sergio

2010-01-01

We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from F(R,G)-gravity, where R and G are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of F(R,G)-gravity, we also investigate modified Gauss-Bonnet gravity, so-called F(G)-gravity. In particular, we reconstruct the F(G)-gravity and F(R,G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F(G)-gravity and F(R,G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory a non-singular one as well. (orig.)

Numerical method for solving integral equations of neutron transport. II

International Nuclear Information System (INIS)

Loyalka, S.K.; Tsai, R.W.

1975-01-01

In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)

Are naked singularities really visible

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; De Felice, F [Alberta Univ., Edmonton (Canada); Nobili, L [Padua Univ. (Italy). Ist. di Fisica

1978-12-09

The question whether a Kerr naked singularity is actually visible from infinity is investigated; it is shown that in fact any signal which could be emitted from the singularity is infinitely red-shifted. This implies that naked singularities would be indistinguishable from a black hole.

Residues and duality for singularity categories of isolated Gorenstein singularities

OpenAIRE

Murfet, Daniel

2009-01-01

We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.

String theory and cosmological singularities

Indian Academy of Sciences (India)

Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.

Automatic numerical integration methods for Feynman integrals through 3-loop

International Nuclear Information System (INIS)

De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K

2015-01-01

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)

On a class of singular hyperbolic equation with a weighted integral condition

Directory of Open Access Journals (Sweden)

Said Mesloub

1999-01-01

for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

Singular perturbation theory for interacting fermions in two dimensions

International Nuclear Information System (INIS)

Chubukov, A.V.; Maslov, D.L.; Gangadharaiah, S.; Glazman, L.I.

2004-11-01

We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a nonperturbative effect: an interaction with the zero-sound mode. Resuming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, C(T) ∝T 2 . It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in C(T) due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of C(T). We also obtain a general form of the non-analytic term in C(T), valid for the case of a generic Fermi liquid, i.e., beyond the perturbation theory. (author)

Holographic complexity and spacetime singularities

Energy Technology Data Exchange (ETDEWEB)

Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)

2016-01-15

We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

Holographic complexity and spacetime singularities

International Nuclear Information System (INIS)

Barbón, José L.F.; Rabinovici, Eliezer

2016-01-01

We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

Weak fault detection and health degradation monitoring using customized standard multiwavelets

Science.gov (United States)

Yuan, Jing; Wang, Yu; Peng, Yizhen; Wei, Chenjun

2017-09-01

Due to the nonobvious symptoms contaminated by a large amount of background noise, it is challenging to beforehand detect and predictively monitor the weak faults for machinery security assurance. Multiwavelets can act as adaptive non-stationary signal processing tools, potentially viable for weak fault diagnosis. However, the signal-based multiwavelets suffer from such problems as the imperfect properties missing the crucial orthogonality, the decomposition distortion impossibly reflecting the relationships between the faults and signatures, the single objective optimization and independence for fault prognostic. Thus, customized standard multiwavelets are proposed for weak fault detection and health degradation monitoring, especially the weak fault signature quantitative identification. First, the flexible standard multiwavelets are designed using the construction method derived from scalar wavelets, seizing the desired properties for accurate detection of weak faults and avoiding the distortion issue for feature quantitative identification. Second, the multi-objective optimization combined three dimensionless indicators of the normalized energy entropy, normalized singular entropy and kurtosis index is introduced to the evaluation criterions, and benefits for selecting the potential best basis functions for weak faults without the influence of the variable working condition. Third, an ensemble health indicator fused by the kurtosis index, impulse index and clearance index of the original signal along with the normalized energy entropy and normalized singular entropy by the customized standard multiwavelets is achieved using Mahalanobis distance to continuously monitor the health condition and track the performance degradation. Finally, three experimental case studies are implemented to demonstrate the feasibility and effectiveness of the proposed method. The results show that the proposed method can quantitatively identify the fault signature of a slight rub on

On the singularities of solutions to singular perturbation problems

International Nuclear Information System (INIS)

Fruchard, A; Schaefke, R

2005-01-01

We consider a singularly perturbed complex first order ODE εu ' Φ(x, u, a, ε), x, u element of C, ε > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot

Singularities in four-body final-state amplitudes

International Nuclear Information System (INIS)

Adhikari, S.K.

1978-01-01

Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering

Local and nonlocal space-time singularities

International Nuclear Information System (INIS)

Konstantinov, M.Yu.

1985-01-01

The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established

On the singularities of solutions to singular perturbation problems

Energy Technology Data Exchange (ETDEWEB)

Fruchard, A [Laboratoire de Mathematiques, Informatique et Applications, Faculte des Sciences et Techniques, Universite de Haute Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse cedex (France); Schaefke, R [Departement de Mathematiques, Universite Louis Pasteur, 7 rue Rene-Descartes, 67084 Strasbourg cedex (France)

2005-01-01

We consider a singularly perturbed complex first order ODE {epsilon}u ' {phi}(x, u, a, {epsilon}), x, u element of C, {epsilon} > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot.

Singular Solutions to a (3 + 1-D Protter-Morawetz Problem for Keldysh-Type Equations

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Nedyu Popivanov

2017-01-01

Full Text Available We study a boundary value problem for (3 + 1-D weakly hyperbolic equations of Keldysh type (problem PK. The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations which, in part, are closely connected with transonic fluid dynamics. We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. It is known that it may have a strong power-type singularity at one boundary point even for very smooth right-hand sides of the equation. In the present paper we study the asymptotic behavior of the generalized solutions of problem PK at the singular point. There are given orthogonality conditions on the right-hand side of the equation, which are necessary and sufficient for the existence of a generalized solution with fixed order of singularity.

Singularity kinematics principle and position-singularity analyses of the 6-3 Stewart-Gough parallel manipulators

International Nuclear Information System (INIS)

Cao, Yi; Zhou, Hui; Li, Baokun; Shen, Long

2011-01-01

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived: and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes

On important precursor of singular optics (tutorial)

Science.gov (United States)

Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.

2018-01-01

The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].

Properties of kinematic singularities

Energy Technology Data Exchange (ETDEWEB)

Coley, A A [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada); Hervik, S [Department of Mathematics and Natural Sciences, University of Stavanger, N-4036 Stavanger (Norway); Lim, W C [Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); MacCallum, M A H, E-mail: aac@mathstat.dal.c, E-mail: sigbjorn.hervik@uis.n, E-mail: wclim@aei.mpg.d, E-mail: m.a.h.maccallum@qmul.ac.u [School of Mathematical Sciences, Queen Mary University of London, E1 4NS (United Kingdom)

2009-11-07

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.

Integrated Urban System and Energy Consumption Model: Public and Singular Buildings

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Rocco Papa

2014-05-01

Full Text Available The present paper illustrates the results of the first steps of a study on one aspect investigated as the preliminary step of the definition of the analysis - comprehension model of the relation between: city, buildings, and user behavior, for the reduction of energy consumption within the research project “Smart Energy Master” for the energetic governance of the territory (PON_MIUR n. pos. 04a2_00120 CUP Ricerca: E61H12000130005, at the Department of Civil, Building and Environmental Engineering - University of Naples Federico II, principal investigator prof. Carmela Gargiulo.Specifically the literary review aimed at determining if, and in what measure, the presence of public and singular buildings is present in the energy consumption estimate models,  proposed by the scientific community, for the city or neighborhood scale.The difficulties in defining the weight of these singular buildings on the total energy consumption and the impossibility to define mean values that are significant for all subsets and different types as well as for each one, have forced model makers to either ignore them completely or chose a portion of this specific stock to include.

3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities

CERN Document Server

Neto, Aurélio; Mond, David; Saia, Marcelo; Snoussi, Jawad; BMMS 2/NBMS 3; ENSINO; Singularities and foliations geometry, topology and applications

2018-01-01

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

New dual conformally invariant off-shell integrals

International Nuclear Information System (INIS)

Nguyen, Dung; Spradlin, Marcus; Volovich, Anastasia

2008-01-01

Evidence has recently emerged for a hidden symmetry of planar scattering amplitudes in N=4 super-Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS 5 . In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities

Computational singular perturbation analysis of stochastic chemical systems with stiffness

Science.gov (United States)

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

2017-04-01

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

Topological resolution of gauge theory singularities

Science.gov (United States)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-01

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

Topological resolution of gauge theory singularities

Energy Technology Data Exchange (ETDEWEB)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

The geometry of warped product singularities

Science.gov (United States)

Stoica, Ovidiu Cristinel

In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

The Big Bang Singularity

Science.gov (United States)

Ling, Eric

The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

Singular surfaces in the open field line region of a diverted tokamak

International Nuclear Information System (INIS)

Reiman, A.

1995-05-01

The structure of the open field lines of a slightly nonaxisymmetric, poloidally diverted tokamak is explored by numerical integration of the field line equations for a simple model field. In practice, the nonaxisymmetry could be produced self-consistently by the nonlinear evolution of a free-boundary MHD mode, or it could be produced by field errors, or it could be imposed externally by design. In the presence of a nonaxisymmetric perturbation, the tokamak is shown to develop open field line regions of differing topology separated by singular surfaces. It is argued that the singular surfaces can be expected to play a role analogous to that of rational toroidal flux surfaces, in terms of constraining ideal MHD perturbations and thus constraining the free-energy that can be tapped by ideal MHD instabilities. The possibility of active control of free-boundary instabilities by means of currents driven on the open singular surfaces, which are directly accessible from the divertor plates, is discussed. Also discussed is the possibility of early detection of imminent disruptions through localized measurement of the singular surface currents

Nonlinear singular perturbation problems of arbitrary real orders

International Nuclear Information System (INIS)

Bijura, Angelina M.

2003-10-01

Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

Comment on 'The equations for electronegative plasmas are not singular at the plasma centre at low pressures' by R N Franklin

International Nuclear Information System (INIS)

Lampe, Martin; Manheimer, Wallace M; Fernsler, Richard F; Slinker, Steven P; Joyce, Glenn

2006-01-01

Franklin's criticism (Franklin R N 2005 J. Phys. D: Appl. Phys. 38 2790) of our previous paper (Lampe M et al 2004 Plasma Sources Sci. Technol. 13 15-26) is based on three arguments: (1) that the limit of weak attachment is equivalent to low pressure, where our model is inappropriate; (2) that our use of the T n → 0 limit is inappropriate; (3) that the negative ion density n n is never singular at the centre. We point out that the weak attachment limit also corresponds (at high pressure) to low fraction of attaching gas, give conditions for the T n → 0 limit and discuss its consequences, and reiterate that we never argued that n n (0) is infinite, but rather discussed a quite different type of singularity. This correspondence is now closed. (comment)

From symplectic integrator to Poincare map: Spline expansion of a map generator in Cartesian coordinates

International Nuclear Information System (INIS)

Warnock, R.L.; Ellison, J.A.; Univ. of New Mexico, Albuquerque, NM

1997-08-01

Data from orbits of a symplectic integrator can be interpolated so as to construct an approximation to the generating function of a Poincare map. The time required to compute an orbit of the symplectic map induced by the generator can be much less than the time to follow the same orbit by symplectic integration. The construction has been carried out previously for full-turn maps of large particle accelerators, and a big saving in time (for instance a factor of 60) has been demonstrated. A shortcoming of the work to date arose from the use of canonical polar coordinates, which precluded map construction in small regions of phase space near coordinate singularities. This paper shows that Cartesian coordinates can also be used, thus avoiding singularities. The generator is represented in a basis of tensor product B-splines. Under weak conditions the spline expansion converges uniformly as the mesh is refined, approaching the exact generator of the Poincare map as defined by the symplectic integrator, in some parallelepiped of phase space centered at the origin

On local invariants of singular symplectic forms

Science.gov (United States)

Domitrz, Wojciech

2017-04-01

We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.

Singularity now: using the ventricular assist device as a model for future human-robotic physiology.

Science.gov (United States)

Martin, Archer K

2016-04-01

In our 21 st century world, human-robotic interactions are far more complicated than Asimov predicted in 1942. The future of human-robotic interactions includes human-robotic machine hybrids with an integrated physiology, working together to achieve an enhanced level of baseline human physiological performance. This achievement can be described as a biological Singularity. I argue that this time of Singularity cannot be met by current biological technologies, and that human-robotic physiology must be integrated for the Singularity to occur. In order to conquer the challenges we face regarding human-robotic physiology, we first need to identify a working model in today's world. Once identified, this model can form the basis for the study, creation, expansion, and optimization of human-robotic hybrid physiology. In this paper, I present and defend the line of argument that currently this kind of model (proposed to be named "IshBot") can best be studied in ventricular assist devices - VAD.

Worldline path integrals for a Dirac particle in a weak gravitational plane wave

International Nuclear Information System (INIS)

Haouat, S.; Chetouani, L.

2008-01-01

The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted. (orig.)

Spacetime averaging of exotic singularity universes

International Nuclear Information System (INIS)

Dabrowski, Mariusz P.

2011-01-01

Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.

The Semantics of Plurals: A Defense of Singularism

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Florio, Salvatore

2010-01-01

In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

Quantum cosmology and late-time singularities

International Nuclear Information System (INIS)

Kamenshchik, A Yu

2013-01-01

The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)

One dimensional systems with singular perturbations

International Nuclear Information System (INIS)

Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P

2011-01-01

This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.

Minimal solution for inconsistent singular fuzzy matrix equations

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M. Nikuie

2013-10-01

Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps with prescribed singular fibers

OpenAIRE

Kalmar, Boldizsar

2006-01-01

We give a Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of -1 codimensional stable maps with prescribed singular fibers.

Approaches to the summability of divergent multidimensional integrals

International Nuclear Information System (INIS)

Vainikko, G M; Lifanov, I K

2003-01-01

Under discussion are various approaches to the concept of summability (finding the finite part - (f.p.)) of divergent integrals with integrand represented as a product of two functions, one with a parameter-dependent non-integrable singularity at one point of the integration and the other absolutely integrable. A study is made of summability methods which are based on the expansion of the absolutely integrable function in a Taylor series with centre at the singular point (f.p.), on the analytic continuation with respect to the parameter of the singularity (a.f.p.), and on integration by parts (f.p.p.). Formulae of changes of variables in such integrals are presented

Relation of extended Van Hove singularities to high-temperature superconductivity within strong-coupling theory

International Nuclear Information System (INIS)

Radtke, R.J.; Norman, M.R.

1994-01-01

Recent angle-resolved photoemission (ARPES) experiments have indicated that the electronic dispersion in some of the cuprates possesses an extended saddle point near the Fermi level which gives rise to a density of states that diverges like a power law instead of the weaker logarithmic divergence usually considered. We investigate whether this strong singularity can give rise to high transition temperatures by computing the critical temperature T c and isotope effect coefficient α within a strong-coupling Eliashberg theory which accounts for the full energy variation of the density of states. Using band structures extracted from ARPES measurements, we demonstrate that, while the weak-coupling solutions suggest a strong influence of the strength of the Van Hove singularity on T c and α, strong-coupling solutions show less sensitivity to the singularity strength and do not support the hypothesis that band-structure effects alone can account for either the large T c 's or the different T c 's within the copper oxide family. This conclusion is supported when our results are plotted as a function of the physically relevant self-consistent coupling constant, which shows universal behavior at very strong coupling

Scalar Green's functions in an Euclidean space with a conical-type line singularity

International Nuclear Information System (INIS)

Guimaraes, M.E.X.; Linet, B.

1994-01-01

In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux. (orig.)

Singularities in FLRW spacetimes

Science.gov (United States)

het Lam, Huibert; Prokopec, Tomislav

2017-12-01

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.

The theory of singular perturbations

CERN Document Server

De Jager, E M

1996-01-01

The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

Naked singularity in the global structure of critical collapse spacetimes

International Nuclear Information System (INIS)

Frolov, Andrei V.; Pen, U.-L.

2003-01-01

We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity

Singular potentials in quantum mechanics

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Koo, E. Ley

1995-10-01

This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs

Analyticity in a phenomenology of electro-weak structure of hadrons

International Nuclear Information System (INIS)

Dubnicka, S.; Dubnickova, A. Z.

2010-01-01

The utility of an application of the analyticity in a phenomenology of electro-weak structure of hadrons is demonstrated in a number of obtained new and experimentally verifiable results. With this aim first the problem of an inconsistency of the asymptotic behavior of vector-meson-dominance model with the asymptotic behavior of form factors of baryons and nuclei is solved generally and a general approach for determination of the lowest normal and anomalous singularities of form factors from the corresponding Feynman diagrams is reviewed. Then many useful applications by making use of the analytic properties of electro-weak form factors and amplitudes of various electromagnetic processes of hadrons are carried out. (Author)

Analysis of singularity in redundant manipulators

International Nuclear Information System (INIS)

Watanabe, Koichi

2000-03-01

In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)

Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

Science.gov (United States)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2016-01-01

Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

Biclustering via Sparse Singular Value Decomposition

KAUST Repository

Lee, Mihee

2010-02-16

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.

Patterns and singular features of extreme fluctuational paths of a periodically driven system

International Nuclear Information System (INIS)

Chen, Zhen; Liu, Xianbin

2016-01-01

Large fluctuations of an overdamped periodically driven oscillating system are investigated theoretically and numerically in the limit of weak noise. Optimal paths fluctuating to certain point are given by statistical analysis using the concept of prehistory probability distribution. The validity of statistical results is verified by solutions of boundary value problem. Optimal paths are found to change topologically when terminating points lie at opposite side of a switching line. Patterns of extreme paths are plotted through a proper parameterization of Lagrangian manifold having complicated structures. Several extreme paths to the same point are obtained by multiple solutions of boundary value solutions. Actions along various extreme paths are calculated and associated analysis is performed in relation to the singular features of the patterns. - Highlights: • Both extreme and optimal paths are obtained by various methods. • Boundary value problems are solved to ensure the validity of statistical results. • Topological structure of Lagrangian manifold is considered. • Singularities of the pattern of extreme paths are studied.

Noncrossing timelike singularities of irrotational dust collapse

International Nuclear Information System (INIS)

Liang, E.P.T.

1979-01-01

Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)

Singular surfaces in the open field line region of a diverted tokamak

International Nuclear Information System (INIS)

Reiman, A.

1996-01-01

The structure of the open field lines of a slightly nonaxisymmetric, poloidally diverted tokamak is explored by numerical integration of the field line equations for a simple model field. In practice, the nonaxisymmetry could be produced self-consistently by the nonlinear evolution of a free-boundary magnetohydrodynamic (MHD) mode, or it could be produced by field errors, or it could be imposed externally by design. In the presence of a nonaxisymmetric perturbation, the tokamak is shown to develop open field line regions of differing topology separated by singular surfaces. It is argued that the singular surfaces can be expected to play a role analogous to that of rational toroidal flux surfaces, in terms of constraining ideal MHD perturbations and thus constraining the free-energy that can be tapped by ideal MHD instabilities. The possibility of active control of free-boundary instabilities by means of currents driven on the open singular surfaces, which are directly accessible from the divertor plates, is discussed. copyright 1996 American Institute of Physics

Dressing up a Kerr naked singularity

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Nobili, L [Padua Univ. (Italy). Ist. di Fisica

1979-06-11

The evolution of a naked singularity surrounded by an accreting disk of matter is studied; two kinds of disks are considered: the standard thin-disk model and the thick barytropic model, for several initial conditions. It is shown that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. The final mass, the luminosity and the time of evolution of the singularity are evaluated.

Singularities in cosmologies with interacting fluids

International Nuclear Information System (INIS)

Cotsakis, Spiros; Kittou, Georgia

2012-01-01

We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for ‘phantom’ matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding to a logarithmic branch point that resembles a cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.

Observational constraints on cosmological future singularities

International Nuclear Information System (INIS)

Beltran Jimenez, Jose; Lazkoz, Ruth; Saez-Gomez, Diego; Salzano, Vincenzo

2016-01-01

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)

Observational constraints on cosmological future singularities

Energy Technology Data Exchange (ETDEWEB)

Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)

2016-11-15

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)

Special frequencies and Lifshitz singularities in binary random harmonic chains

International Nuclear Information System (INIS)

Nieuwenhuizen, T.M.; Luck, J.M.; Canisius, J.; van Hemmen, J.L.; Ventevogel, W.J.

1986-01-01

The authors consider a one-dimensional chain of coupled harmonic oscillators; the mass of each atom is a random variable taking only two values (M or 1). They investigate the integrated density of states H(omega 2 ) near special frequencies: a given frequency omega/sub s/ with rational wavelength becomes special if the mass ratio M exceeds a certain critical value M/sub c/. They show that H has essential singularities of the types H/sub sg/∼ exp(-C 1 absolute value of omega 2 -omega/sub s/ 2 /sup 1/2/) or exp(-C 2 absolute value of omega 2 -omega/sub s/ 2 -1 ), according to the value of M and the sign of (omega 2 -omega/sub s/ 2 ). The Lifshitz singularity at the band edge is analyzed in the same way. In each case, the constant C 1 or C 2 is evaluated explicitly and compared with a vast amount of numerical work. All these exponential singularities are modulated by periodic amplitudes. The properties of the eigenfunctions with frequencies close to the special values are also discussed, and are illustrated by numerical data

Classical integrability for three-point functions: cognate structure at weak and strong couplings

Energy Technology Data Exchange (ETDEWEB)

Kazama, Yoichi [Research Center for Mathematical Physics, Rikkyo University,Toshima-ku, Tokyo 171-8501 (Japan); Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198 (Japan); Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902 (Japan); Komatsu, Shota [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada); Nishimura, Takuya [Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902 (Japan)

2016-10-10

In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the N=4 super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis. The structure threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix. We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model. Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified. To determine the analyticity, we develop a new universal logic applicable at both weak and strong couplings. As a result, compact semi-classical formulas are obtained for a general class of three-point functions at weak coupling including the ones whose semi-classical behaviors were not known before. In addition, the new analyticity argument applied to the strong coupling analysis leads to a modification of the integration contour, producing the results consistent with the recent hexagon bootstrap approach. This modification also makes the Frolov-Tseytlin limit perfectly agree with the weak coupling form.

Non-singular string-cosmologies from exact conformal field theories

International Nuclear Information System (INIS)

Vega, H.J. de; Larsen, A.L.; Sanchez, N.

2001-01-01

Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular space-times with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation

Asymptotic safety, singularities, and gravitational collapse

International Nuclear Information System (INIS)

Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz

2011-01-01

Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.

Singularity resolution in quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity

Challenging the weak cosmic censorship conjecture with charged quantum particles

International Nuclear Information System (INIS)

Richartz, Mauricio; Saa, Alberto

2011-01-01

Motivated by the recent attempts to violate the weak cosmic censorship conjecture for near-extreme black holes, we consider the possibility of overcharging a near-extreme Reissner-Nordstroem black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-(1/2) particles by the black hole in a unified framework and obtain analytically, for the first time, the pertinent reflection and transmission coefficients without any small charge approximation. Based on these results, we propose some gedanken experiments that could lead to the violation of the weak cosmic censorship conjecture due to the (classically forbidden) absorption of small energy charged particles by the black hole. As for the case of scattering in Kerr spacetimes, our results demonstrate explicitly that scalar fields are subject to (electrical) superradiance phenomenon, while spin-(1/2) fields are not. Superradiance impose some limitations on the gedanken experiments involving spin-0 fields, favoring, in this way, the mechanisms for creation of a naked singularity by the quantum tunneling of spin-(1/2) charged fermions. We also discuss the implications that vacuum polarization effects and quantum statistics might have on these gedanken experiments. In particular, we show that they are not enough to prevent the absorption of incident small energy particles and, consequently, the formation of a naked singularity.

Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

Science.gov (United States)

Pan, Supriya

2018-01-01

Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

Singular multiparameter dynamic equations with distributional ...

African Journals Online (AJOL)

Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.

Is the cosmological singularity compulsory

International Nuclear Information System (INIS)

Bekenstein, J.D.; Meisels, A.

1980-01-01

The cosmological singularity is inherent in all conventional general relativistic cosmological models. There can be no question that it is an unphysical feature; yet there does not seem to be any convervative way of eliminating it. Here we present singularity-free isotropic cosmological models which are indistinguishable from general relativistic ones at late times. They are based on the general theory of variable rest masses that we developed recently. Outside cosmology this theory simulates general relativity well. Thus it provides a framework incorporating those features which have made geneal relativity so sucessful while providing a way out of singularity dilemma. The cosmological models can be made to incorporate Dirac's large numbers hypothesis. G(now)/G(0)approx.10 -38

Finite-time singularities and flow regularization in a hydromagnetic shell model at extreme magnetic Prandtl numbers

International Nuclear Information System (INIS)

Nigro, G; Carbone, V

2015-01-01

Conventional surveys on the existence of singularities in fluid systems for vanishing dissipation have hitherto tried to infer some insight by searching for spatial features developing in asymptotic regimes. This approach has not yet produced a conclusive answer. One of the difficulties preventing us from getting a definitive answer is the limitations of direct numerical simulations which do not yet have a high enough resolution so far as to properly describe spatial fine structures in asymptotic regimes. In this paper, instead of searching for spatial details, we suggest seeking a principle, that would be able to discriminate between singular or not-singular behavior, among the integral and purely dynamical properties of a fluid system. We investigate the singularities developed by a hydromagnetic shell model during the magnetohydrodynamic turbulent cascade. Our results show that when the viscosity is equal to the magnetic diffusivity (unit magnetic Prandtl number) singularities appear in a finite time. A complex behavior is observed at extreme magnetic Prandtl numbers. In particular, the singularities persist in the limit of vanishing viscosity, while a complete regularization is observed in the limit of vanishing diffusivity. This dynamics is related to differences between the magnetic and the kinetic energy cascades towards small scales. Finally a comparison between the three-dimensional and the two-dimensional cases leads to conjecture that the existence of singularities may be related to the conservation of different ideal invariants. (paper)

Analysis of singular interface stresses in dissimilar material joints for plasma facing components

Energy Technology Data Exchange (ETDEWEB)

You, J.H. E-mail: jeong-ha.you@ipp.mpg.de; Bolt, H

2001-10-01

Duplex joint structures are typical material combinations for the actively cooled plasma facing components of fusion devices. The structural integrity under the incident heat loads from the plasma is one of the most crucial issues in the technology of these components. The most critical domain in a duplex joint component is the free surface edge of the bond interface between heterogeneous materials. This is due to the fact that the thermal stress usually shows a singular intensification in this region. If the plasma facing armour tile consists of a brittle material, the existence of the stress singularity can be a direct cause of failure. The present work introduces a comprehensive analytical tool to estimate the impact of the stress singularity for duplex PFC design and quantifies the relative stress intensification in various materials joints by use of a model formulated by Munz and Yang. Several candidate material combinations of plasma facing armour and metallic heat sink are analysed and the results are compared with each other.

Analysis of singular interface stresses in dissimilar material joints for plasma facing components

International Nuclear Information System (INIS)

You, J.H.; Bolt, H.

2001-01-01

Duplex joint structures are typical material combinations for the actively cooled plasma facing components of fusion devices. The structural integrity under the incident heat loads from the plasma is one of the most crucial issues in the technology of these components. The most critical domain in a duplex joint component is the free surface edge of the bond interface between heterogeneous materials. This is due to the fact that the thermal stress usually shows a singular intensification in this region. If the plasma facing armour tile consists of a brittle material, the existence of the stress singularity can be a direct cause of failure. The present work introduces a comprehensive analytical tool to estimate the impact of the stress singularity for duplex PFC design and quantifies the relative stress intensification in various materials joints by use of a model formulated by Munz and Yang. Several candidate material combinations of plasma facing armour and metallic heat sink are analysed and the results are compared with each other

São Carlos Workshop on Real and Complex Singularities

CERN Document Server

Ruas, Maria

2007-01-01

The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19–23, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.

Asymptotics of bivariate generating functions with algebraic singularities

Science.gov (United States)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Bright, dark and singular optical solitons in a cascaded system

International Nuclear Information System (INIS)

Zhou, Qin; Zhu, Qiuping; Yu, Hua; Liu, Yaxian; Wei, Chun; Yao, Ping; Bhrawy, Ali H; Biswas, Anjan

2015-01-01

This work studies nonlinear dynamics of optical solitons in a cascaded system with Kerr law nonlinearity and spatio-temporal dispersion. The mathematical model that describes the propagation of optical solitons through a cascaded system is given by the vector-coupled nonlinear Schrödinger equation. It is investigated analytically using three integration algorithms. The Jacobian elliptic equation expansion method, Bernoulli equation expansion approach and Riccati equation expansion scheme are the integration tools of this model that are recruited to extract singular, bright and dark solitons. The restrictions that need to hold for the existence of these solitons are derived. (paper)

One-dimensional Schroedinger operators with interactions singular on a discrete set

International Nuclear Information System (INIS)

Gesztesy, F.; Kirsch, W.

We study the self-adjointness of Schroedinger operators -d 2 /dx 2 +V(x) on an arbitrary interval, (a,b) with V(x) locally integrable on (a,b)inverse slantX where X is a discrete set. The treatment of quantum mechanical systems describing point interactions or periodic (possibly strongly singular) potentials is thereby included and explicit examples are presented. (orig.)

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...

Topological Signals of Singularities in Ricci Flow

Directory of Open Access Journals (Sweden)

Paul M. Alsing

2017-08-01

Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.

δ- and δ'-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes

International Nuclear Information System (INIS)

Shelkovich, V M

2008-01-01

This is a survey of some results and problems connected with the theory of generalized solutions of quasi-linear conservation law systems which can admit delta-shaped singularities. They are the so-called δ-shock wave type solutions and the recently introduced δ (n) -shock wave type solutions, n=1,2,..., which cannot be included in the classical Lax-Glimm theory. The case of δ- and δ'-shock waves is analyzed in detail. A specific analytical technique is developed to deal with such solutions. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. Solutions of Cauchy problems are constructed for some typical systems of conservation laws. Also investigated are multidimensional systems of conservation laws (in particular, zero-pressure gas dynamics systems) which admit δ-shock wave type solutions. A geometric aspect of such solutions is considered: they are connected with transport and concentration processes, and the balance laws of transport of 'volume' and 'area' to δ- and δ'-shock fronts are derived for them. For a 'zero-pressure gas dynamics' system these laws are the mass and momentum transport laws. An algebraic aspect of these solutions is also considered: flux-functions are constructed for them which, being non-linear, are nevertheless uniquely defined Schwartz distributions. Thus, a singular solution of the Cauchy problem generates algebraic relations between its components (distributions).

Reasons for singularity in robot teleoperation

DEFF Research Database (Denmark)

Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth

2014-01-01

In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and dela...

7 CFR 61.1 - Words in singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...

Identification of discrete chaotic maps with singular points

Directory of Open Access Journals (Sweden)

P. G. Akishin

2001-01-01

Full Text Available We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.

Maslov indices, Poisson brackets, and singular differential forms

Science.gov (United States)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

7 CFR 46.1 - Words in singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...

EDITORIAL: The plurality of optical singularities

Science.gov (United States)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the

On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

Directory of Open Access Journals (Sweden)

Yoshitsugu Takei

2015-01-01

Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

Stable computation of generalized singular values

Energy Technology Data Exchange (ETDEWEB)

Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)

1996-12-31

We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.

Singularly perturbed Burger-Huxley equation: Analytical solution ...

African Journals Online (AJOL)

user

solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.

The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack

KAUST Repository

Zemlyanova, A. Y.

2013-03-08

A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.

Observer-dependent sign inversions of polarization singularities.

Science.gov (United States)

Freund, Isaac

2014-10-15

We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

Singular spectrum analysis of sleep EEG in insomnia.

Science.gov (United States)

Aydın, Serap; Saraoǧlu, Hamdi Melih; Kara, Sadık

2011-08-01

In the present study, the Singular Spectrum Analysis (SSA) is applied to sleep EEG segments collected from healthy volunteers and patients diagnosed by either psycho physiological insomnia or paradoxical insomnia. Then, the resulting singular spectra computed for both C3 and C4 recordings are assigned as the features to the Artificial Neural Network (ANN) architectures for EEG classification in diagnose. In tests, singular spectrum of particular sleep stages such as awake, REM, stage1 and stage2, are considered. Three clinical groups are successfully classified by using one hidden layer ANN architecture with respect to their singular spectra. The results show that the SSA can be applied to sleep EEG series to support the clinical findings in insomnia if ten trials are available for the specific sleep stages. In conclusion, the SSA can detect the oscillatory variations on sleep EEG. Therefore, different sleep stages meet different singular spectra. In addition, different healthy conditions generate different singular spectra for each sleep stage. In summary, the SSA can be proposed for EEG discrimination to support the clinical findings for psycho-psychological disorders.

Generalized teleparallel cosmology and initial singularity crossing

Energy Technology Data Exchange (ETDEWEB)

Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg [Center for Theoretical Physics, the British University in Egypt, Suez Desert Road, Sherouk City 11837 (Egypt)

2017-02-01

We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.

Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability

Science.gov (United States)

Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady

2016-08-01

As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.

Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe–Strogatz integrability

International Nuclear Information System (INIS)

Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady

2016-01-01

As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations. (letter)

Transmutation of singularities in optical instruments

Energy Technology Data Exchange (ETDEWEB)

Tyc, Tomas [Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno (Czech Republic); Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom)], E-mail: tomtyc@physics.muni.cz

2008-11-15

We propose a method for eliminating a class of singularities in optical media where the refractive index goes to zero or infinity at one or more isolated points. Employing transformation optics, we find a refractive index distribution equivalent to the original one that is nonsingular but shows a slight anisotropy. In this way, the original singularity is 'transmuted' into another, weaker type of singularity where the permittivity and permeability tensors are discontinuous at one point. The method is likely to find applications in designing and improving optical devices by making them easier to implement or to operate in a broad band of the spectrum.

Multifractal signal reconstruction based on singularity power spectrum

International Nuclear Information System (INIS)

Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning

2016-01-01

Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.

Cosmologies with quasiregular singularities. II. Stability considerations

International Nuclear Information System (INIS)

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

1985-01-01

The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R 1 x T 3 and R 3 x S 1 flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

Energy Technology Data Exchange (ETDEWEB)

Chen, Baoyi; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua, Zhejiang (China); Nanjing University, Department of Physics, Nanjing (China)

2017-02-15

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable. (orig.)

Exact solutions and singularities in string theory

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail

Singular solitons of generalized Camassa-Holm models

International Nuclear Information System (INIS)

Tian Lixin; Sun Lu

2007-01-01

Two generalizations of the Camassa-Holm system associated with the singular analysis are proposed for Painleve integrability properties and the extensions of already known analytic solitons. A remarkable feature of the physical model is that it has peakon solution which has peak form. An alternative WTC test which allowed the identifying of such models directly if formulated in terms of inserting a formed ansatz into these models. For the two models have Painleve property, Painleve-Baecklund systems can be constructed through the expansion of solitons about the singularity manifold. By the implementations of Maple, plentiful new type solitonic structures and some kink waves, which are affected by the variation of energy, are explored. If the energy is infinite in finite time, there will be a collapse in soliton systems by direct numerical simulations. Particularly, there are two collapses coexisting in our regular solitons, which occurred around its central regions. Simulation shows that in the bottom of periodic waves arises the non-zero parts of compactons and anti-compactons. We also get floating solitary waves whose amplitude is infinite. In contrary to which a finite-amplitude blow-up soliton is obtained. Periodic blow-ups are found too. Special kinks which have periodic cuspons are derived

Technological Singularity: What Do We Really Know?

Directory of Open Access Journals (Sweden)

Alexey Potapov

2018-04-01

Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.

Normal forms of Hopf-zero singularity

International Nuclear Information System (INIS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)

Normal forms of Hopf-zero singularity

Science.gov (United States)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

Radioanatomy of the singular nerve canal

Energy Technology Data Exchange (ETDEWEB)

Muren, C. [Dept. of Diagnostic Radiology, Sabbatsbergs Hospital, Stockholm (Sweden); Wadin, K. [University Hospital, Uppsala (Sweden); Dimopoulos, P. [University Hospital, Uppsala (Sweden)

1991-08-01

The singular canal conveys vestibular nerve fibers from the ampulla of the posterior semicircular canal to the posteroinferior border of the internal auditory meatus. Radiographic identification of this anatomic structure helps to distinguish it from a fracture. It is also a landmark in certain surgical procedures. Computed tomography (CT) examinations of deep-frozen temporal bone specimens were compared with subsequently prepared plastic casts of these bones, showing good correlation between the anatomy and the images. The singular canal and its variable anatomy were studied in CT examinations of 107 patients. The singular canal could be identified, in both the axial and in the coronal planes. Its point of entry into the internal auditory meatus varied considerably. (orig.)

Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type

International Nuclear Information System (INIS)

Maltsev, A Ya

2005-01-01

We consider the special type of field-theoretical symplectic structures called weakly nonlocal. The structures of this type are, in particular, very common for integrable systems such as KdV or NLS. We introduce here the special class of weakly nonlocal symplectic structures which we call weakly nonlocal symplectic structures of hydrodynamic type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of 'averaging' the weakly nonlocal symplectic structures. The averaging procedure gives the weakly nonlocal symplectic structure of hydrodynamic type for the corresponding Whitham system. The procedure also gives 'action variables' corresponding to the wave numbers of m-phase solutions of the initial system which give the additional conservation laws for the Whitham system

Singularities in the delta = 3 Tomimatsu-Sato space-time

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Turolla, R [International School for Advanced Studies, Trieste (Italy)

1980-08-02

The existence of singularities outside the equatorial plane is investigated. We show that when the specific angular momentum a exceeds the mass m of the source, there are six ring singularities, while when asingularities lie only in the equatorial plane.

Complexity, Analysis and Control of Singular Biological Systems

CERN Document Server

Zhang, Qingling; Zhang, Xue

2012-01-01

Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling  the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...

Coefficients of singularities and mixed methods for the mixed Dirichlet-Neumann problem for the Stokes operator on a polygon

International Nuclear Information System (INIS)

Chettab, M.; Lubuma, M.S.

1990-08-01

The behaviour of the weak solution of the Stokes problem on a polygon is considered with emphasis on the maximal regularity of the solution and on global formulae for the coefficients of singularities. This regularity leads to a slow convergent mixed finite element method of fractional order less than one while the use of the above formulae provides better approximations for the solution and for the coefficients. (author). 32 refs

Can non-commutativity resolve the big-bang singularity?

Energy Technology Data Exchange (ETDEWEB)

Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)

2004-08-01

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)

Remarks on gauge variables and singular Lagrangians

International Nuclear Information System (INIS)

Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.

1977-01-01

The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)

Tangled nonlinear driven chain reactions of all optical singularities

Science.gov (United States)

Vasil'ev, V. I.; Soskin, M. S.

2012-03-01

Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

Workshop on Singularities in Geometry, Topology, Foliations and Dynamics

CERN Document Server

Lê, Dung; Oka, Mutsuo; Snoussi, Jawad

2017-01-01

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Cusp singularities in f(R) gravity: pros and cons

International Nuclear Information System (INIS)

Chen, Pisin; Yeom, Dong-han

2015-01-01

We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvature singularity that can be interpreted by a firewall

Dual Vector Spaces and Physical Singularities

Science.gov (United States)

Rowlands, Peter

Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

Naked singularities and cosmic censorship: comment on the current situation

International Nuclear Information System (INIS)

Seifert, H.J.

1979-01-01

The current discussion is mainly concerned with how, or indeed, whether space-times possessing naked singularities can be ruled out as being too unrealistic or not being singular at all. The present position is summarized, with references, under the following headings: the Hawking-Penrose existence theorems, hydrodynamical singularities and the strength of naked singularities. (UK)

Numerical investigation of stress singularities in cracked bimaterial body

Czech Academy of Sciences Publication Activity Database

Náhlík, Luboš; Šestáková, Lucie; Hutař, Pavel

2008-01-01

Roč. 385-387, - (2008), s. 125-128 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics /7./. Seoul, 09.09.2008-11.09.2008] R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GP106/06/P239; GA ČR GA106/08/1409 Institutional research plan: CEZ:AV0Z20410507 Keywords : bimaterial interface * stress singularity exponent * corner singularity * vertex singularity * general singular stress concentrator Subject RIV: JL - Materials Fatigue, Friction Mechanics

On the nature of naked singularities in Vaidya spacetimes

Energy Technology Data Exchange (ETDEWEB)

Dwivedi, I.H. (Aligarh Muslim Univ. (India). Dept. of Physics); Joshi, P.S. (Tata Inst. of Fundamental Research, Bombay (India))

1989-11-01

The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author).

On the nature of naked singularities in Vaidya spacetimes

International Nuclear Information System (INIS)

Dwivedi, I.H.

1989-01-01

The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author)

Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields

International Nuclear Information System (INIS)

Tóth, Gábor Zsolt

2016-01-01

It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr–Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of the conversion is a direct consequence of the fact that the Einstein–Hilbert energy-momentum tensor of the classical Dirac field does not satisfy the null energy condition, and is therefore not in contradiction with the weak cosmic censorship conjecture. We give a derivation of the absence of superradiance of the Dirac field without making use of the complete separability of the Dirac equation in the dyonic Kerr–Newman background, and we determine the range of superradiant frequencies of the scalar field. The range of frequencies of the Dirac field that can be used to convert a black hole into a naked singularity partially coincides with the superradiant range of the scalar field. We apply horizon-penetrating coordinates, as our arguments involve calculating quantities at the event horizon. We describe the separation of variables for the Dirac equation in these coordinates, although we mostly avoid using it. (paper)

Ambient cosmology and spacetime singularities

CERN Document Server

Antoniadis, Ignatios

2015-01-01

We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.

Naked singularities in self-similar spherical gravitational collapse

International Nuclear Information System (INIS)

Ori, A.; Piran, T.

1987-01-01

We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (Γ-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold

Phase structure of NJL model with weak renormalization group

Science.gov (United States)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Building Reproducible Science with Singularity Containers

CERN Multimedia

CERN. Geneva

2018-01-01

Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...

Oscillations and concentrations generated by A-free mappings and weak lower semicontinuity of integral functionals

Czech Academy of Sciences Publication Activity Database

Fonseca, I.; Kružík, Martin

Roč.16, č. 2 (2010), s. 472-502 ISSN 1262-3377 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : oscillations * concentrations Subject RIV: BA - General Mathematics Impact factor: 1.084, year: 2009 http://library.utia.cas.cz/separaty/2009/MTR/kruzik-oscillations and concentrations generated by a-free mappings and weak lower semicontinuity of integral functionals.pdf

Phantom cosmology without Big Rip singularity

Energy Technology Data Exchange (ETDEWEB)

Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)

2012-03-23

We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

Phantom cosmology without Big Rip singularity

International Nuclear Information System (INIS)

Astashenok, Artyom V.; Nojiri, Shin'ichi; Odintsov, Sergei D.; Yurov, Artyom V.

2012-01-01

We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers

Science.gov (United States)

Prybol, Cameron J.; Kurtzer, Gregory M.

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub’s primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers. PMID:29186161

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.

Directory of Open Access Journals (Sweden)

Vanessa V Sochat

Full Text Available Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.

Yangian-type symmetries of non-planar leading singularities

Energy Technology Data Exchange (ETDEWEB)

Frassek, Rouven [Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom); Meidinger, David [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany)

2016-05-18

We take up the study of integrable structures behind non-planar contributions to scattering amplitudes in N = 4 super Yang-Mills theory. Focusing on leading singularities, we derive the action of the Yangian generators on color-ordered subsets of the external states. Each subset corresponds to a single boundary of the non-planar on-shell diagram. While Yangian invariance is broken, we find that higher-level Yangian generators still annihilate the non-planar on-shell diagram. For a given diagram, the number of these generators is governed by the degree of non-planarity. Furthermore, we present additional identities involving integrable transfer matrices. In particular, for diagrams on a cylinder we obtain a conservation rule similar to the Yangian invariance condition of planar on-shell diagrams. To exemplify our results, we consider a five-point MHV on-shell function on a cylinder.

Curing Black Hole Singularities with Local Scale Invariance

Directory of Open Access Journals (Sweden)

Predrag Dominis Prester

2016-01-01

Full Text Available We show that Weyl-invariant dilaton gravity provides a description of black holes without classical space-time singularities. Singularities appear due to the ill behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are as follows: (1 singularities signal a phase transition from broken to unbroken phase of Weyl symmetry; (2 instead of a singularity, there is a “baby universe” or a white hole inside a black hole; (3 in the baby universe scenario, there is a critical mass after which reducing mass makes the black hole larger as viewed by outside observers; (4 if a black hole could be connected with white hole through the “singularity,” this would require breakdown of (classical geometric description; (5 the singularity of Schwarzschild BH solution is nongeneric and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information loss puzzle. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point.

7 CFR 1200.50 - Words in the singular form.

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2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

7 CFR 900.1 - Words in the singular form.

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2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.100 - Words in the singular form.

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2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.50 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

Global quantal canonical symmetry properties for a system with a singular Lagrangian

International Nuclear Information System (INIS)

Li Ziping

1996-01-01

Starting from the quantization formalism of the phase-space path integral for a system with a singular Lagrangian, the generalized canonical Ward identities and conserved charged at quantum level are deduced under the global transformation in extended phase space. In general, the quantal conserved charges are different from classical ones. We give a preliminary application to Yang-Mills theory, the new quantal conserved charges are found

Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)

Czech Academy of Sciences Publication Activity Database

Černý, R.; Hencl, S.; Kolář, Jan

2009-01-01

Roč. 71, 7-8 (2009), s. 2753-2763 ISSN 0362-546X R&D Projects: GA ČR GA201/06/0018 Institutional research plan: CEZ:AV0Z10190503 Keywords : weak continuity * nonlinear integral functional * Sobolev spaces * linearity Subject RIV: BA - General Mathematics Impact factor: 1.487, year: 2009

Simpson's neutrino and the singular see-saw

International Nuclear Information System (INIS)

Allen, T.J.; Johnson, R.; Ranfone, S.; Schechter, J.; Walle, J.W.F.

1991-01-01

The authors of this paper derive explicit forms for the neutrino and lepton mixing-matrices which describe the generic singular see-saw model. The dependence on the hierarchy parameter is contrasted with the non-singular case. Application is made to Simpson's 17 keV neutrino

Supersymmetric quantum mechanics under point singularities

International Nuclear Information System (INIS)

Uchino, Takashi; Tsutsui, Izumi

2003-01-01

We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

Ambient cosmology and spacetime singularities

International Nuclear Information System (INIS)

Antoniadis, Ignatios; Cotsakis, Spiros

2015-01-01

We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)

Singular moduli and Arakelov intersection

International Nuclear Information System (INIS)

Weng Lin.

1994-05-01

The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs

Solutions of dissimilar material singularity and contact problems

International Nuclear Information System (INIS)

Yang, Y.

2003-09-01

Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)

Metric dimensional reduction at singularities with implications to Quantum Gravity

International Nuclear Information System (INIS)

Stoica, Ovidiu Cristinel

2014-01-01

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained

7 CFR 900.20 - Words in the singular form.

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2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

7 CFR 900.36 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...

Beyond the singularity of the 2-D charged black hole

International Nuclear Information System (INIS)

Giveon, Amit; Rabinovici, Eliezer; Sever, Amit

2003-01-01

Two dimensional charged black holes in string theory can be obtained as exact SL(2,R) x U(1)/U(1) quotient CFTs. The geometry of the quotient is induced from that of the group, and in particular includes regions beyond the black hole singularities. Moreover, wavefunctions in such black holes are obtained from gauge invariant vertex operators in the SL(2,R) CFT, hence their behavior beyond the singularity is determined. When the black hole is charged we find that the wavefunctions are smooth at the singularities. Unlike the uncharged case, scattering waves prepared beyond the singularity are not fully reflected; part of the wave is transmitted through the singularity. Hence, the physics outside the horizon of a charged black hole is sensitive to conditions set behind the past singularity. (author)

THE EXT RACORPOREAL FERTILIZATION TECHNOLOGIES AND THE SINGULARITY PROBLEMS

Directory of Open Access Journals (Sweden)

S. V. Denysenko

2013-05-01

Full Text Available The peculiarities of modern medicine development connected with the technological and informative singularity are analyzed. The risks of realization of extracorporeal fertilization are examined from positions of development of informative singularity. The warning problems of origin of singularity are discussed on t h e base of t h e newest technologies development.

M theory and singularities of exceptional holonomy manifolds

International Nuclear Information System (INIS)

Acharya, Bobby S.; Gukov, Sergei

2004-12-01

M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)

Enveloping branes and brane-world singularities

Energy Technology Data Exchange (ETDEWEB)

Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)

2014-12-01

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)

Holographic subregion complexity for singular surfaces

Energy Technology Data Exchange (ETDEWEB)

Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)

2017-10-15

Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)

The cosmological singularity

CERN Document Server

Belinski, Vladimir

2018-01-01

Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...

The new PV prescription for IR singularities of NLO splitting functions

International Nuclear Information System (INIS)

Skrzypek, M.; Jadach, S.; Kusina, A.

2014-07-01

In this note we outline the Monte Carlo project KrkMC. The goal of this project is to construct a QCD Parton Shower accurate to NLO level in both coefficient function and splitting function (shower) parts. We discuss in detail one of its aspects - the evolution kernels. The kernels had to be recalculated in a new regularisation scheme, called NPV. In this scheme all the singularities in the plus component of the integration momenta are regularised by means of principal value prescription. This is in contrast to the standard approach, in which only the spurious axial singularities are regularised by principal value. As a result, the triple poles in the dimensional regularisation parameter ε are replaced by a combination of ε-poles and logarithms of geometrical cut-off δ. The resulting exclusive parton densities are more suitable for stochastic applications in four dimensions. Simultaneously, at the inclusive level, the standard and new prescriptions give the same results provided appropriate real and virtual contributions are added.

Naked singularities in higher dimensional Vaidya space-times

International Nuclear Information System (INIS)

Ghosh, S. G.; Dadhich, Naresh

2001-01-01

We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension

Quantum gravitational collapse: non-singularity and non-locality

International Nuclear Information System (INIS)

Greenwood, Eric; Stojkovic, Dejan

2008-01-01

We investigate gravitational collapse in the context of quantum mechanics. We take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning the horizon is not an obstacle for him. However, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Also, near the classical singularity, some non-local effects become important. In the Schrodinger equation describing behavior near the origin, derivatives of the wave function at one point are related to the value of the wave function at some other distant point.

7 CFR 900.80 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...

SOLUTION OF SINGULAR INTEGRAL EQUATION FOR ELASTICITY THEORY WITH THE HELP OF ASYMPTOTIC POLYNOMIAL FUNCTION

Directory of Open Access Journals (Sweden)

V. P. Gribkova

2014-01-01

Full Text Available The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points using a method of mechanical quadrature  and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation, which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.

An investigation of singular Lagrangians as field systems

International Nuclear Information System (INIS)

Rabei, E.M.

1995-07-01

The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs

Weak lensing galaxy cluster field reconstruction

Science.gov (United States)

Jullo, E.; Pires, S.; Jauzac, M.; Kneib, J.-P.

2014-02-01

In this paper, we compare three methods to reconstruct galaxy cluster density fields with weak lensing data. The first method called FLens integrates an inpainting concept to invert the shear field with possible gaps, and a multi-scale entropy denoising procedure to remove the noise contained in the final reconstruction, that arises mostly from the random intrinsic shape of the galaxies. The second and third methods are based on a model of the density field made of a multi-scale grid of radial basis functions. In one case, the model parameters are computed with a linear inversion involving a singular value decomposition (SVD). In the other case, the model parameters are estimated using a Bayesian Monte Carlo Markov Chain optimization implemented in the lensing software LENSTOOL. Methods are compared on simulated data with varying galaxy density fields. We pay particular attention to the errors estimated with resampling. We find the multi-scale grid model optimized with Monte Carlo Markov Chain to provide the best results, but at high computational cost, especially when considering resampling. The SVD method is much faster but yields noisy maps, although this can be mitigated with resampling. The FLens method is a good compromise with fast computation, high signal-to-noise ratio reconstruction, but lower resolution maps. All three methods are applied to the MACS J0717+3745 galaxy cluster field, and reveal the filamentary structure discovered in Jauzac et al. We conclude that sensitive priors can help to get high signal-to-noise ratio, and unbiased reconstructions.

Fundamental solutions of singular SPDEs

International Nuclear Information System (INIS)

Selesi, Dora

2011-01-01

Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

Integration of a hydraulic production plant in a weak power system on a long radial line

Energy Technology Data Exchange (ETDEWEB)

Lariviere, P. [Hydro-Quebec TransEnergie, 5655 de Marseille, Montreal, Quebec (Canada); Racine, M. [Hydro-Quebec TransEnergie, C.P. 10 000, Montreal, Quebec (Canada)

2009-03-15

Integrating power plants on long lines and weak power systems requires some care. To this effect, a study was conducted to determine if severe disturbances could result when a hydraulic production plant is integrated along a very long radial transmission line. Frequency responses were evaluated to identify possible resonant system operating conditions. Many events such as faults, transformer energyzing and line opening were investigated. All power plant synchronous machines were represented including exciter and governor regulators. Impact of dynamic modeling of the load was examined. The study demonstrates that the overall protective strategy implemented will limit worst overvoltage constraints imposed to equipment and load within an acceptable level. (author)

Singularities: the Brieskorn anniversary volume

National Research Council Canada - National Science Library

Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M

1998-01-01

...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...

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.

Singularity Theory and its Applications

CERN Document Server

Stewart, Ian; Mond, David; Montaldi, James

1991-01-01

A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

Role of Van Hove singularities and momentum-space structure in high-temperature superconductivity

International Nuclear Information System (INIS)

Radtke, R.J.; Levin, K.; Schuettler, H.; Norman, M.R.

1993-01-01

There is a great deal of interest in attributing the high critical temperatures of the cuprates to either the proximity of the Fermi level to a Van Hove singularity or to structure of the superconducting pairing potential in momentum space far from the Fermi surface; the latter is particularly important for spin-fluctuation-mediated pairing mechanisms. We examine these ideas by calculating the critical temperature T c for model Einstein-phonon- and spin-fluctuation-mediated superconductors within both the standard, Fermi-surface-restricted Eliashberg theory and the exact Eliashberg theory, which accounts for the full momentum structure of the pairing potential and the energy dependence of the density of states. Our computations employ band structures chosen to model both the La 2 Sr 2-x CuO 4 and YBa 2 Cu 3 O 7-δ families. For our spin fluctuation calculations, we take the dynamical susceptibility to be the pairing potential and examine two models of this susceptibility in the cuprates. We compare and contrast these models with available magnetic neutron-scattering data, since these data provide the most direct constraints on the susceptibility. We conclude that a model constrained by neutron-scattering measurements will not yield the observed 90-K T c 's regardless of the strength of the electron-spin fluctuation coupling, even when the Van Hove singularity and momentum-space structure are accounted for; moreover, when transport constraints are applied to this type of model, we expect T c ∼10 K, as was found in an earlier paper. We also find that the Van Hove singularity enhances T c much less effectively than weak-coupling calculations would suggest

Preventing singularities in the Einstein-Cartan cosmology

International Nuclear Information System (INIS)

Kuchowicz, B.

1977-01-01

The singularity in expanding cosmological models is an undesirable consequence of general relativity. It may be removed in the Einstein-Cartan theory of gravitation which is an extension of general relativity (''general relativity with spin''). In the Einstein-Cartan theory there appears a characteristic spin-spin interaction which counteracts the contraction of matter above a certain critical density, and thus prevents any singularity. Generalizations of homogeneous cosmological models may contain either locally aligned spins (along an asymmetry axis) or randomly distributed spins (and then only the mean spin density square is macroscopically meaningful). In both cases the singularity can be removed, if only the spin density does increase at a sufficiently fast rate with the contraction of matter. (author)

Initial singularity and pure geometric field theories

Science.gov (United States)

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

2018-01-01

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

Singularity hypotheses a scientific and philosophical assessment

CERN Document Server

Moor, James; Søraker, Johnny; Steinhart, Eric

2012-01-01

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.

Van Hove singularities revisited

International Nuclear Information System (INIS)

Dzyaloshinskii, I.

1987-07-01

Beginning with the work of Hirsch and Scalapino the importance of ln 2 -Van Hove singularity in T c -enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle-particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit (one bare charge) is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel (attraction) and SDW (repulsion) and CDW (attraction) in the ph-channel. It is natural that Umklapps produce an SDW + CDW mixture at either sign of the interaction. What is unusual is that both the pp-ph interplay and the Umklapps give rise to a monster-coherent SS + SDW + CDW mixture, again at either sign of the bare charge. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. 10 refs, 5 figs

Finger image quality based on singular point localization

DEFF Research Database (Denmark)

Wang, Jinghua; Olsen, Martin A.; Busch, Christoph

2014-01-01

Singular points are important global features of fingerprints and singular point localization is a crucial step in biometric recognition. Moreover the presence and position of the core point in a captured fingerprint sample can reflect whether the finger is placed properly on the sensor. Therefore...... and analyze the importance of singular points on biometric accuracy. The experiment is based on large scale databases and conducted by relating the measured quality of a fingerprint sample, given by the positions of core points, to the biometric performance. The experimental results show the positions of core...

Repulsive and attractive timelike singularities in vacuum cosmologies

International Nuclear Information System (INIS)

Miller, B.D.

1979-01-01

Spherically symmetric cosmologies whose big bang is partially spacelike and partially timelike are constrained to occur only in the presence of certain types of matter, and in such cosmologies the timelike part of the big bang is a negative-mass singularity. In this paper examples are given of cylindrically symmetric cosmologies whose big bang is partially spacelike and partially timelike. These cosmologies are vacuum. In some of them, the timelike part of the big bang is clearly a (generalized) negative-mass singularity, while in others it is a (generalized) positive-mass singularity

Singularity theorems from weakened energy conditions

International Nuclear Information System (INIS)

Fewster, Christopher J; Galloway, Gregory J

2011-01-01

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

Managing focal fields of vector beams with multiple polarization singularities.

Science.gov (United States)

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Adaptive control in multi-threaded iterated integration

International Nuclear Information System (INIS)

Doncker, Elise de; Yuasa, Fukuko

2013-01-01

In recent years we have developed a technique for the direct computation of Feynman loop-integrals, which are notorious for the occurrence of integrand singularities. Especially for handling singularities in the interior of the domain, we approximate the iterated integral using an adaptive algorithm in the coordinate directions. We present a novel multi-core parallelization scheme for adaptive multivariate integration, by assigning threads to the rule evaluations in the outer dimensions of the iterated integral. The method ensures a large parallel granularity as each function evaluation by itself comprises an integral over the lower dimensions, while the application of the threads is governed by the adaptive control in the outer level. We give computational results for a test set of 3- to 6-dimensional integrals, where several problems exhibit a loop integral behavior.

Nonlinear singular elliptic equations

International Nuclear Information System (INIS)

Dong Minh Duc.

1988-09-01

We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

Transmutations between singular and subsingular vectors of the N = 2 superconformal algebras

International Nuclear Information System (INIS)

Doerrzapf, Matthias; Gato-Rivera, Beatriz

1999-01-01

We present subsingular vectors of the N = 2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the topological algebra become subsingular vectors of the antiperiodic NS algebra under the topological untwistings. These classes consist of BRST-invariant singular vectors with relative charges q = -2, -1 and zero conformal weight, and nolabel singular vectors with q = 0, -1. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2

Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases

International Nuclear Information System (INIS)

Sobolev, Vladimir

2016-01-01

We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples. (paper)

Infinite derivative gravity : non-singular cosmology & blackhole solutions

NARCIS (Netherlands)

Mazumdar, Anupam

2017-01-01

Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and

Consideration on Singularities in Learning Theory and the Learning Coefficient

Directory of Open Access Journals (Sweden)

Miki Aoyagi

2013-09-01

Full Text Available We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy in learning theory.

Singular trajectories: space-time domain topology of developing speckle fields

Science.gov (United States)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Singularities in Free Surface Flows

Science.gov (United States)

Thete, Sumeet Suresh

Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental

Singular vectors of Malikov-Fagin-Fux in topological theories

International Nuclear Information System (INIS)

Semikhatov, A.M.

1993-01-01

Coincidence of singular vectors in relation to the sl(2) Katza-Mudi algebra and the algebra of the N=2 (twisted) supersymmetry is established. On the base of the Kazama-Suzuki simplest model is obtained a representation for the sl(2) currents in terms of an interacting with mater gravitation. From the Malikov-Fagin-Fux formulae for the sl(2) singular currents is obtained the general expression for singular vectors in topological theories

Transmutation of planar media singularities in a conformal cloak.

Science.gov (United States)

Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K

2013-11-01

Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Global embeddings for branes at toric singularities

CERN Document Server

Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki

2012-01-01

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

Boundary singularities produced by the motion of soap films.

Science.gov (United States)

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

2014-06-10

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

Fold points and singularity induced bifurcation in inviscid transonic flow

International Nuclear Information System (INIS)

Marszalek, Wieslaw

2012-01-01

Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.

Thermal boundary conditions for electrons in a weakly ionized gas near a catalytic wall

International Nuclear Information System (INIS)

Chekmarev, I.

1981-01-01

A technique of matched asymptotic expansions is used to examine the derivation of hydrodynamic transport equations for the external region of a weakly ionized multitemperature gas near an absorbing and conducting wall. An approximate moment solution is constructed for the Knudsen boundary layer. The conditions for the matching of the external and internal expansions lead to a new form of the hydrodynamic boundary conditions, from which the singular behavior of the energy equation for electrons near the wall has been eliminated

Dissipation, intermittency, and singularities in incompressible turbulent flows

Science.gov (United States)

Debue, P.; Shukla, V.; Kuzzay, D.; Faranda, D.; Saw, E.-W.; Daviaud, F.; Dubrulle, B.

2018-05-01

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

Randomised multichannel singular spectrum analysis of the 20th century climate data

Directory of Open Access Journals (Sweden)

Teija Seitola

2015-12-01

Full Text Available In this article, we introduce a new algorithm called randomised multichannel singular spectrum analysis (RMSSA, which is a generalisation of the traditional multichannel singular spectrum analysis (MSSA into problems of arbitrarily large dimension. RMSSA consists of (1 a dimension reduction of the original data via random projections, (2 the standard MSSA step and (3 a recovery of the MSSA eigenmodes from the reduced space back to the original space. The RMSSA algorithm is presented in detail and additionally we show how to integrate it with a significance test based on a red noise null-hypothesis by Monte-Carlo simulation. Finally, RMSSA is applied to decompose the 20th century global monthly mean near-surface temperature variability into its low-frequency components. The decomposition of a reanalysis data set and two climate model simulations reveals, for instance, that the 2–6 yr variability centred in the Pacific Ocean is captured by all the data sets with some differences in statistical significance and spatial patterns.

On the singular perturbations for fractional differential equation.

Science.gov (United States)

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Singular perturbation of simple eigenvalues

International Nuclear Information System (INIS)

Greenlee, W.M.

1976-01-01

Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

Singular continuous spectrum for palindromic Schroedinger operators

International Nuclear Information System (INIS)

Hof, A.; Knill, O.; Simon, B.

1995-01-01

We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)

Non-perturbative string theories and singular surfaces

International Nuclear Information System (INIS)

Bochicchio, M.

1990-01-01

Singular surfaces are shown to be dense in the Teichmueller space of all Riemann surfaces and in the grasmannian. This happens because a regular surface of genus h, obtained identifying 2h disks in pairs, can be approximated by a very large genus singular surface with punctures dense in the 2h disks. A scale ε is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius ε. The non-perturbative partition function is proposed to be a scaling limit of the partition function on such infinite genus singular surfaces with a weight which is the coupling constant g raised to the approximate genus. For a gaussian model in any space-time dimension the regularized partition function on singular surfaces of infinite genus is the partition function of a two-dimensional lattice gas of charges and monopoles. It is shown that modular invariance of the partition function implies a version of the Dirac quantization condition for the values of the e/m charges. Before the scaling limit the phases of the lattice gas may be classified according to the 't Hooft criteria for the condensation of e/m operators. (orig.)

An integral equation arising in two group neutron transport theory

International Nuclear Information System (INIS)

Cassell, J S; Williams, M M R

2003-01-01

An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically

The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram

Science.gov (United States)

Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.

2016-09-01

The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).

Light-like big bang singularities in string and matrix theories

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg

2011-01-01

Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.

Deficiency indices and singular boundary conditions in quantum mechanics

International Nuclear Information System (INIS)

Bulla, W.

1984-01-01

We consider Schroedinger operators H in L 2 (Rsup(n)), n from IN, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions

The road to singularities, and the roses on the way

International Nuclear Information System (INIS)

Collins, C.B.

1978-01-01

A survey of current investigations of space-time singularities is given. The different approaches adopted by various research schools is discussed, and an analogy is drawn between this study and the mounting of an expedition that sets out on a long trail of discovery. A heuristic discussion is given of the latest classification of singularities and some brief comments are made on how physically relevant each type of singularity is. Roughly speaking, it seems that the milder types (at which quantities remain well behaved) are pathological cases, whereas the crude 'big-bang' type of singularity is more generic. (author)

On the singular Sturm-Liouville problems that have the same spectrum

Energy Technology Data Exchange (ETDEWEB)

Gulsen, Tuba [Department of Mathematics, Firat University, 23119, Elazig (Turkey); Ulusoy, Ismail [Department of Mathematics, Adiyaman University, 02040,Adiyaman (Turkey)

2016-06-08

The problem of efficaciously constucting the potential q (x) and the numbers h and H was solved in [1]. Trubowitz [2] investigated the isospectrality problem which have the same spectrum with other same type of problems. Then Jodeit and Levitan [3] considered this problem with a different approach, based on transmutation operators and integral equation. In this work, we discussed this problem for singular Sturm-Liouville operator and obtained some important formulas for the number H, the potential q (x) and the norming constants α{sub n}.

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

International Nuclear Information System (INIS)

Zawaideh, E.; Najmabadi, F.; Conn, R.W.

1986-01-01

A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)

On the Singular Perturbations for Fractional Differential Equation

Directory of Open Access Journals (Sweden)

Abdon Atangana

2014-01-01

Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Singularities and the geometry of spacetime

Science.gov (United States)

Hawking, Stephen

2014-11-01

The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

Integrated ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection

Science.gov (United States)

Yuan, Jing; Ji, Feng; Gao, Yuan; Zhu, Jun; Wei, Chenjun; Zhou, Yu

2018-05-01

A new branch of fault detection is utilizing the noise such as enhancing, adding or estimating the noise so as to improve the signal-to-noise ratio (SNR) and extract the fault signatures. Hereinto, ensemble noise-reconstructed empirical mode decomposition (ENEMD) is a novel noise utilization method to ameliorate the mode mixing and denoised the intrinsic mode functions (IMFs). Despite the possibility of superior performance in detecting weak and multiple faults, the method still suffers from the major problems of the user-defined parameter and the powerless capability for a high SNR case. Hence, integrated ensemble noise-reconstructed empirical mode decomposition is proposed to overcome the drawbacks, improved by two noise estimation techniques for different SNRs as well as the noise estimation strategy. Independent from the artificial setup, the noise estimation by the minimax thresholding is improved for a low SNR case, which especially shows an outstanding interpretation for signature enhancement. For approximating the weak noise precisely, the noise estimation by the local reconfiguration using singular value decomposition (SVD) is proposed for a high SNR case, which is particularly powerful for reducing the mode mixing. Thereinto, the sliding window for projecting the phase space is optimally designed by the correlation minimization. Meanwhile, the reasonable singular order for the local reconfiguration to estimate the noise is determined by the inflection point of the increment trend of normalized singular entropy. Furthermore, the noise estimation strategy, i.e. the selection approaches of the two estimation techniques along with the critical case, is developed and discussed for different SNRs by means of the possible noise-only IMF family. The method is validated by the repeatable simulations to demonstrate the synthetical performance and especially confirm the capability of noise estimation. Finally, the method is applied to detect the local wear fault

Periodic solutions to second-order indefinite singular equations

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Zamora, M.

2017-01-01

Roč. 263, č. 1 (2017), s. 451-469 ISSN 0022-0396 Institutional support: RVO:67985840 Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039617301134

A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

Energy Technology Data Exchange (ETDEWEB)

Bruno, Oscar P., E-mail: obruno@caltech.edu; Lintner, Stéphane K.

2013-11-01

We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.

Prompt form of relativistic equations of motion in a model of singular lagrangian formalism

International Nuclear Information System (INIS)

Gajda, R.P.; Duviryak, A.A.; Klyuchkovskij, Yu.B.

1983-01-01

The purpose of the paper is to develope the way of transition from equations of motion in singular lagrangian formalism to three-dimensional equations of Newton type in the prompt form of dynamics in the framework of c -2 parameter expansion (s. c. quasireltativistic approaches), as well as to find corresponding integrals of motion. The first quasirelativistifc approach for Dominici, Gomis, Longhi model was obtained and investigated

Segmentation of singularity maps in the context of soil porosity

Science.gov (United States)

Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

2016-04-01

Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in

Singular vectors, predictability and ensemble forecasting for weather and climate

International Nuclear Information System (INIS)

Palmer, T N; Zanna, Laure

2013-01-01

The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system’s predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean–atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (review)

Quantum propagation across cosmological singularities

Science.gov (United States)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

The integral form of D = 3 Chern-Simons theories probing C{sup n}/Γ singularities

Energy Technology Data Exchange (ETDEWEB)

Fre, P. [Dipartimento di Fisica, Universita di Torino (Italy); INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); National Research Nuclear University MEPhI, (Moscow Engineering Physics Institute), Moscow (Russian Federation); Grassi, P.A. [INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); DISIT, Universita del Piemonte Orientale, Alessandria (Italy); Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University (Japan)

2017-10-15

We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS{sub 4}/CFT{sub 3} correspondence. From the structural view-point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kaehler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS{sub 4}/CFT{sub 3} correspondence and more generally of M2-branes we emphasize the role of the Kaehler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kaehler quotient K{sub 4} of some flat variety with respect to a suitable group. The crepant resolutions of C{sup n}/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium

International Nuclear Information System (INIS)

Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho

2004-01-01

Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)

Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept

Directory of Open Access Journals (Sweden)

M. Y. Barabanenkov

2012-07-01

Full Text Available If a scatterer and an observation point (receive both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

Science.gov (United States)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

Analytical singular-value decomposition of three-dimensional, proximity-based SPECT systems

Energy Technology Data Exchange (ETDEWEB)

Barrett, Harrison H. [Arizona Univ., Tucson, AZ (United States). College of Optical Sciences; Arizona Univ., Tucson, AZ (United States). Center for Gamma-Ray Imaging; Holen, Roel van [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Arizona Univ., Tucson, AZ (United States). Center for Gamma-Ray Imaging

2011-07-01

An operator formalism is introduced for the description of SPECT imaging systems that use solid-angle effects rather than pinholes or collimators, as in recent work by Mitchell and Cherry. The object is treated as a 3D function, without discretization, and the data are 2D functions on the detectors. An analytic singular-value decomposition of the resulting integral operator is performed and used to compute the measurement and null components of the objects. The results of the theory are confirmed with a Landweber algorithm that does not require a system matrix. (orig.)

Five-dimensional null-cone structure of big bang singularity

Energy Technology Data Exchange (ETDEWEB)

Lauro, S.; Schucking, E.L.

1985-04-01

The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space MV is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in MV there is a motion of MV such that F'= F. The big bang singularity is the vertex of a null half-cone in MV. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.

Five-dimensional null-cone structure of big bang singularity

International Nuclear Information System (INIS)

Lauro, S.; Schucking, E.L.

1985-01-01

The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space M 5 is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in M 5 there is a motion π of M 5 such that F'=π 0 F. The big bang singularity is the vertex of a null half-cone in M 5 . Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group. (author)

Logarithmic of mass singularities theorem in non massive quantum electrodynamics

International Nuclear Information System (INIS)

Mares G, R.; Luna, H.

1997-01-01

We give an explicit example of the use of dimensional regularization to calculate in a unified approach, all the ultraviolet, infrared and mass singularities, by considering the LMS (logarithms of mass singularities) theorem in the frame of massless QED (Quantum electrodynamics). In the calculation of the divergent part of the cross section, all singularities are found to cancel provided soft and hard photon emission are both taken into account. (Author)

The analysis of optimal singular controls for SEIR model of tuberculosis

Science.gov (United States)

Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.

2014-12-01

The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.

Singularities of elastic scattering amplitude by long-range potentials

International Nuclear Information System (INIS)

Kvitsinsky, A.A.; Komarov, I.V.; Merkuriev, S.P.

1982-01-01

The angular peculiarities and the zero energy singularities of the elastic scattering amplitude by a long-range potential are described. The singularities of the elastic (2 → 2) scattering amplitude for a system of three Coulomb particles are considered [ru

Influence of the non-singular stress on the crack extension and fatigue life

International Nuclear Information System (INIS)

Cheng, C.Z.; Recho, N.; Niu, Z.R.

2012-01-01

Highlights: ► BEM is combined by characteristic analysis to calculate the singular stress field. ► A new method is proposed to evaluate the full stress field at crack tip region. ► Effect of non-singular stress on the propagation direction of the fatigue crack is analyzed. ► The influence of non-singular stress on the fatigue crack life is evaluated. - Abstract: The complete elasticity stress field at a crack tip region can be presented by the sum of the singular stress and several non-singular stress terms according to the Williams asymptotic expansion theory. The non-singular stress has a non-negligible influence on the prediction of the crack extension direction and crack growth rate under the fatigue loading. A novel method combining the boundary element method and the singularity characteristic analysis is proposed here to evaluate the complete stress field at a crack tip region. In this new method, any non-singular stress term in the Williams series expansion can be evaluated according to the computational accuracy requirement. Then, a modified Paris law is introduced to predict the crack propagation under the mixed-mode loading for exploring the influence of the non-singular stress on the fatigue life duration. By comparing with the existed experimental results, the predicted crack fatigue life when the non-singular stress is taken into consideration is more accurate than the predicted ones only considering the singular stress.

Pseudospherical surfaces with singularities

DEFF Research Database (Denmark)

Brander, David

2017-01-01

We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...

Branes at Singularities in Type 0 String Theory

OpenAIRE

Alishahiha, M; Brandhuber, A; Oz, Y

1999-01-01

We consider Type 0B D3-branes placed at conical singularities and analyze in detail the conifold singularity. We study the non supersymmetric gauge theories on their worldvolume and their conjectured dual gravity descriptions. In the ultraviolet the solutions exhibit a logarithmic running of the gauge coupling. In the infrared we find confining solutions and IR fixed points.

Numerical treatments for solving nonlinear mixed integral equation

Directory of Open Access Journals (Sweden)

M.A. Abdou

2016-12-01

Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.

Quantization rules for point singularities in superfluid 3He and liquid crystals

International Nuclear Information System (INIS)

Blaha, S.

1976-01-01

It is shown that pointlike singularities can exist in superfluid 3 He. Integer quantum numbers are associated with these singularities. The quantization rules follow from the single valuedness of the order parameter and quantities derived from it. The results are also easily extended to the quantization of point singularities in nematic liquid crystals. The pointlike singularities in 3 He-A are experimentally accessible analogs of the magnetic monopole

Endpoint singularities in unintegrated parton distributions

CERN Document Server

Hautmann, F

2007-01-01

We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare this with the cut-off regularization method. The counterterms for the distributions with subtractive regularization are given in coordinate space by compact all-order expressions in terms of eikonal-line operators. We carry out an explicit calculation at one loop for the unintegrated quark distribution. We discuss the relation of the unintegrated parton distributions in subtractive regularization with the ordinary parton distributions.

A Note on Inclusion Intervals of Matrix Singular Values

Directory of Open Access Journals (Sweden)

Shu-Yu Cui

2012-01-01

Full Text Available We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.

Singularities in x-ray spectra of metals

International Nuclear Information System (INIS)

Mahan, G.D.

1987-08-01

The x-ray spectroscopies discussed are absorption, emission, and photoemission. The singularities show up in each of them in a different manner. In absorption and emission they show up as power law singularities at the thresholds frequencies. This review will emphasize two themes. First a simple model is proposed to describe this phenomena, which is now called the MND model after MAHAN-NOZIERES-DeDOMINICIS. Exact analytical solutions are now available for this model for the three spectroscopies discussed above. These analytical models can be evaluated numerically in a simple way. The second theme of this review is that great care must be used when comparing the theory to experiment. A number of factors influence the edge shapes in x-ray spectroscopy. The edge singularities play an important role, and are observed in many matals. Quantitative fits of the theory to experiment require the consideration of other factors. 51 refs

Hidden singularities in non-abelian gauge fields

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

1978-01-01

It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt

Physics of singularities in pressure-impulse theory

Science.gov (United States)

Krechetnikov, R.

2018-05-01

The classical solution in the pressure-impulse theory for the inviscid, incompressible, and zero-surface-tension water impact of a flat plate at zero dead-rise angle exhibits both singular-in-time initial fluid acceleration, ∂v /∂ t |t =0˜δ (t ) , and a near-plate-edge spatial singularity in the velocity distribution, v ˜r-1 /2 , where r is the distance from the plate edge. The latter velocity divergence also leads to the interface being stretched infinitely right after the impact, which is another nonphysical artifact. From the point of view of matched asymptotic analysis, this classical solution is a singular limit when three physical quantities achieve limiting values: sound speed c0→∞ , fluid kinematic viscosity ν →0 , and surface tension σ →0 . This leaves open a question on how to resolve these singularities mathematically by including the neglected physical effects—compressibility, viscosity, and surface tension—first one by one and then culminating in the local compressible viscous solution valid for t →0 and r →0 , demonstrating a nontrivial flow structure that changes with the degree of the bulk compressibility. In the course of this study, by starting with the general physically relevant formulation of compressible viscous flow, we clarify the parameter range(s) of validity of the key analytical solutions including classical ones (inviscid incompressible and compressible, etc.) and understand the solution structure, its intermediate asymptotics nature, characteristics influencing physical processes, and the role of potential and rotational flow components. In particular, it is pointed out that sufficiently close to the plate edge surface tension must be taken into account. Overall, the idea is to highlight the interesting physics behind the singularities in the pressure-impulse theory.

Topological regularizations of the triple collision singularity in the 3-vortex problem

International Nuclear Information System (INIS)

Hiraoka, Yasuaki

2008-01-01

The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail

Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams

Science.gov (United States)

Haitao, Chen; Gao, Zenghui; Wang, Wanqing

2017-06-01

The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.

Analytic solution of the BCS gap equation with a logarithmic singularity in the density of states

International Nuclear Information System (INIS)

Bhardwaj, A.; Muthu, S.K.

1999-01-01

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically for a density of states function with a logarithmic singularity. It is an extension of our earlier work where we had assumed a constant density of states. We continue to work in the weak-coupling limit and consider both phononic and non-phononic pairings. Expressions are obtained for T c , Δ 0 (the gap at T=0), and the jump in the electronic specific heat at T=T c . We also calculate the isotope exponent and show that it is possible to reproduce the broad features of the experimental results in this framework. (orig.)

Deformations of surface singularities

CERN Document Server

Szilárd, ágnes

2013-01-01

The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry.  This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...

Practical advantages of almost-balanced-weak-value metrological techniques

Science.gov (United States)

Martínez-Rincón, Julián; Chen, Zekai; Howell, John C.

2017-06-01

Precision measurements of ultrasmall linear velocities of one of the mirrors in a Michelson interferometer are performed using two different weak-value techniques. We show that the technique of almost-balanced weak values (ABWV) offers practical advantages over the technique of weak-value amplification, resulting in larger signal-to-noise ratios and the possibility of longer integration times due to robustness to slow drifts. As an example of the performance of the ABWV protocol we report a velocity sensitivity of 60 fm/s after 40 h of integration time. The sensitivity of the Doppler shift due to the moving mirror is 150 nHz.

Singularity, initial conditions and quantum tunneling in modern cosmology

International Nuclear Information System (INIS)

Khalatnikov, I M; Kamenshchik, A Yu

1998-01-01

The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties. (special issue)

Rules for integrals over products of distributions from coordinate independence of path integrals

International Nuclear Information System (INIS)

Kleinert, H.; Chervyakov, A.

2001-01-01

In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence of the path integrals. (orig.)

Supersymmetry in singular spaces

NARCIS (Netherlands)

Bergshoeff, Eric

2002-01-01

We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a

Non-singular cosmologies in the conformally invariant gravitation theory

International Nuclear Information System (INIS)

Kembhavi, A.K.

1976-01-01

It is shown that in the framework of a conformally invariant gravitation theory, the singularity which is present in some anisotropic universes in general relativity is due to a wrong choice of conformal frame. Frames exist in which these models can be made singularity free. (author)

Controllability of non-linear systems: generic singularities and their stability

International Nuclear Information System (INIS)

Davydov, Alexey A; Zakalyukin, Vladimir M

2012-01-01

This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.

Boundary element analysis of stress singularity in dissimilar metals by friction welding

International Nuclear Information System (INIS)

Chung, N. Y.; Park, C. H.

2012-01-01

Friction welded dissimilar metals are widely applied in automobiles, rolling stocks, machine tools, and various engineering fields. Dissimilar metals have several advantages over homogeneous metals, including high strength, material property, fatigue endurance, impact absorption, high reliability, and vibration reduction. Due to the increased use of these metals, understanding their behavior under stress conditions is necessary, especially the analysis of stress singularity on the interface of friction-welded dissimilar metals. To establish a strength evaluation method and a fracture criterion, it is necessary to analyze stress singularity on the interface of dissimilar metals with welded flashes by friction welding under various loads and temperature conditions. In this paper, a method analyzing stress singularity for the specimens with and without flashes set in friction welded dissimilar metals is introduced using the boundary element method. The stress singularity index (λ) and the stress singularity factor (Γ) at the interface edge are computed from the stress analysis results. The shape and flash thickness, interface length, residual stress, and load are considered in the computation. Based on these results, the variations of interface length (c) and the ratio of flash thickness (t2 t1) greatly influence the stress singularity factors at the interface edge of friction welded dissimilar metals. The stress singularity factors will be a useful fracture parameter that considers stress singularity on the interface of dissimilar metals

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

Science.gov (United States)

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

2015-09-01

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

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

Energy Technology Data Exchange (ETDEWEB)

Stuchlik, Z.; Pugliese, D.; Schee, J.; Kucakova, H. [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Opava (Czech Republic)

2015-09-15

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

On the collinear singularity problem of hot QCD

International Nuclear Information System (INIS)

Candelpergher, B.; Grandou, T.

2002-01-01

The collinear singularity problem of hot QCD is revisited within a perturbative resummation scheme (PR) of the leading thermal fluctuations. On the basis of actual calculations, new aspects are discovered concerning the origin of the singularity plaguing the soft real photon emission rate out of a quark-gluon plasma at thermal equilibrium, when the latter is calculated by means of the Resummation Program (RP)

Singularity: Raychaudhuri equation once again

Indian Academy of Sciences (India)

Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.

Singularities in FLRW Spacetimes

NARCIS (Netherlands)

Lam, Huibert het; Prokopec, Tom

2017-01-01

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept

Dyslexia singular brain

International Nuclear Information System (INIS)

Habis, M.; Robichon, F.; Demonet, J.F.

1996-01-01

Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.)

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

International Nuclear Information System (INIS)

Unver, O.; Gurtug, O.

2010-01-01

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.

Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

KAUST Repository

Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M.

2015-01-01

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

KAUST Repository

Paszyńska, Anna

2015-06-01

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

Characteristic classes, singular embeddings, and intersection homology.

Science.gov (United States)

Cappell, S E; Shaneson, J L

1987-06-01

This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.

Microlocal study of S-matrix singularity structure

International Nuclear Information System (INIS)

Kawai, Takahiro; Kyoto Univ.; Stapp, H.P.

1975-01-01

Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.) [de

Can noncommutativity resolve the Big-Bang singularity?

CERN Document Server

Maceda, M; Manousselis, P; Zoupanos, George

2004-01-01

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.

Geometric singular perturbation analysis of systems with friction

DEFF Research Database (Denmark)

Bossolini, Elena

This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter......, two mechanical problems with two different formulations of the friction force are introduced and analysed. The first mechanical problem is a one-dimensional spring-block model describing earthquake faulting. The dynamics of earthquakes is naturally a multiple timescale problem: the timescale...... scales. The action of friction is generally explained as the loss and restoration of linkages between the surface asperities at the molecular scale. However, the consequences of friction are noticeable at much larger scales, like hundreds of kilometers. By using geometric singular perturbation theory...

From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

International Nuclear Information System (INIS)

Ganapol, B.D.

2001-01-01

A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

Solitary wave solution to a singularly perturbed generalized Gardner ...

Indian Academy of Sciences (India)

2017-03-24

Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...

7 CFR 1200.1 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...

Analysis of flexible-membrane aerofoils by a method of velocity singularities

International Nuclear Information System (INIS)

Mateescu, D.; Newman, B.G.

1985-01-01

Two dimensional sails were originally treated as flexible, impervious, inextensible membranes. These methods are developed in the context of thin aerofoil theory, the membrane being replaced by a vortex sheet and the boundary conditions satisfied at the corresponding positions on the aerofoil chord. The present present methos is developed as a linear potential theory, although it may be further extended to include non-linear and viscous effects. The new analysis is based on the method of velocity singularities associated with the changes in aerofoil slope developed for rigid aerofoils; it eliminates the need of formally solving an integral equation

Assessing the relationships between phylogenetic and functional singularities in sharks (Chondrichthyes).

Science.gov (United States)

Cachera, Marie; Le Loc'h, François

2017-08-01

The relationships between diversity and ecosystem functioning have become a major focus of science. A crucial issue is to estimate functional diversity, as it is intended to impact ecosystem dynamics and stability. However, depending on the ecosystem, it may be challenging or even impossible to directly measure ecological functions and thus functional diversity. Phylogenetic diversity was recently under consideration as a proxy for functional diversity. Phylogenetic diversity is indeed supposed to match functional diversity if functions are conservative traits along evolution. However, in case of adaptive radiation and/or evolutive convergence, a mismatch may appear between species phylogenetic and functional singularities. Using highly threatened taxa, sharks, this study aimed to explore the relationships between phylogenetic and functional diversities and singularities. Different statistical computations were used in order to test both methodological issue (phylogenetic reconstruction) and overall a theoretical questioning: the predictive power of phylogeny for function diversity. Despite these several methodological approaches, a mismatch between phylogeny and function was highlighted. This mismatch revealed that (i) functions are apparently nonconservative in shark species, and (ii) phylogenetic singularity is not a proxy for functional singularity. Functions appeared to be not conservative along the evolution of sharks, raising the conservational challenge to identify and protect both phylogenetic and functional singular species. Facing the current rate of species loss, it is indeed of major importance to target phylogenetically singular species to protect genetic diversity and also functionally singular species in order to maintain particular functions within ecosystem.

Charged singularities: repulsive effects

Energy Technology Data Exchange (ETDEWEB)

De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia

1980-07-01

The repulsive phenomena which a particle experiences in the vicinity of a naked singularity are investigated in the Kerr-Newman space-time. The aim is to extend the knowledge of this fact to charged solutions and to have a direct indication of how, in these situations, the gravitational and electrostatic interactions are competing.

Singular f-sum rule for superfluid 4He

International Nuclear Information System (INIS)

Wong, V.K.

1979-01-01

The validity and applicability to inelastic neutron scattering of a singular f-sum rule for superfluid helium, proposed by Griffin to explain the rhosub(s) dependence in S(k, ω) as observed by Woods and Svensson, are examined in the light of similar sum rules rigorously derived for anharmonic crystals and Bose liquids. It is concluded that the singular f-sum rules are only of microscopic interest. (Auth,)

Dimension counts for singular rational curves via semigroups

OpenAIRE

Cotterill, Ethan; Feital, Lia; Martins, Renato Vidal

2015-01-01

We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\\mb{P}^n$, holds whenever $g$ is small.

On singular interaction potentials in classical statistical mechanics

International Nuclear Information System (INIS)

Zagrebnov, V.A.; Pastur, L.A.

1978-01-01

A classical system of particles with stable two-body interaction potential is considered. It is shown that for a certain class of highly singular stable two-body potentials a cut-off procedure preserves the stability of the potential. The thermodynamical potentials (pressure and free energy density) and correlation functions are proved to have the property of asymptotic independence with respect to the continuation of the interaction potentials near singularity

Current singularities at finitely compressible three-dimensional magnetic null points

International Nuclear Information System (INIS)

Pontin, D.I.; Craig, I.J.D.

2005-01-01

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

Quantum fate of singularities in a dark-energy dominated universe

International Nuclear Information System (INIS)

Bouhmadi-Lopez, Mariam; Kiefer, Claus; Sandhoefer, Barbara; Moniz, Paulo Vargas

2009-01-01

Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue of whether some of these singularities, the big freeze and the big demarrage, can be avoided in quantum cosmology. We use the framework of quantum geometrodynamics. We restrict our attention to a class of models whose matter content can be described by a generalized Chaplygin gas and be represented by a scalar field with an appropriate potential. Employing the DeWitt criterion that the wave function be zero at the classical singularity, we show that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found. These solutions thus avoid the classical singularity. We discuss the reasons for the remaining ambiguity in fixing the solution.

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

Science.gov (United States)

Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni

2016-09-01

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

FN approximation of the solution to a singular integral equation of classical reactor physics

Energy Technology Data Exchange (ETDEWEB)

Ganapol, B.D. [Department of Aerospace and Mechanical Engineering, University of Arizona, AME Building, Tucson, AZ 85721 (United States)]. E-mail: ganapol@ame.arizona.edu

2004-11-01

The iterated FN method is applied to a singular integral equation arising from a classical problem of reactor physics to determine the distribution of fissile material giving a spatially uniform flux. The FN iterations are accelerated toward convergence through the Wynn-algorithm - but first - Happy Birthday 'Fast Eddie' Larsen Why do I refer to the well known, most proper and exquisitely accomplished Edward W. Larsen as 'Fast Eddie'. Well our story begins in a small back bar room in the lobby of one of Los Alamos' finest and most luxurious hotels. Two young men were having a transport theoretic discussion while they were engaged in a serious game of pool with monetary benefits going to the winner. In addition, the two were sipping their most favorite lavation in rather large quantities - one, a short stocky man with thinning hair, was sipping to forget the cost of his recent divorce, and the other, a shorter stockier man also with thinning hair, was drinking, well because he liked to drink and it just made him silly. As they continued their transport discussion, one stocky man turned to the other and said, 'I wonder what 'Fast Eddie' Larsen would say to our transport question'. The other stocky man immediately thought the 'Fast Eddie' reference was to Paul Newman who played 'Fast Eddie', an expert at applied particle transport theory (a pool player) in the movie the Hustler and asked if indeed this was the case. The first stocky man said 'No. I call everyone with the name Ed 'Fast Eddie' ' - and that's the story of how 'Fast Eddie' Larsen got his name. Happy 60th Ed and thanks for all the great transport theory - from one of your biggest fans.

FN approximation of the solution to a singular integral equation of classical reactor physics

International Nuclear Information System (INIS)

Ganapol, B.D.

2004-01-01

The iterated FN method is applied to a singular integral equation arising from a classical problem of reactor physics to determine the distribution of fissile material giving a spatially uniform flux. The FN iterations are accelerated toward convergence through the Wynn-algorithm - but first - Happy Birthday 'Fast Eddie' Larsen Why do I refer to the well known, most proper and exquisitely accomplished Edward W. Larsen as 'Fast Eddie'. Well our story begins in a small back bar room in the lobby of one of Los Alamos' finest and most luxurious hotels. Two young men were having a transport theoretic discussion while they were engaged in a serious game of pool with monetary benefits going to the winner. In addition, the two were sipping their most favorite lavation in rather large quantities - one, a short stocky man with thinning hair, was sipping to forget the cost of his recent divorce, and the other, a shorter stockier man also with thinning hair, was drinking, well because he liked to drink and it just made him silly. As they continued their transport discussion, one stocky man turned to the other and said, 'I wonder what 'Fast Eddie' Larsen would say to our transport question'. The other stocky man immediately thought the 'Fast Eddie' reference was to Paul Newman who played 'Fast Eddie', an expert at applied particle transport theory (a pool player) in the movie the Hustler and asked if indeed this was the case. The first stocky man said 'No. I call everyone with the name Ed 'Fast Eddie' ' - and that's the story of how 'Fast Eddie' Larsen got his name. Happy 60th Ed and thanks for all the great transport theory - from one of your biggest fans

Non-uniqueness of the source for singular gauge fields

International Nuclear Information System (INIS)

Lanyi, G.; Pappas, R.

1977-01-01

It is shown that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a 'smeared' potential or a 'smeared' field strength. (Auth.)

Invariant identification of naked singularities in spherically symmetric spacetimes

International Nuclear Information System (INIS)

Torres, R

2012-01-01

The study of generic naked singularities and their implications for the cosmic censorship conjecture is still an open issue in the framework of general relativity. One of the obstacles can be traced to the procedures for identifying naked singularities. Usually, the methods applied are not only model and coordinate dependent, but they very often rely in some strong assumptions on the degree of differentiability of the physical magnitudes of the model (such as the mass, density, etc) in the singularity. In this paper, we present a coordinate independent framework for identifying naked singularities based on invariants which is also devoid of strong differentiability requirements. The approach is intended to analyse whole families of models and to provide general results related to the cosmic censorship conjecture. Moreover, since the framework has a strict geometrical nature it can be used with alternative theories of gravitation as long as they assume the existence of a Lorentzian manifold. We exemplify its strength by applying it to the study of the collapse of radiation in radiative coordinates and the collapse of dust in comoving coordinates. (paper)

Connection conditions and the spectral family under singular potentials

International Nuclear Information System (INIS)

Tsutsui, Izumi; Fueloep, Tamas; Cheon, Taksu

2003-01-01

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wavefunctions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well defined even if the wavefunctions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential V(x)=-e 2 vertical bar x vertical bar and the harmonic oscillator with square inverse potential V(x)=(mω 2 /2)x 2 +g/x 2 , and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potential V(-x)=V(x), the spectrum is determined solely by the eigenvalues of the characteristic matrix U element of U(2)

Fermi-edge singularity and the functional renormalization group

Science.gov (United States)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

Families of singular and subsingular vectors of the topological N=2 superconformal algebra

International Nuclear Information System (INIS)

Gato-Rivera, B.; Rosado, J.I.

1998-01-01

We analyze several issues concerning the singular vectors of the topological N=2 superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties, finding four different types in chiral Verma modules and twenty-nine different types in complete Verma modules. Then we study the family structure of the singular vectors, every member of a family being mapped to any other member by a chain of simple transformations involving the spectral flows. The families of singular vectors in chiral Verma modules follow a unique pattern (four vectors) and contain subsingular vectors. We write down these families until level 3, identifying the subsingular vectors. The families of singular vectors in complete Verma modules follow infinitely many different patterns, grouped roughly in five main kinds. We present a particularly interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the complete set of singular vectors at level 1 (twenty-eight different types). Finally we analyze the Doerrzapf conditions leading to two linearly independent singular vectors of the same type, at the same level in the same Verma module, and we write down four examples of those pairs of singular vectors, which belong to the same thirty-eight-member family. (orig.)

Body frames and frame singularities for three-atom systems

International Nuclear Information System (INIS)

Littlejohn, R.G.; Mitchell, K.A.; Aquilanti, V.; Cavalli, S.

1998-01-01

The subject of body frames and their singularities for three-particle systems is important not only for large-amplitude rovibrational coupling in molecular spectroscopy, but also for reactive scattering calculations. This paper presents a geometrical analysis of the meaning of body frame conventions and their singularities in three-particle systems. Special attention is devoted to the principal axis frame, a certain version of the Eckart frame, and the topological inevitability of frame singularities. The emphasis is on a geometrical picture, which is intended as a preliminary study for the more difficult case of four-particle systems, where one must work in higher-dimensional spaces. The analysis makes extensive use of kinematic rotations. copyright 1998 The American Physical Society

Polarization singularities of the object field of skin surface

International Nuclear Information System (INIS)

Angelsky, O V; Ushenko, A G; Ushenko, Yu A; Ushenko, Ye G

2006-01-01

The paper deals with the investigation of formation mechanisms of laser radiation polarization structure scattered by an optically thin surface layer of human skin in two registration zones: a boundary field and a far zone of Fraunhofer diffraction. The conditions of forming polarization singularities by such an object in the scattered radiation field have been defined. Statistical and fractal polarization structure of object fields of physiologically normal and pathologically changed skin has been studied. It has been shown that polarization singularities of radiation scattered by physiologically normal skin samples have a fractal coordinate structure. It is characteristic for fields of pathologically changed skin to have a statistical coordinate structure of polarization singularities in all diffraction zones

TRUST MODEL FOR SOCIAL NETWORK USING SINGULAR VALUE DECOMPOSITION

Directory of Open Access Journals (Sweden)

Davis Bundi Ntwiga

2016-06-01

Full Text Available For effective interactions to take place in a social network, trust is important. We model trust of agents using the peer to peer reputation ratings in the network that forms a real valued matrix. Singular value decomposition discounts the reputation ratings to estimate the trust levels as trust is the subjective probability of future expectations based on current reputation ratings. Reputation and trust are closely related and singular value decomposition can estimate trust using the real valued matrix of the reputation ratings of the agents in the network. Singular value decomposition is an ideal technique in error elimination when estimating trust from reputation ratings. Reputation estimation of trust is optimal at the discounting of 20 %.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

Directory of Open Access Journals (Sweden)

L.-P. Wang

2015-09-01

Full Text Available Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2 (Edinburgh, UK during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

Science.gov (United States)

Wang, L.-P.; Ochoa-Rodríguez, S.; Onof, C.; Willems, P.

2015-09-01

Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

KAUST Repository

Abdulle, Assyr

2012-01-01

© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

String theory and cosmological singularities

Indian Academy of Sciences (India)

recent times, string theory is providing new perspectives of such singularities which .... holes appear as stacks of a large number of D-branes wrapped in internal .... results into a well-known measure factor which makes the wave function into a.

Interval matrices: Regularity generates singularity

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří; Shary, S.P.

2018-01-01

Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

On reliability of singular-value decomposition in attractor reconstruction

International Nuclear Information System (INIS)

Palus, M.; Dvorak, I.

1990-12-01

Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs

Algebraic method for constructing singular steady solitary waves: a case study

Science.gov (United States)

Clamond, Didier; Dutykh, Denys; Galligo, André

2016-07-01

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.

Constraint theory, singular lagrangians and multitemporal dynamics

International Nuclear Information System (INIS)

Lusanna, L.

1988-01-01

Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory

Weak limits for quantum random walks

International Nuclear Information System (INIS)

Grimmett, Geoffrey; Janson, Svante; Scudo, Petra F.

2004-01-01

We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X n denoting position at time n, we show that X n /n converges weakly as n→∞ to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods

Singularities of robot mechanisms numerical computation and avoidance path planning

CERN Document Server

Bohigas, Oriol; Ros, Lluís

2017-01-01

This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves...

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Directory of Open Access Journals (Sweden)

Borbon Martin de

2017-02-01

Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

Asymptotic expansions close to the singularity in Gowdy spacetimes[04.20.Dw Singularities and cosmic censorship;

Energy Technology Data Exchange (ETDEWEB)

Ringstroem, Hans [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany)

2004-02-07

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In a paper by Grubisic and Moncrief, a formal expansion of solutions in the direction towards the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In a previous paper, we proved that one can put a condition on initial data that leads to asymptotic expansions. However, control of up to and including three derivatives in L{sup 2} was necessary, and the condition was rather technical. The main point of the present paper is to demonstrate the existence of certain monotone quantities and to illustrate how these can be used to weaken the assumptions to one derivative in the sup norm. Furthermore, we demonstrate that the false spikes do not appear in the disc model. Finally, we show that knowledge concerning the behaviour of the solution (as time tends to the singularity) for one fixed spatial point in some situations can be used to conclude that there are smooth expansions in the neighbourhood of that spatial point.

Singularity detection by wavelet approach: application to electrocardiogram signal

Science.gov (United States)

Jalil, Bushra; Beya, Ouadi; Fauvet, Eric; Laligant, Olivier

2010-01-01

In signal processing, the region of abrupt changes contains the most of the useful information about the nature of the signal. The region or the points where these changes occurred are often termed as singular point or singular region. The singularity is considered to be an important character of the signal, as it refers to the discontinuity and interruption present in the signal and the main purpose of the detection of such singular point is to identify the existence, location and size of those singularities. Electrocardiogram (ECG) signal is used to analyze the cardiovascular activity in the human body. However the presence of noise due to several reasons limits the doctor's decision and prevents accurate identification of different pathologies. In this work we attempt to analyze the ECG signal with energy based approach and some heuristic methods to segment and identify different signatures inside the signal. ECG signal has been initially denoised by empirical wavelet shrinkage approach based on Steins Unbiased Risk Estimate (SURE). At the second stage, the ECG signal has been analyzed by Mallat approach based on modulus maximas and Lipschitz exponent computation. The results from both approaches has been discussed and important aspects has been highlighted. In order to evaluate the algorithm, the analysis has been done on MIT-BIH Arrhythmia database; a set of ECG data records sampled at a rate of 360 Hz with 11 bit resolution over a 10mv range. The results have been examined and approved by medical doctors.

Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach

Directory of Open Access Journals (Sweden)

Ayman A. El-Badawy

2016-01-01

Full Text Available Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.

Mathematical models with singularities a zoo of singular creatures

CERN Document Server

Torres, Pedro J

2015-01-01

The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.

Experimental verification of free-space singular boundary conditions in an invisibility cloak

International Nuclear Information System (INIS)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Zhang, Baile; Chen, Huanyang

2016-01-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak. (paper)

Experimental verification of free-space singular boundary conditions in an invisibility cloak

Science.gov (United States)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

2016-04-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

Screw Theory Based Singularity Analysis of Lower-Mobility Parallel Robots considering the Motion/Force Transmissibility and Constrainability

Directory of Open Access Journals (Sweden)

Xiang Chen

2015-01-01

Full Text Available Singularity is an inherent characteristic of parallel robots and is also a typical mathematical problem in engineering application. In general, to identify singularity configuration, the singular solution in mathematics should be derived. This work introduces an alternative approach to the singularity identification of lower-mobility parallel robots considering the motion/force transmissibility and constrainability. The theory of screws is used as the mathematic tool to define the transmission and constraint indices of parallel robots. The singularity is hereby classified into four types concerning both input and output members of a parallel robot, that is, input transmission singularity, output transmission singularity, input constraint singularity, and output constraint singularity. Furthermore, we take several typical parallel robots as examples to illustrate the process of singularity analysis. Particularly, the input and output constraint singularities which are firstly proposed in this work are depicted in detail. The results demonstrate that the method can not only identify all possible singular configurations, but also explain their physical meanings. Therefore, the proposed approach is proved to be comprehensible and effective in solving singularity problems in parallel mechanisms.

Generic phase transitions and profit singularities in Arnol'd's model

International Nuclear Information System (INIS)

Davydov, Aleksei A; Matos, Helena Mena

2007-01-01

For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families. Bibliography: 16 titles.

Classical resolution of black hole singularities via wormholes

Energy Technology Data Exchange (ETDEWEB)

Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)

2016-03-15

In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)

Singular value correlation functions for products of Wishart random matrices

International Nuclear Information System (INIS)

Akemann, Gernot; Kieburg, Mario; Wei, Lu

2013-01-01

We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalizes the classical Wishart–Laguerre Gaussian unitary ensemble with M = 1. In this paper, we first compute the joint probability distribution for the singular values of the product matrix when the matrix size N and the number M are fixed but arbitrary. This leads to a determinantal point process which can be realized in two different ways. First, it can be written as a one-matrix singular value model with a non-standard Jacobian, or second, for M ⩾ 2, as a two-matrix singular value model with a set of auxiliary singular values and a weight proportional to the Meijer G-function. For both formulations, we determine all singular value correlation functions in terms of the kernels of biorthogonal polynomials which we explicitly construct. They are given in terms of the hypergeometric and Meijer G-functions, generalizing the Laguerre polynomials for M = 1. Our investigation was motivated from applications in telecommunication of multi-layered scattering multiple-input and multiple-output channels. We present the ergodic mutual information for finite-N for such a channel model with M − 1 layers of scatterers as an example. (paper)

A ferromagnetic chain in a random weak field

Science.gov (United States)

Avgin, I.

1996-10-01

The harmonic magnon modes in a Heisenberg ferromagnetic chain in a random weak field are studied. The Lyapunov exponent for the uniform ( k = 0) mode is computed using the coherent potential approximation (CPA) in the weak-disorder limit. The CPA results are compared with the numerical and weak-disorder expansions of various random systems. We have found that the inverse localization length and the integrated density of states have anomalous power law behaviour as reported earlier. The CPA also reproduces the dispersion law for the same system, calculated by Pimentel and Stinchcombe using the real space renormalization scaling technique. A brief comment is also made for the uniform weak-field case.

Cosmic censorship and the strengths of singularities

International Nuclear Information System (INIS)

Newman, R.P.

1986-01-01

This paper considers the principal definitions concerning limiting curvature strength on geodesics, and on non-spacelike geodesics in particular. They are formulated in terms of focussing conditions. Two definitions suggest themselves, and these are given in terms of a concept of a generalized Jacobi field. An historical survey is presented on some important developments concerning examples of naked singularities. The historical context is recalled in which these models, and cosmic censorship in general, have arisen. It is the author's opinion that one can expect to obtain theoretical limitations on the strengths of any naked singularities which do occur

Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions

International Nuclear Information System (INIS)

Albeverio, S; Khrennikov, A Yu; Shelkovich, V M

2005-01-01

We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed

K3-fibered Calabi-Yau threefolds II, singular fibers

OpenAIRE

Hunt, Bruce

1999-01-01

In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur. This differs from previous work since the fibrations we discuss have constant modulus, and the singular fibers have torsion monodromy.

Cosmological singularities in electrovacuum spacetimes with two-parameter spacelike isometry groups

International Nuclear Information System (INIS)

Mansfield, P.A.

1989-01-01

The big bang singularities occurring in an infinite-dimensional class of solutions to the source-free Einstein-Maxwell equations are presented. These solutions are essentially Gowdy three-torus universes (not necessarily polarized) with electromagnetic radiation added. The problem is reformulated in terms of complex potentials analogous to those used by Ernst in the study of stationary axisymmetric metrics. It is shown that in these new variables the problem admits a harmonic map formulation. Its general solution is written as a perturbation series, where the background solutions being perturbed are a special class of real analytic functions obtained by evolving analytic data specified right at the singularity. The perturbation problem is solved to all orders, and terms which dominate as the singularity is approached are identified at each order. It is possible to sum the dominant terms, and thereby obtain explicit expressions representing the asymptotic structure of the singularities. This representation of asymptotic structure is developed into a simple geometric model. Specializing to the case of no electromagnetic fields, the model is then used to determine asymptotic metric and curvature properties in Gowdy spacetimes. The Gowdy metrics are Kasner-like near their singularity, which is generically a curvature singularity. Curvature-nonsingular solutions can be constructed, and extended into the past beyond a Cauchy horizon. However, such solutions are unstable, a fact which is consistent with Strong Cosmic Censorship

Weak disorder expansion of the invariant measure for the one-dimensional Anderson model

International Nuclear Information System (INIS)

Bovier, A.; Klein, A.

1988-01-01

We show that the formal perturbation expansion of the invariant measure for the Anderson model in one dimension has singularities at all energies E 0 = 2 cos π(p/q); we derive a modified expansion near these energies that we show to have finite coefficients to all orders. Moreover, we show that the first q - 3 of them coincide with those of the naive expansion, while there is an anomaly in the (q - 2)th term. This also gives a weak disorder expansion for the Liapunov exponent and for the density of states. This generalizes previous results of Kappus and Wegner and of Derrida and Gardner

Travelling wave solutions for a singularly perturbed Burgers–KdV ...

Indian Academy of Sciences (India)

This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

Friedmann-like cosmological models without singularity

International Nuclear Information System (INIS)

Kuchowicz, B.

1978-01-01

The Einstein-Cartan theory of gravitation ('general relativity with spin') provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in cosmological models. it is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a micro-physical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid. (author)

Geometric singularities and spectra of Landau-Ginzburg models

International Nuclear Information System (INIS)

Greene, B.R.; Roan, S.S.; Yau, S.T.

1991-01-01

Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginsburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complementary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance of unorbifolded Landau-Ginzburg theories. (orig.)

Non-Gaussian ground-state deformations near a black-hole singularity

Science.gov (United States)

Hofmann, Stefan; Schneider, Marc

2017-03-01

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows us to probe the spacelike singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The physical relevance of different completeness concepts for black holes is discussed.

Image Denoising Using Singular Value Difference in the Wavelet Domain

Directory of Open Access Journals (Sweden)

Min Wang

2018-01-01

Full Text Available Singular value (SV difference is the difference in the singular values between a noisy image and the original image; it varies regularly with noise intensity. This paper proposes an image denoising method using the singular value difference in the wavelet domain. First, the SV difference model is generated for different noise variances in the three directions of the wavelet transform and the noise variance of a new image is used to make the calculation by the diagonal part. Next, the single-level discrete 2-D wavelet transform is used to decompose each noisy image into its low-frequency and high-frequency parts. Then, singular value decomposition (SVD is used to obtain the SVs of the three high-frequency parts. Finally, the three denoised high-frequency parts are reconstructed by SVD from the SV difference, and the final denoised image is obtained using the inverse wavelet transform. Experiments show the effectiveness of this method compared with relevant existing methods.

Singular problems in shell theory. Computing and asymptotics

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM

2010-07-01

It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)

Do sewn up singularities falsify the Palatini cosmology?

Energy Technology Data Exchange (ETDEWEB)

Szydlowski, Marek [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Krakow (Poland); Stachowski, Aleksander [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Borowiec, Andrzej [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Wojnar, Aneta [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Universita di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica, Naples (Italy)

2016-10-15

We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R + γR{sup 2} in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the Ω{sub γ} > 0 is favored by data only very small values of Ω{sub γ} parameter are allowed if we require agreement with the ΛCDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of Ω{sub γ} cannot be rejected. Therefore, observation data favor the universe without the ghost states (f{sup '}(R) > 0) and tachyons (f''(R) > 0). (orig.)

The method of rigged spaces in singular perturbation theory of self-adjoint operators

CERN Document Server

Koshmanenko, Volodymyr; Koshmanenko, Nataliia

2016-01-01

This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...

The exotic heat-trace asymptotics of a regular-singular operator revisited

OpenAIRE

Vertman, Boris

2013-01-01

We discuss the exotic properties of the heat-trace asymptotics for a regular-singular operator with general boundary conditions at the singular end, as observed by Falomir, Muschietti, Pisani and Seeley as well as by Kirsten, Loya and Park. We explain how their results alternatively follow from the general heat kernel construction by Mooers, a natural question that has not been addressed yet, as the latter work did not elaborate explicitly on the singular structure of the heat trace expansion...

OVERGENERALIZATION IN SINGULAR/PLURAL NOUNS AND SUFFIXED NOUNS OF IELTS COURSE STUDENTS

Directory of Open Access Journals (Sweden)

Gharizi Matiini

2016-12-01

Full Text Available This study aims to investigate the morphological overgeneralization of IELTS students. It focuses on the singular/plural nouns and suffixed nouns that are overgeneralized by those students. Three students are chosen as the participants of the study by collecting their writing exercises. Three writing texts are gathered taken from several weeks and materials. The writings are analyzed by sorting the nouns they produced and categorizing them according to the singular/plural nouns and suffixed nouns. The results reveal that the students over extended the rules of singular/plural nouns and suffixed nouns. However, recovery occurs very varied in both singular/plural nouns and suffixed nouns. They tend to be better in mentioning singular/plural nouns, yet they are being selective and careful in writing suffixed nouns. In conclusion, even though the language learners can mark their overgeneralization, it is still difficult for them to recover their errors. It is recommended here that longitudinal study that has more time to examine students recovery from overgeneralization can be conducted for the further study to give more detail evidence in students’ overgeneralizations. Keywords: overgeneralization, singular/plural nouns, suffixed nouns

Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy

Science.gov (United States)

Perelman, Carlos Castro

2016-01-01

A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a spatial singularity at the origin r = 0 is found. These solutions are parametrized by a real valued parameter λ (ranging from 0 to 1) and such that the radial horizon's location is displaced continuously towards the singularity ( r = 0 ) as λ increases. In the extreme limit λ = 1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at r = 0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3.

Quantum jump from singularity to outside of black hole

Energy Technology Data Exchange (ETDEWEB)

Dündar, Furkan Semih [Physics and Mathematics Departments, Sakarya University, 54050, Sakarya (Turkey); Hajian, Kamal [School of Physics, Institute for Research in Fundamental Sciences, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Department of Physics, Sharif University of Technology, P.O. Box 11365-8639, Tehran (Iran, Islamic Republic of)

2016-02-26

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

Singularity-free interpretation of the thermodynamics of supercooled water

International Nuclear Information System (INIS)

Sastry, S.; Debenedetti, P.G.; Sciortino, F.; Stanley, H.E.

1996-01-01

The pronounced increases in isothermal compressibility, isobaric heat capacity, and in the magnitude of the thermal expansion coefficient of liquid water upon supercooling have been interpreted either in terms of a continuous, retracing spinodal curve bounding the superheated, stretched, and supercooled states of liquid water, or in terms of a metastable, low-temperature critical point. Common to these two scenarios is the existence of singularities associated with diverging density fluctuations at low temperature. We show that the increase in compressibility upon lowering the temperature of a liquid that expands on cooling, like water, is not contingent on any singular behavior, but rather is a thermodynamic necessity. We perform a thermodynamic analysis for an anomalous liquid (i.e., one that expands when cooled) in the absence of a retracing spinodal and show that one may in general expect a locus of compressibility extrema in the anomalous regime. Our analysis suggests that the simplest interpretation of the behavior of supercooled water consistent with experimental observations is free of singularities. We then develop a waterlike lattice model that exhibits no singular behavior, while capturing qualitative aspects of the thermodynamics of water. copyright 1996 The American Physical Society

Quantum jump from singularity to outside of black hole

International Nuclear Information System (INIS)

Dündar, Furkan Semih; Hajian, Kamal

2016-01-01

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

Relating hard QCD processes through universality of mass singularities

International Nuclear Information System (INIS)

Amati, D.; Petronzio, R.; Veneziano, G.

1978-01-01

Hard QCD processes involving final jets are studied and compared by means of a simple approach to mass singularities. This is based on the Lee-Nauenberg-Kinoshita theorem and on a rather subtle use of gauge invariance in hard collinear gluon bremsstrahlung. One-loop results are easily derived for processes involving any number of initial quarks and/or currents. The method greatly simplifies the computation of higher-order loops at the leading log level and the preliminary results allow one to conclude that the crucial features encountered at the one-loop level will persist. The authors are thus able to relate different hard processes and to show that suitable ratios of cross sections, being free from mass singularities, can be computed perturbatively, as usually assumed in QCD-inspired parton models. It is also possible to relate the universal leading mass singularities to leading scaling violations and to extend therefor the results of the operator product expansion method to processes outside the range of the light-cone analysis. Some delicate points caused by confinement-related singularities (e.g. narrow resonance poles) are also discussed. (Auth.)

Split-and-Combine Singular Value Decomposition for Large-Scale Matrix

Directory of Open Access Journals (Sweden)

Jengnan Tzeng

2013-01-01

Full Text Available The singular value decomposition (SVD is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.

How far is it to a sudden future singularity of pressure?

International Nuclear Information System (INIS)

DaPbrowski, Mariusz P.; Denkiewicz, Tomasz; Hendry, Martin A.

2007-01-01

We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within 10x10 6 years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompleteness, which means that the evolution of the universe may eventually be continued throughout until another 'more serious' singularity such as a big crunch or big rip

Classification of subsurface objects using singular values derived from signal frames

Science.gov (United States)

Chambers, David H; Paglieroni, David W

2014-05-06

The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.

Multiscale singularity trees

DEFF Research Database (Denmark)

Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter

2007-01-01

We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....

Evaluation of mobile systems: an integrative framework.

NARCIS (Netherlands)

Högler, T.; Versendaal, J.; Batenburg, R.

2015-01-01

This work presents an integrative framework for the evaluation of mobile systems. In comparison to stationary systems, mobile systems have a bundle of specific singularities that should be considered for evaluation. Further analysis of existing approaches clarifies that an integrative approach for

Singularities and horizons in the collisions of gravitational waves

International Nuclear Information System (INIS)

Yurtsever, U.H.

1989-01-01

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and the generic initial data for the colliding plane waves always produce pure spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction. In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wave-fronts; i.e., it must leave behind tails in the spacetime region through which is passes

Analytic Evolution of Singular Distribution Amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Radyushkin, Anatoly V. [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Tandogan Kunkel, Asli [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

2014-03-01

We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

Singular ways to search for the Higgs boson

CERN Document Server

De Rújula, A

2012-01-01

The discovery or exclusion of the fundamental standard scalar is a hot topic, given the data of LEP, the Tevatron and the LHC, as well as the advanced status of the pertinent theoretical calculations. With the current statistics at the hadron colliders, the workhorse decay channel, at all relevant H masses, is H to WW, followed by W to light leptons. Using phase-space singularity techniques, we construct and study a plethora of "singularity variables" meant to facilitate the difficult tasks of separating signal and backgrounds and of measuring the mass of a putative signal. The simplest singularity variables are not invariant under boosts along the collider's axes and the simulation of their distributions requires a good understanding of parton distribution functions, perhaps not a serious shortcoming during the boson hunting season. The derivation of longitudinally boost-invariant variables, which are functions of the four charged-lepton observables that share this invariance, is quite elaborate. But their u...

On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation

KAUST Repository

Miroshnikov, Alexey

2014-08-21

We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation. For dimensions d=2,3 we show that cavity formation is necessarily associated with a unique precursor shock. We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation as a function of the cavity speed of the self-similar profiles. We show that for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents.

Breakdown of predictability: an investigation on the nature of singularities

International Nuclear Information System (INIS)

Tahir Shah, K.

1980-12-01

When relations are extrapolated beyond their premises of discovery, the operation sometimes results in an undefined object, i.e., one which cannot be identified within the given structure. The thesis is put forth that the occurrence of singularities is due to ''incompleteness'' in knowledge. An intuitive answer on how to deal with singularities (in, for instance, the real number system, space-time, quantum field theory) is presented first. Then a quasi-formalistic approach, e.g. non-standard models in higher-order languages and Lawvere's axiomatic formulation of categories, is set out. The independence of singularity with respect to other primitive notions of the Universe of knowledge is noted

Singularities: the state of the art

International Nuclear Information System (INIS)

Clarke, C.J.S.; Schmidt, B.G.

1977-01-01

A brief, but precise and unified account is given of the results that have been rigorously established at the time of writing concerning the existence and nature of singularities in classical relativity. (author)

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Is the shell-focusing singularity of Szekeres space-time visible?

International Nuclear Information System (INIS)

Nolan, Brien C; Debnath, Ujjal

2007-01-01

The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach

Surface singularities in Eddington-inspired Born-Infeld gravity.

Science.gov (United States)

Pani, Paolo; Sotiriou, Thomas P

2012-12-21

Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubt on its viability.

Energy conditions of non-singular black hole spacetimes in conformal gravity

International Nuclear Information System (INIS)

Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Abdujabbarov, Ahmadjon; Stuchlik, Zdenek

2017-01-01

Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)

Energy conditions of non-singular black hole spacetimes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Toshmatov, Bobir [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic); Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany); Ahmedov, Bobomurat [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Abdujabbarov, Ahmadjon [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Tashkent University of Information Technologies, Tashkent (Uzbekistan); Stuchlik, Zdenek [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)

2017-08-15

Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)

Short time propagation of a singular wave function: Some surprising results

Science.gov (United States)

Marchewka, A.; Granot, E.; Schuss, Z.

2007-08-01

The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.

Singular tachyon kinks from regular profiles

International Nuclear Information System (INIS)

Copeland, E.J.; Saffin, P.M.; Steer, D.A.

2003-01-01

We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately

Matrix analysis of the asymmetrical bending of conical shell-beams and their singular assemblies

International Nuclear Information System (INIS)

Kiedrzynski, A.; Coppens, L.

1979-01-01

As an alternative to refined finite element methodology a new method has been derived to investigate in much detail the linear static behaviour of singular assemblies of moderately thick conical shells of revolution submitted to non-axisymmetrical loads at their ends (an assembly of conical sections is said to be singular when the geometrical discontinuities are deformable, i.e. not stiffened by diaphragms). A detailed preliminary study has shown that the currently adopted simplifying assumptions in shell theories for moderate thickness lead to unconsistencies at any departure from axisymmetric loading. Therefore, FLUEGGE's general shell theory has been applied to a conical section, yielding a set of mixed first order differential equations in terms of displacements and conjuguated stress resultants well suited for a matrix formalism. The numerical integration is based on a fourth-order Runge-Kutta method and provides an 8 x 8 mixed matrix. This matrix contains complete information on the distribution of the displacements (exhibiting the warping and ovalization of the cross-section) and of the stress resultants along the meridian; also the stiffness coefficients proceed from it. (orig.)

Linear integral equations and soliton systems

International Nuclear Information System (INIS)

Quispel, G.R.W.

1983-01-01

A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

Long Range Prospects of Education – from Now until Singularity

Directory of Open Access Journals (Sweden)

Vatroslav Zovko

2014-04-01

Full Text Available This work describes key characteristics and genesis of educational system today. As it is considered that we live in information society, presented are major goals of information society education and the school system in general in relation to the labour market. Briefly is described the concept of singularity and how it will make a quantum leap in the history of human development. Education is briefly put in the singularity framework and the concept of future society that is more technologically advanced. This paper also discusses the chronology of future technological development until the singularity age. It is argued that once we reach the singularity age the consequence will be the shift away from economic centered education and employment and toward humanities research. Ultimately, the goal of this paper is to open up a discussion about the different possible future scenarios of education, its long term perspective and the role in society rather than making a precise forecast about the education in mid-21st century.

Charged singularities: the causality violation

Energy Technology Data Exchange (ETDEWEB)

De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia

1980-12-01

A search is made for examples of particle trajectories which, approaching a naked singularity from infinity, make up for lost time before going back to infinity. In the Kerr-Newman metric a whole family of such trajectories is found showing that the causality violation is indeed a non-avoidable pathology.

Harnack's Inequality for Degenerate and Singular Parabolic Equations

CERN Document Server

DiBenedetto, Emmanuele; Vespri, Vincenzo

2012-01-01

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive

Three dimensional nilpotent singularity and Sil'nikov bifurcation

International Nuclear Information System (INIS)

Li Xindan; Liu Haifei

2007-01-01

In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions

Symposium on Singularities, Representation of Algebras, and Vector Bundles

CERN Document Server

Trautmann, Günther

1987-01-01

It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

General Principles of Integrity Checking of Digital Images and Application for Steganalysis

Directory of Open Access Journals (Sweden)

Kobozeva Alla A.

2016-06-01

Full Text Available The new common approach for integrity checking of digital images is developed. The new features of formal parameters defining image are revealed, theoretically grounded and practically tested. The characteristics of the mutual arrangement of left and right singular vectors corresponding to the largest singular value of the image’s matrix (block of matrix and the vector composed of singular numbers is obtained. Formal parameters are obtained using normal singular decomposition of matrix (block of matrix which is uniquely determined. It is shown that for most blocks of original image (no matter lossy or lossless the angle between the left (right mentioned singular vector and vector composed of singular numbers is defined by the angle between the n-optimal vector and the vector of standard basis of the range corresponding dimension. It is shown that the determined feature brakes for the mentioned formal parameters in a non-original image. This shows the integrity violation of the image, i.e. the existence of the additional information embedded using steganography algorithms. So this can be used as a basis for development of new universal steganography methods and algorithms, and one example of the realization is proposed. The efficiency of the proposed algorithm won’t depend on the details of steganography method used for embedding. All the obtained results can be easily adapted for the digital video and audio analysis.

Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

OpenAIRE

García Planas, María Isabel; Tarragona Romero, Sonia

2014-01-01

The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family

Hybrid direct and iterative solvers for h refined grids with singularities

KAUST Repository

Paszyński, Maciej R.

2015-04-27

This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to the standard algorithm performing static condensation over the entire mesh and executing the ILUPCG algorithm on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2], and the optimal refinements are selected using the projection based interpolation. The computational mesh is partitioned into sub-meshes with local point and edge singularities separated. This is done by using the following greedy algorithm.

Removal of apparent singularity in grid computations

International Nuclear Information System (INIS)

Jakubovics, J.P.

1993-01-01

A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward

Stochastic singular optics

CSIR Research Space (South Africa)

Roux, FS

2013-09-01

Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...

Irreducibility and co-primeness as an integrability criterion for discrete equations

International Nuclear Information System (INIS)

Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji

2014-01-01

We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)

Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

Directory of Open Access Journals (Sweden)

S. A. El-Wakil

2012-01-01

Full Text Available The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Application of local singularity in prospecting potential oil/gas Targets

Directory of Open Access Journals (Sweden)

Zhengyu Bao

2007-06-01

Full Text Available Together with generalized self-similarity and the fractal spectrum, local singularity analysis has been introduced as one part of the new 3S principle and technique for mineral resource assessment based on multifractal modeling, which has been demonstrated to be useful for anomaly delineation. Local singularity is used in this paper to characterize the property of multifractal distribution patterns of geochemical indexes to delineate potential areas for oil/gas exploration using the advanced GeoDAS GIS technology. Geochemical data of four oil/gas indexes, consisting of acid-extracted methane (SC1, ethane (SC2, propane (SC3, and secondary carbonate (ΔC, from 9637 soil samples amassed within a large area of 11.2×104 km2 in the Songpan-Aba district, Sichuan Province, southwestern China, were analyzed. By eliminating the interference of geochemical oil/gas data with the method of media-modification and Kriging, the prospecting area defined by the local singularity model is better identified and the results show that the subareas with higher singularity exponents for the four oil/gas indexes are potential targets for oil/gas exploration. These areas in the shape of rings or half-rings are spatially associated with the location of the known producing drilling well in this area. The spatial relationship between the anomalies delineated by oil/gas geochemical data and distribution patterns of local singularity exponents is confirmed by using the stable isotope of δ13C.

Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

Science.gov (United States)

Cormann, Mirko; Caudano, Yves

2017-07-01

We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N  -  1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N  -  1 contributions. Their modulus is determined by the product of N  -  1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N  -  1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.

On the complete and partial integrability of non-Hamiltonian systems

Science.gov (United States)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Directory of Open Access Journals (Sweden)

Rakowski Waldemar

2015-12-01

Full Text Available In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters associated with cubic box wavelets that are applied in implementing the discrete dyadic wavelet transform are defined. The filters and the algorithme à trous of the discrete dyadic wavelet transform are used in detecting signal singularities and in calculating the measures of signal singularities in the form of a Lipschitz exponent. The article presents examples illustrating the use of cubic box spline wavelets in the analysis of signal singularities.

A locally convergent Jacobi iteration for the tensor singular value problem

NARCIS (Netherlands)

Shekhawat, Hanumant Singh; Weiland, Siep

2018-01-01

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to

Removability of singularity for nonlinear elliptic equations with p(x-growth

Directory of Open Access Journals (Sweden)

Yongqiang Fu

2013-09-01

Full Text Available Using Moser's iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.

Further holographic investigations of big bang singularities

Energy Technology Data Exchange (ETDEWEB)

Engelhardt, Netta [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States); Hertog, Thomas [Institute for Theoretical Physics, KU Leuven,3001 Leuven (Belgium); Horowitz, Gary T. [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States)

2015-07-09

We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.

Further holographic investigations of big bang singularities

Science.gov (United States)

Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T.

2015-07-01

We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.

Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem

Directory of Open Access Journals (Sweden)

Lubomir Dechevski

2012-01-01

Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.

Non-singular bounce transitions in the multiverse

International Nuclear Information System (INIS)

Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun

2013-01-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ c . This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ c . We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua

Non-singular bounce transitions in the multiverse

Energy Technology Data Exchange (ETDEWEB)

Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, 08028, Barcelona (Spain); Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2013-11-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.

The singular weapon. What remains from the atomic age?; Die Singulaere Waffe. Was bleibt vom Atomzeitalter?

Energy Technology Data Exchange (ETDEWEB)

Eisenbart, Constanze (ed.) [Forschungsstaette der Evangelischen Studiengemeinschaft (FEST), Heidelberg (Germany)

2012-07-01

The book contains the following contributions: Why do we talk about the atomic age? The language of the atomic myth - comments to a protestant debate. Nuclear singularity between fiction and reality. Only one can get through: military singularity of nuclear weapons. Physical singularity of nuclear weapons. Nuclear weapons test and fall-out. Quantitative disarmament and qualitative rearmament. Do mini nukes neutralize the singularity? The vulnerability of the industrial society by the nuclear electromagnetic momentum. Nuclear weapons as national status symbol - the example of India. The general regulations of international laws and the singularity of nuclear weapons. The construction of normative singularity - development and change of the nuclear taboo.

Simulation of generation and dynamics of polarization singularities with circular Airy beams.

Science.gov (United States)

Ye, Dong; Peng, Xinyu; Zhou, Muchun; Xin, Yu; Song, Minmin

2017-11-01

The generation and dynamics of polarization singularities have been underresearched for years, while the focusing property of the topological configuration has not been explored much. In this paper, we simulated the generation of low-order polarization singularities with a circular Airy beam and explored the focusing property of the synthetic light field during propagation due to the autofocusing of the component. Our work researched the focusing properties of the polarization singularity configuration, which may help to develop its application prospect.

Numerical static state feedback laws for closed-loop singular optimal control

NARCIS (Netherlands)

Graaf, de S.C.; Stigter, J.D.; Straten, van G.

2005-01-01

Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper,

On the C(R) stability of uncertain singularly perturbed systems

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this paper, a simple criterion for the C(R) stability of uncertain singularly perturbed systems is proposed. Such a criterion can be easily checked by some algebraic inequality. The upper bound of the singular perturbation parameter ε is also given by estimating the unique positive zero of specific function. Finally, a numerical example is provided to illustrate the main result

Propagation of singularities for linearised hybrid data impedance tomography

DEFF Research Database (Denmark)

Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim

2017-01-01

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con......For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...

Cosmic ray-modified stellar winds. I. Solution topologies and singularities

International Nuclear Information System (INIS)

Ko, C.M.; Webb, G.M.

1987-01-01

In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P/sub c/)-space, or a two-dimensional hypersurface of singularities in (r, u, P/sub c/, dP/sub c/dr)-space, where r, u, and P/sub c/ are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points. 64 references

Singular lensing from the scattering on special space-time defects

Energy Technology Data Exchange (ETDEWEB)

Mavromatos, Nick E. [University of Valencia - CSIC, Department of Theoretical Physics and IFIC, Valencia (Spain); King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Papavassiliou, Joannis [University of Valencia - CSIC, Department of Theoretical Physics and IFIC, Valencia (Spain)

2018-01-15

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (''singular lensing''). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals. (orig.)

Singular lensing from the scattering on special space-time defects

International Nuclear Information System (INIS)

Mavromatos, Nick E.; Papavassiliou, Joannis

2018-01-01

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (''singular lensing''). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals. (orig.)

Singular lensing from the scattering on special space-time defects

Science.gov (United States)

Mavromatos, Nick E.; Papavassiliou, Joannis

2018-01-01

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.

Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems

CERN Document Server

Burban, Igor

2017-01-01

In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \\mathbb{k} x,y,z/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.

Reconstructing weak values without weak measurements

International Nuclear Information System (INIS)

Johansen, Lars M.

2007-01-01

I propose a scheme for reconstructing the weak value of an observable without the need for weak measurements. The post-selection in weak measurements is replaced by an initial projector measurement. The observable can be measured using any form of interaction, including projective measurements. The reconstruction is effected by measuring the change in the expectation value of the observable due to the projector measurement. The weak value may take nonclassical values if the projector measurement disturbs the expectation value of the observable

Tensor renormalization group with randomized singular value decomposition

Science.gov (United States)

Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai; Kawashima, Naoki

2018-03-01

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.

Weak Lower Semicontinuity of Integral Functionals and Applications

Czech Academy of Sciences Publication Activity Database

Benešová, B.; Kružík, Martin

2017-01-01

Roč. 59, č. 4 (2017), s. 703-766 ISSN 0036-1445 R&D Projects: GA ČR GA14-15264S; GA ČR(CZ) GF16-34894L Grant - others:GA AV ČR(CZ) DAAD-16-14 Program:Bilaterální spolupráce Institutional support: RVO:67985556 Keywords : calculus of variations * weak lower semi-continuity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 4.897, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0481321.pdf

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

Science.gov (United States)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

Singularity Analysis: a powerful image processing tool in remote sensing of the oceans

Science.gov (United States)

Turiel, A.; Umbert, M.; Hoareau, N.; Ballabrera-Poy, J.; Portabella, M.